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PUBLIC SECTOR ECONOMICS
EC408 CLASS NOTES
Authors:
CHARUMBIRA M. & SUNDE T.
Department of Economics
Faculty of Commerce
Midlands State University
Office: Syndicate Room 4
[email protected]
011880695
©2007
CHAPTER 1
INTRODUCTION
1.0 Definition of Public Sector Economics
Public sector economics deals with the raising and spending of funds by the government
as well as the comparison of alternative economic states in terms of efficiency and
distribution or equity. Both equity and efficiency are desired goals of government.
Unfortunately it is not always the case that these goals are compatible. In most cases
there is a tradeoff between these objectives necessitating a policy compromise in favour
of one or the other. For instance, the policy to redistribute land from the white
commercial farmers to the indigenous subsistence farmers adopted by the Zimbabwean
government since the late 1990s can be considered as an attempt to achieve equitable
redistribution. However, if the same policy is viewed from the efficiency perspective, one
may argue that the smaller farming units that were created are less efficient compared to
the vast tracts that existed in the previous scenario. This can be explained by the loss of
productivity due to diminished economies of scale.
1.1 The Social Welfare Function (SWF)
A social welfare function is a mathematical representation of the combined utilities or
lumped utilities of all economic agents.
You probably recall from intermediate microeconomics that the utility of an individual
can be represented by either a direct utility function of the form:
U i  U i ( x1 ; x2 ;.......; xn )
Or by an indirect utility function of the form:
U i  Vi ( P1 ; P2 ;.......; Pn ; I i )
Where: Ui is the utility of the ith individual.
xj is the quantity of the jth commodity consumed.
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Pj is the price of the jth commodity.
Ii is the income of the ith consumer
The issue that arises then is to translate the individual’s utility function into a social
welfare function. The exact form of the social welfare function is not known. There is no
consensus as to how the social welfare function should be specified or derived from the
individual’s utility function. There is need to consider the alternative forms of the social
welfare function.
1.2 Alternative Social Welfare Functions
The social welfare functions discussed below are some of the most widely used in most
of the analyses involving the assessment of social well-being. At the end of this section
you should then be able to identify which of the alternative specifications best suits the
circumstances of your country.
1.2.1 Bergsonian Social Welfare Function
The Bergsonian Social Welfare Function considers the welfare of society to be reliant on
certain measurable variables that directly impact on the wellbeing of citizens. Some such
variables include individual incomes, total output, weather, peace or war among others.
All these variables depend on the state of the world. The social welfare function is thus
specified as:
W  W (s)  W [V1 (s); V2 (s);........;Vn ]
Where: W is the welfare of the society.
Vi(s) is the value of some measurable variable i in state of the world s that is
relevant for measuring collective or social welfare.
The above specification implies that each of the variables has effect on the welfare, much
as the state of the world also affects each of the variables. The extent to which weather
affects the social well-being can probably be best understood if you consider how the
living standards in Zimbabwe respond to drought situations. The standard of living in
1991/92 drought was clearly worse than the period immediately before and after the
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drought. The impact of war is probably evident, though less obvious. That such events
directly affect the utility of society is subject to empirical investigation, but has sufficient
theoretical basis.
1.2.2 Samuelsonian Social Welfare Function
The underlying argument in the Samuelsonian social welfare function is that collective
wellbeing depends on the utilities of the individuals that constitute the society. The utility
derived by each individual is in turn dependent on the state of the world s. The social
welfare function is thus specified as:
W  W (s)  W [U1 (s); U 2 ( s);........ ;U m ( s)]
Where: Ui(s) is the utility of the ith individual in state s.
The Samuelsonian Social Welfare Function is based on the principle of individualism. In
the above case utility depends on the utilities enjoyed by each of the m individuals in the
society. This presupposes an additive form of the utility function such that:
m
W  U i
i 1
1.2.3 Multiplicative Social Welfare Function
In this formulation the collective utility for the society is determined by the individuals’
utility functions that are related in a multiplicative form to give:
W   Wi  W1.W2 ..........Wm
where: Wi is the utility of the ith individual in the society.
There seems to be no clear basis of believing that the utilities of the various individuals
are combined in a multiplicative way, and not any other.
1.2.4 Rawlsian Social Welfare Function1
This is based on the notion that in order to maximize social welfare, the critical individual
is the one who has the lowest utility. In other words the Rawlsian social welfare function
The Rawlsian Social Welfare Function is based on the concept of ‘social justice’ that was popularised by
John Rawls.
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3
assumes that society begins in an original state or position in which no individual knows
who or where he is going to be in the society whose principles are being formulated. This
creates a conservative perception where each individual attempts to escape or avoid the
worst-case scenario. This implies a social welfare based on the Maxmin criterion. The
Maxmin criterion involves maximizing the minimum by ensuring that the minimum is
not extremely low. Students who have studied Game Theory would probably understand
better how the ideal strategy can be identified where the Maxmin is a guiding principle.
This is typically associated with pessimistic decision-making. The Rawlsian Social
Welfare Function can thus be referred to as the Maxmin SWF. The Rawlsian Social
Welfare Function puts maximum emphasis on equality such that the society’s welfare can
be viewed from the perspective of the welfare of the worst-off person in society. Rawls
assumes that the society is structured as if citizens did not know what social position they
would ultimately occupy. The function is specified as:
W  min[ U1 ;U 2 ;...........;U m ]
The ‘min’ operator outside the bracket implies that the smallest of the utilities in bracket
is active with the rest being dormant, and thus not having any material effect on the social
welfare. For instance, if individual 2 has the lowest utility, then the above expression
reduces to: W  U 2
The utility of the society is as good as that of the poorest person, with the utilities of the
individuals above that of the poorest person being disregarded in the consideration. An
assessment of the poverty levels in Zimbabwe makes better sense if the surveys and
conclusions are based on the least affluent districts such Chiredzi, Muzarabani and
Mwenezi, rather than just summarizing the exaggerated lifestyles of people in Harare,
Bulawayo and other major cities. In countries like the United Arab Emirates and Saudi
Arabia, the ‘oil barons’ are extremely rich, bringing sharp contrast with the poverty in the
general populace. The Rawlsian specification of the social welfare function says the
evaluation of the well-being of society in such cases should be based on the
circumstances of the poor rather than the icons of extravagance.
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1.2.5 Benthamite Social Welfare Function2
The Benthamite Social Welfare Function is motivated by marginalism or individualism.
W  W [U1 ( x); U 2 ( x);........ ...;U m ( x)]
Where: x is the vector of commodities consumed by the ith individual. In other words we
could well write it as x  x1 , x2 ,.........., xn in the case where the consumer
consumes n commodities.
Ui is the direct utility function of individual i.
The above specification has the usual shortcomings that are ordinarily associated with
utilitarianism, and the accompanying assumptions. The marginalists typically believe that
society is the sum of its constituent parts. They consider the welfare of society to be a
simple total of the individual utilities of its members.
1.3 Pareto Optimality3
Is a situation where the distribution or allocation of output is such that it is not possible to
make one person better off without making someone else worse-off. More simply, it is a
state of equilibrium in distribution.
Assumptions

There are only two commodities in the economy and the commodities are X and
Y.

There are only two individuals in the economy and these are A and B.

The total endowment of X in the economy is known to be R and that of Y is also
known to be S.
The above assumptions make it possible to represent the indifference curves of the two
individuals in one graph, popularly known as the Edgeworth Box.
2
The Benthamite Social Welfare Function is named after Jeremy Bentham, a utilitarian, who argued that
the prime objective of society is to maximise the greatest good for the greatest number.
3
This concept is named after the Italian economist Vilfredo Pareto (1939), who first alluded to it.
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Point h is not Pareto optimal because the marginal rate of substitution between X and Y
for consumer A is not equal to the marginal rate of substitution between the two
commodities for consumer B. This means it is possible to make consumer B better-off by
moving him from indifference curve I 2B to a higher indifference curve I 3B without
affecting the utility of consumer A. Points such as e, f and g are Pareto optimal because
A
B
they are along the contract curve, where MRS XY
. You are going to encounter
 MRS XY
the applications of the Pareto optimality concept quite frequently in subsequent chapters.
1.4 Welfare Theorems
1.4.1 First Welfare Theorem
Any market equilibrium is Pareto optimal. If there is a competitive equilibrium such that
all goods can be assigned property rights; if no individual and no firm can affect the
prices; if producers are maximizing their profits and if consumers are maximizing their
utilities and if all markets clear, then the resulting allocation of resources is Pareto
optimal.
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Implication of the theorem
If the market is left to guide the allocation of resources in the economy, then Pareto
optimality is likely to be achieved.
1.4.2 Second Welfare Theorem
If production sets are convex and closed; if preferences are convex and continuous; and if
all goods can be assigned property rights, then to each desired Pareto optimal allocation
there is an initial distribution of wealth such that the resulting equilibrium is the desired
allocation.
Implication of the theorem
Each Pareto optimal allocation has a supporting set of prices.
1.5 Walras’Law
The law says if there is excess demand in one market in the economy, then there should
be another market where there is excess supply. In other words, it is not possible to have
disequilibrium in only one market, when all other markets in the economy are in
equilibrium. The magnitude of the excess demand in the economy should be exactly
equivalent to the excess supply. Excess supply in certain markets should be balanced by
excess demand in other markets.
The law is valid under the following assumptions:

The economy has n-commodities and

There are m-individuals

Consumers cannot spend beyond the income they have generated

The producers in some markets ultimately become consumers in other markets.
The above assumption then facilitates the derivation of the famous Walras’ law.
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1.5.1 Formal Derivation of Walras’ Law
In the next few paragraphs summation notation is invoked to provide a formal derivation
of Walras’ Law.
Now, whether or not prevailing market prices are such as to equate demand with supply
for each commodity, the money value of all commodities which an individual transactor
(i.e. a household, a firm, or the government) plans to buy in any period must be equal to
the money value of all commodities offered for sale by that transactor at the same time.
For example, if an individual plans to purchase $30 000 worth of commodities then,
simultaneously, he or she must also plan to sell commodities to the value of $30 000.
In general, the total money value of what the jth individual transactor plans to purchase
can be written symbolically as:
n
P1D1 j  P2 D2 j  ..............  Pn Dnj   Pi Dij -------------------(1)
i 1
Where: P1, P2. . . Pn are the prices of the n commodities, and D1j, D2j . . . Dnj are the
quantities of those commodities that the jth individual plans to purchase.
Similarly, the total money value of what the jth individual plans to sell can be written
represented as:
n
P1S1 j  P2 S2 j  .................  Pn Snj   Pi Sij ------------------------------------(2)
i 1
Where: S1j, S2j, . . . Snj are the quantities of the n commodities that the jth individual plans
to sell.
The money value of all the commodities that the jth individual plans to buy must always
be equal to the money value of all the commodities that individual plans to sell, assuming
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that money accrued from selling commodities is translated to finance purchases. We can
therefore equate (1) and (2) to come up with:
n
n
i 1
i 1
 Pi Dij   Pi Sij -------------------------(3)
Extending condition (3) to all individuals would imply that the aggregate money value of
the quantities demanded by all individuals must be equal to the aggregate money value of
the quantities offered for sale by all individuals. We can see this by summing condition
(3) over all m individual transactors to obtain:
m

j 1
n
m
i 1
j 1
 Pi Dij  
n
 PS
i 1
i ij
-----------------------(4)
Factoring out the price variables from each side of expression (4) yields:
m
 n m 
P
D

i  ij    Pi  Sij  --------------------(5)
i 1
 j 1  i 1  j 1 
n
The expression in parentheses on the left-hand side is simply the total market demand for
the ith commodity, since it is the sum of the individual transactors demands for that
commodity. We will write this total market demand for the ith commodity as Di.
Similarly, the expression in parentheses on the right-hand side is simply the total market
supply of the ith commodity, since it is the sum of the individual transactors' supplies of
that commodity. We will write the total market supply of the ith commodity as Si.
Thus, expression (5) can be summarized as:
n
n
i 1
i 1
 Pi Di   Pi Si ---------------------(6)
This proposition is known as Walras Identity. Verbalised, it states that the money value
of all planned market purchases when added together are identically equal to the
aggregate money value of all planned market sales.
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Implications of Walras Identity
As indicated by our derivation, Walras Identity is valid whether or not market prices
equate demand with supply for each individual commodity. It has, however, two very
important implications. One implication relates to the 'generality' of equilibria. The other
refers to states of disequilibrium. We will allude to each in turn.
First Implication: The Generality of Equilibrium
Assume that a set of prices has been established which will equate demand with supply in
every market except the nth market. Since all n-1 markets are in equilibrium, then:
D1 = S1, D2 = S2, . . . , Dn-1 = Sn-1
Next, multiply through by the set of prices that put these n-1 markets in equilibrium.
Then:
P1D1 = P1S1, P2D2 = P2S2, . . . , Pn-1Dn-1 = Pn-1Sn-1
and summing, we obtain for all n-1 markets:
n 1
n 1
 P D   P S ----------------(7)
i 1
i
i
i 1
i
i
If we subtract expression (7) from Walras Identity (expression (6) we obtain:
Pn Dn  Pn Sn ---------------------(8)
from which it follows that:
Dn  Sn ---------------------------(9)
which implies immediately that the nth market is also in equilibrium.
To recapitulate verbally, we have shown that if all but one of the markets in an economy
are in equilibrium, then that other market must also be in equilibrium.
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Second Implication: Walras Law
We now look at the implications of Walras Identity for disequilibrium.
Assume that one market (the nth market) is in disequilibrium. This may take the form of
either (positive) excess demand (where PiDi > PiSi) or excess supply, also known as
negative excess demand (where PiDi < PiSi).
It is an implication of Walras Identity that for all markets taken as a whole there can be
neither excess supply nor excess demand when we sum over all markets. We can see this
by rearranging (6) to give:
n
 P D  P S   0 ----------------------------(10)
i 1
i
i
i
i
In order for this condition to be satisfied in the presence of disequilibrium in the nth
market, it must be the case that there is an 'off-setting' disequilibrium in at least one other
market in the economy. This result is known as Walras Law. The law states that the sum
of excess demands over all the markets in the economy must equal zero and this applies
whether or not all markets are in (general) equilibrium. So if there is excess supply in one
market (that being negative excess demand) then there must, corresponding to this, be
positive excess demand in at least one other market. (But it is important to notice that the
excess demands and supplies are measured as differences between planned (or notional)
demands and supplies and not necessarily actual demands and supplies).
1.6 The Role of Government in the Economy
The role of government or the extent of government involvement in economic activities
generally depends on the economic system operating in the particular country. We would
obviously expect a lot of centralization and direct government intervention in the
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command-type of economies (such as Cuba and the former Soviet Union) where social
services provision and state enterprises are commonplace.
In a laissez faire economy the role of government is limited to:
1) The duty of protecting the society from violence and invasion by other societies.
2) The duty of protecting every member of a society from the injustice or oppression
of every other member of the society. This involves the obligation of establishing
an administration of justice, law and order to facilitate the functioning of the
market economy.
3) The duty of establishing and monitoring those highly beneficial public institutions
and public works which are of such a nature that the profit they earn would never
repay the expense to any individual or small number of individuals. The
commodities provided by such public institutions cannot therefore be expected to
be supplied in adequate quantities by the market.
4) The duties of meeting the expenses of the bureaucrats or civil service. Nozick
(1974) proposes that the role of the government in the economic affairs should be
relegated to facilitating the activities of the market system. He proposes the
‘minimal state’ where the government should prescribe:
a) A description of how people can legitimately acquire their endowments.
b) A description of how people can transfer their endowments.
c) A description of how past injustices are to be rectified through
redistribution and taxation.
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CHAPTER 2
THEORIES OF GROWTH OF THE PUBLIC SECTOR
2.0 Introduction
The theories of government growth seek to explain the various factors that contribute
towards the expansion of government over time.
2.1 Measures/Indices of Government Growth
The following are the measures/indices that give an indication of how government is
growing:
1. The ratio of public expenditures to GDP
GovernmentExpenditure
GDP
2. The ratio of public sector employment to overall employment
PublicSect orEmployment
OverallEmployment
3. The ratio of government revenue to GDP
GovernmentRe venue
GDP
2.2 Types of Government Expenditure

Recurrent expenditure

Capital expenditure

Transfers (subsidies, grants, pensions, etc)

Repayments of debt and interest

Net lending to the private sector
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2.3 Functional Composition of Public Expenditure

Defense

Education

Health

General administration

Industry, agriculture, social security, housing, interest on debt etc.
NB.
Defense and Education constitute almost 50% of government expenditure in
Zimbabwe.
Tax revenue for oil producing and mineral producing countries is very high.
2.4 Formal Models of Public Expenditure Growth
2.4.1 Wagner Hypothesis
There is an inevitable increase in the share of government expenditure in the total output
over time. Wagner argued that an expanding government will always accompany social
progress and rising incomes. The model recognises three functions of the state, all of
which have a tendency of demanding an increasingly large amount of funds from the
fiscus, and these are:
a)
Providing administration and protection
b)
Ensuring stability
c)
Providing for the economic and social welfare of society as a whole. Public
expenditure would increase because of urbanisation that leads to the breakdown of
communal relationships.
The breakdown of communal relationships would require the government to take over the
functions previously carried out by families and local communities. This creates a
centralized administration with large administrative units that can only be supported with
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higher government expenditure. Technological progress will also lead to growth of
monopolies in the private sector. Private sector monopolies will not adequately take into
consideration the needs of the society as a whole. The government will eventually be
forced to intervene and replace them with public corporations or parastatals. This creates
the need for government to expand inorder to provide the social benefits for services that
are not open to economic evaluation by the market system, and such services include
education, health care among others.
2.4.2 Musgrave-Rostow Model
This is linked to development theory. The theory is derived from the growth model.
According to the theory, the growth in public expenditure is related to economic growth
and development of societies. The theory identifies three phases in the development
process each of which is associated with a certain level of government expenditure.
Phase 1
This is the early development stage where considerable expenditure is directed to
education and infrastructure of the economy, which are roughly referred to as social
overhead capital. This involves setting the pre-requisites for growth. In this phase private
saving is inadequate to finance the necessary expenditure. The government must
therefore intervene to finance the infrastructure development.
Phase 2
This is the phase of rapid growth and economic expansion. There is a large increase in
private saving and public investment falls proportionately. There is thus lower
government expenditure.
Phase 3
It is that phase of high-income societies that have increased demand for private goods
such as vehicles. Such private goods would need some complementary public
infrastructure that can only be availed if the government increased capital budget, and we
should expect high levels of government expenditure. Increased population movements
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that are characteristic of phase 2 eventually lead to the development of urban slumps.
Such factors, and others, once again lead to an increase in public expenditure relative to
output.
Applicability of the Theory
The Musgrave-Theory is severely weakened by its reliance on the phase-by-phase
analysis. Such forms of analysis tend to tempt researchers as well as readers to attempt to
classify countries into the specified phases. The impression that is then given is that some
countries are ahead of others, and that those that are behind shall at some point in the
future attain the later stages. Unfortunately, this implies convergence all countries
towards phase 3 in the very long run. There is, however, no good reason to believe that
there can be economic evolution in Zimbabwe and other less developed countries when
just at the same time the developed countries remain economically static.
2.4.3 The Displacement Theory
This theory was developed by Peacock and Wiseman and is based on the following key
ideas:
a) Societies that are not subject to unusual pressures, such as wars and droughts,
have fairly stable ideas about the tax burden which they regard as tolerable.
b) Large scale social disturbances however weaken these ideas of the tolerable tax
burden. If for instance there is an emergency, government expenditure is accepted
and so too are the higher rates of taxation needed to pay for it. People become
used to higher tax rates and their notions of the tolerable tax burden are displaced
upwards. After the disturbance there is increased scope for government
expenditure to increase and it does not fall back to its original level. This is
because of the ‘ratchet effect’4. The ‘ratchet effect’ implies that certain economic
variables are quite flexible upwards and relatively inflexible in the downward
This word ‘ratchet’ is borrowed from engineering, where it refers to a wheel-shaped, toothed object that
allows movement in one direction and resists movement in the reverse direction. In economics, it generally
explains why it takes long to establish stability in the economy once instability has ensued.
4
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direction. Government expenditure is one variable that typically displays such
behaviour.
c) People observe the social needs during the crisis and accept that there is a case for
increased social spending.
According to this model government expenditure does not follow a smooth trend but
instead is characterized by upward jumps at discrete intervals. The model identifies the
major social events singling out World War II for particular attention. According to
Peacock and Wiseman, at the end of the hostilities/war social expenditure will displace
military expenditure to the extent that the post-war spending by the government remains
high. The citizens/voters perception of what a fair or just amount of tax places a ceiling
on the maximum amount of revenue that the government will generate. In times of a
national emergency the citizens become more accepting of tax increases. The tolerable
tax levels are thus displaced upwards by national emergencies. After a period of exposure
to the new tax regime the maximum tolerable taxation level is raised as people become
increasingly familiar with the new high tax system. The government is therefore able to
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maintain high expenditure even though the period of crisis or emergency has passed.
Government spending exhibits persistence in the face of temporary shocks.
2.4.4 Niskanen Model (Agenda-Setting Model)
The Niskanen model gives some insight into the bureaucratic behaviour. It focuses on the
relationship between the legislature and the agencies, also referred to as the bureaucracy.
The model describes the budgetary interaction in which the legislature has demand for the
output of the agency and the agency also has demand for funds from the legislature. In
this relationship the legislature has the power to approve expenditures that are proposed
by the bureaucracy or civil service. The bureaucracy has certain information that the
legislature does not have and a single goal of the bureaucracy is a perpetually rising
budget from which it derives power, pay and prestige. These three Ps are correlated with
the size of the Bureau (resources available to the bureaucrat)
Assumptions of the model
a) The agency has perfect knowledge about the legislature’s demand and budgetary
ceiling.
b) The agency is not required to itemize and cost the individual output that the
various components constitutes.
c) The agency can present an all-or-nothing proposal. The agency’s budget is always
too large and the output too great with the effect that the legislature never receives
a fair level of service for the funds spent.
Niskanen concludes that the forces motivating the agency always produce a government
which is too large.
Analyzing the model
Suppose B is the total benefit derived from the public goods and services, such that the
benefit function is represented by the following quadratic function:
B  aQ  bQ 2 -------------(1)
Where: Q is the output of public goods and services.
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a and b are constants
The total cost function is similarly represented by:
C  dQ  eQ 2 --------------(2)
d and e are constants
Then the maximum that the legislature can accept in the case of the public goods and
services can be identified where marginal benefit is equal to zero. Marginal benefit (MB)
can be identified from expression (1) by differentiation to get:
MB 
B
 a  2bQ  0 ------(3)
Q
Making Q the subject of the formula gives the maximum acceptable to the legislature as:
Qmax 
a
-----------------------(4)
2b
Expression (4) says the rational legislature seeks increased output of the public goods as
long as the value of an additional unit is greater than the cost of that additional unit. The
minimum amount that the agency proposes directly follows from the fact that the agency
is interested in spending off the allocated amount. This is therefore determined where
total benefit (B) is equal to total cost(C):
19
B(Q)  C (Q) ---------------------(5) i.e equating expression (1) and expression (2)
further implies that:
dQ  eQ2  aQ  bQ2 --------------(6)
Making Q the subject of the formula in the above expression leads to:
Qmin 
(a  d )
-----------------------------------------(7)
(e  b )
The socially optimal output in the Niskanen model can be derived by equating marginal
benefit and marginal cost, such that:
a  2bQ  dQ  eQ2 ----------------------------------(8)
If Q is made the subject of the formula, then the result will be:
Qopt 
(a  d )
--------------------------------------------------(9)
2(b  e)
It emerges from the comparison of (7) and (9) that the socially optimal output level is half
of the amount proposed by the bureaucracy. In other words the agents will propose an
amount of expenditure which is double the socially optimal output level. Given that the
agency has the full knowledge about the maximum expected level of expenditure that the
legislature is prepared to approve, then it is going to propose an amount slightly less than
the maximum accepted. The legislator will accept the proposal on the basis of the fact
that it is below the maximum acceptable, but without noticing that it is double the
socially optimal. Overally, this creates a situation where public expenditures are larger
than the desirable levels as shown in graph below:
20
Alternatively, the graph can be drawn as follows:
21
In the above graph the socially optimal output level is indicated as Qopt , with the bureau
proposing Qmin , which is likely to face prompt approval by the legislator since it is well
below the maximum acceptable ( Qmax ). The information asymmetry creates an
opportunity for the bureaucracy to deceive the legislator in the direction of higher
government expenditure than actually deserved and/or desired by society. In this model
the power to “set the agenda” (propose expenditure levels) places the bureaucracy in a
convenient position to influence the decision. In other words the bureau knows fully well
that the legislator will endorse the proposal unless it significantly exceeds the required.
Acting on such information, the bureau then proposes a budget still larger than required
but with the acceptable range.
Applicability of the Model
In almost every country, it is common to have the civil service possessing more
information than the parliament, tempting the later to ‘rubber stamp’ the proposal. In
Zimbabwe, the National Budget Statement is presented in such a way that some proposed
measures take immediate effect. The Budget Statement is then debated over several
months, and in most cases passes with minor amendments. The bids submitted by various
government departments to the Ministry of Finance prior to the announcement of the
National Budget are often ‘exaggerated’, indicating how much the heads of such
departments attempt to have a wider financial domain, thus confirming the propositions
of the Niskanen model. The technocrats at the Ministry of Finance normally slash the
bids down. This raises a question as to whether the bureaucracy is a uniform unit short of
contradictions within itself. There are checks and balances within the bureaucracy itself
which the Niskanen model either disregarded or never considered. The expenditurelimiting forces within the bureaucracy itself can result in an outcome which is contrary to
the Niskanen prediction. There is no doubt that the Parliament of Zimbabwe was
generally an agreeable body for the larger part of the period 1980-98. The Parliamentary
Reform Committee launched in 1998 was an attempt to depart from that tradition.
2.4.5 Baumol Model
The Baumol model assumes an economy composed of 2 sectors, one of which is the
progressive sector and the other is the non-progressive sector. The progressive sector
produces goods using a method that allows for perfect substitution of labour for capital.
22
The non-progressive sector produces commodities using a method where labour itself is
part of the commodity consumed so that, roughly speaking; it is the public services
sector. Labour cannot be easily replaced by capital. Incidentally most public goods
belong to the non-progressive sector, whilst most private goods belong to the progressive
sector. The absence of perfect factor substitution in the non-progressive sector makes it
more expensive to achieve provision of public goods and services than it is to provide
private goods. The implication then is that since government is responsible for providing
the public goods, thus operating in the non-productive sector, then its expenditure is
likely to increase relative to the private sector growth. This disproportionate growth in
government expenditure relative to the overall economy is what can be referred to as the
‘Baumol effect’.
Applicability of the Baumol Model
Though there is little doubt that most government-provided commodities are services,
there is also evidence of government involvement in the provision of tangible goods, that
in some cases are pure private goods, as opposed to public goods. It is not clear if the
Baumol model carries the artillery to explain such scenarios. A case in point is the
government’s full ownership of parastatals such as Hwange Colliery (mining coal) and
ZiscoSteel (producing metal products). There are also services that are provided by both
the government and the private sector, with no clear evidence that government engages in
such activities at a higher cost than the private sector. If you look at the provision of the
health services, you would identify both the private and public sector providers of the
services. There seems to be no clue at all that the government incurs more costs in the
provision of the health services than the private sector providers. If anything the reverse
could be true.
23
2.4.6 Growth Accounting Model/Economic and Demographic
Explanation of Government Expenditure Growth
It is assumed that the factors that lead to government expenditure growth are:




The growth in real income.
Real price of the government goods and services measured in terms of private
goods.
Population growth and changes in the composition of that population.
Other factors that affect government expenditure growth.
In the General Accounting Model the demand for government goods is represented by the
following function:
Q  Q(Y; q; N; M) ---------------------------(1)
Where: Q is the amount of the public goods
Y = is the growth in real income
q = is the cost per unit of producing the public goods
N = is the population
M = are all the other factors.
We can analyse the rate of public expenditure growth by looking at the changes of each
of these factors.
Total Expenditure = E = P.Q( y, P, N, M ) ………………………….. ….[1]
Finding the total differential of [1] we get
 Q

Q
Q
Q
E  QP  P 
 y 
 P 
 N 
 M  …………….[2]
P
N
M
 y

E
is the rate of change that we are interested in.
E
Divide [2] throughout by QP,
E QP P  Q y Q P Q N Q M 


 





………..[3]
E
QP PQ  y y P P N N M M 
Expressing [3] in elasticities form:
24
E P Q y y Q P P Q N N Q M M


  
 

 

 
E
P y Q y P Q P N Q N M Q M
E P
y
P
N
M

  

E
P
y
P
N
M
E
P
y
N
M
……………………………….[4]
 (1  )
 

E
P
y
N
M
where
E
= rate of change of public expenditure.
E
 = income elasticity of demand for public goods.
 = price elasticity of demand for public goods.
 = elasticity with respect to the population.
 = elasticity of demand with respect to all other goods.
Equation [4] is only useful for very small changes in the variables E, P, y, N,and, M. For
large changes in these variables the differential approach does not work.
When the changes are rather discreet assume a log linear demand for government goods
and services, i.e.
Q(Y, P, N, M)  A  P   Y   N 1  M  …………………………..[5] where,
 = price elasticity of demand.
 = income elasticity of demand.
 = elasticity w.r.t. all other factors.
 = is a measure of the publicness of the good we are looking at. If
 = -1 then
N 1  N 0 , therefore population does not affect the demand of the good. So we have a
pure public good. If  = 0 then we have a pure private good.

we assume that  1    0 .

Assume also that these elasticities are stable over time. This is a heroic
assumption.

A is a scale parameter or an efficiency parameter.
25

Parameters , ,  and  are also assumed to be stable over time.
Assume an exponential growth of the following variables: E, Y, P, N, and M.
For a base period (say 1990) we know the values of the variables, i.e. E0, y0, P0, N0, and
M0.
E t  E 0 e rt where r = annual rate of growth of government expenditure.
From [5] we have
E  P  Q  A  P 1  Y   N 1  M 
Yt = Y0ery.t where ry = annual rate of growth of real income.
Pt = P0erp.t where rp = rate of growth of real prices.
Nt = N0erN.t where rN = rate of growth of the population.
Mt = M0erM.t where rM = rate of growth of all other factors.
E t  APt1 Yt N t 1 M t
This relationship holds at any time t.
E 0 e rt  A(P0 e rPt ) 1 (Y0 e rYt )  ( N 0 e rNt ) 1 (M 0 e rMt ) 
The common base e allows us to add the powers as below:
E 0 e rt  AP01 Y0 N 0 1 M 0  e t[ rP ( 1) rY  rN (1)  rM ]
where AP01 Y0 N 0 1 M 0 is the expenditure at time zero.
E 0 e rt  E 0 e[ rP ( 1) rY  rN (1)  rM ]t
r  (  1)rP  rY  (  1)rN  rM
The growth rate in public expenditure is a weighted sum of the rates of growth of these
variables.
The price elasticity of demand (  )
If we assume that the goods produced are normal goods and not giffen goods  <0. If the
price increases by 10% and Q by less than 10% we have inelastic demand (  <1). This
true for the demand of health services. If price increases by 10% and Q by more than
10% we have elastic demand (  >1). From empirical findings the price elasticity of
demand has been found to be less than one, in most studies. Apriori, we cant say the
demand is elastic or inelastic.
Income elasticity of demand (  )
26
Assuming that the goods provided are normal goods and not inferior we expect  to be
greater than zero (  >0). Demand for telecommunications services is income elastic.
There is no apriori reason to believe that the goods produced by the public sector are
income elastic or income inelastic.
Elasticity of demand with respect to population (  )
The parameter  which lies between –1 and 0 differs from good to good.
These variables normally explain not more than 50% of the rate of growth of public
expenditure from an empirical point of view. What explains the other 50%.
In this model an increase in population is likely to increase the expenditure of
government since the amount required of the public goods would also have increased.
The cost of providing a unit of the public good q is likely to increase over time due to
inflation. Government will also follow the trend of per unit cost.
Applicability of the Model
The Growth Accounting Model has the strength generally shared by other linear
regression models in that it can be used readily in empirical research. The model can,
with appropriate modifications and depending on the particular circumstances, provide
the platform for testing the significance of each of the factors explicitly stated as the
sources of government growth. Given that the factors are largely measurable, the
quantitative appeal of the model gives is a unique feature compared to the other models.
2.3 Trends of Government Expenditure in Zimbabwe
The government expenditure in Zimbabwe over the years has probably not revealed the
obvious growth trends that most models of public sector growth would predict. The graph
below summarises the trends in the proportion of general government expenditure5 to
GDP:
5
General Government is defined by Central Statistical Office to include the activities of both local and
central government.
27
Government expediture (1985-1996)
Govt Exp as % of GDP
30
25
20
15
10
5
0
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
1986
1985
Years
Source: CSO, National Income Accounts (1985-1996)
There was marked public sector growth up to 1988. We are almost compelled to believe
that ideological orientation has some influence on patterns of government expenditure.
Needless to say then that the socialist motives that drove the economy of Zimbabwe
during the ‘lost decade’ may have contributed to the upward trend. The 1990s were
generally characterized by reduced proportion of the public sector in overall economic
activity. The possible explanation of the decline is the inception of Economic Structural
Adjustment Programme (ESAP) that demanded the rationalization of the civil service
through downsizing, reducing social services provision and eliminating unnecessary
duplication. The proportion of government expenditure to GDP in 1992 was 24.2%,
which is in sharp contrast to the 1991 figure of 16.1% and the 1993 figure of 14.9%. This
casts doubts on the validity of the Displacement Theory in the Zimbabwean case. If we
consider that 1992 had a severe drought, requiring massive government expenditure on
relief and related activities, then we should have had some persistence of such high
expenditure levels if the Peacock and Wiseman theory is to be vindicated. Rather we see
the exact opposite, with 1992 being only an isolated peak.
28
CHAPTER 3
OPTIMAL PROVISION OF PUBLIC GOODS
There are various models that have been advanced in order to identify the ideal level of
public goods to be provided.
3.1 Pigouvian Model
In the Pigouvian model the utility of the representative consumer is determined by three
key factors which are: the amount of public goods that he consumes; the amount of
private goods that he consumes; and the amount of tax. This gives the utility function for
individual i of the form:
Ui  U i (Yi ; X i ; T )
Where: U i is the utility of individual i
Yi is the amount of private goods consumed by individual i
X is the amount of public goods consumed by the society or availed to the society
X i  X , implying that the amount of the public goods consumed by individual i is
exactly equal to the total stock of such goods available in the economy. This
follows directly from the non-excludability feature of public goods.
T is the tax.
If the utility is well behaved and the consumer is rational, then increased consumption of
the private goods should not diminish total utility. This can be illustrated by the partial
derivative of the utility function:
U i
 0 The marginal utility of private goods in non-negative.
Yi
The consumer’s utility also increases when the amount of public goods available is
increased. The marginal utility of public goods should thus be non-negative:
U i
U i
0
 0 and
X
X i
29
An increase in taxation levels has marginal disutility to the consumer and can be
represented by the partial derivative of the utility function with respect to the tax:
U i
0
T
The marginal utility of tax is non-positive. That is there is no enjoyment in paying tax.
The optimal level of public expenditure is identified where the marginal utility of
consuming the public goods is equal to the marginal disutility of paying tax at a point
30
such as A. At point B the marginal utility of the public goods is greater than the marginal
disutility of paying tax implying that the consumer would prefer a higher level of
expenditure than the current. At point C the marginal disutility of paying tax is greater
that the marginal utility of public consumption and it implies that the consumers would
prefer a lower level of government expenditure than that prevailing. At the optimal point,
the net marginal utility should be zero where marginal disutility equals marginal utility of
X as shown in the diagram.
3.2 Tiebout Model/ Voting-with-the-Feet
The Tiebout model was developed by economist Charles Tiebout in his article "A Pure
Theory of Local Expenditures" (1956). The model attempts to explain the public choice
in the context of migration, arguing that individuals will move from one local community
to another until they find the one which maximises their personal utility. In the model
mobility is necessitated by the need to enjoy the benefits from consuming locally
provided goods, whereas there are also costs in the form of the necessary taxes that an
individual will pay to his or her local government.
The basic assumptions of the Tiebout model are that:

consumers are free to choose their communities.

consumers enjoy perfect mobility and have perfect information. This essentially
means that they can move from community to community at no cost, and that they
possess the necessary knowledge about services provided by local governments
and the tax rates of all local governments.

The commodities provided are non-perfect public goods that are subject to
congestion with no perfect excludability.
The Tiebout model argues that most of the goods or services provided by the government
could be efficiently provided if only governments could be made competitive with each
other for customers, who happen to be also the citizens in this model. The model assumes
that there is natural setting within a single metropolitan area where there are several
administrative units that are competing for residents. There are variations across the
administrative units in terms of the level of social services or public goods and the tax
31
levels on offer. Each citizen has free choice as to which administrative unit he should
belong to depending on his preferences regarding social services and taxation.
Competition among the administrative or residential units would create technical and
allocative efficiency. If for instance the administrative unit provided too much or too little
of a public good, or were too expensive, the residents would exit to another community
that meets their demands. As new residents enter a community, each additional resident
reduces the consumption of the public goods enjoyed by the existing citizens. This is
because the Tiebout model assumes non-perfect public goods that are subject to
congestion with no perfect excludability. To avoid congestion, that is to keep the
consumed output of the service at the originally chosen level, more of the public facility
must be provided. When the marginal cost of the added facility just equals to the average
cost of providing the chosen level of the public good to all residents, then the community
has achieved its optimal population size for that level of output. The model states that
through the choice process of individuals, jurisdictions (administrative units) and
residents will determine an equilibrium provision of local public goods in accordance
with the tastes of residents, thereby sorting the population into optimum communities.
Applicability of the Model
The Tiebout model has been shown to be most accurate in suburban areas with many
different independent communities. Moving between communities in these areas tends to
have the lowest costs, and the set of possible choices is very diverse. In rural
communities or areas without clusters of communities in geographic proximity, the
Tiebout model seems to have little correlation with reality. There is no need to share the
myopic view which is popularised in this model that switching from one municipality to
the other is costless. There are obviously some significant costs in the form of
transportation and other relocation costs that make it prohibitive for people to ‘go to
where they belong’. People are always kept within certain towns or localities due to a
combination of factors, economic and non-economic. Job-ties can force people to remain
within an administrative unit that may not be providing them with satisfactory social
provisions, or that is charging them exorbitant levies. The model unrealistically assumes
32
a primitive nomadic society that is far from the realities of modern society where people
are largely established and with very little chance of considering relocating. In modern
liberal societies the residents prefer to make their representations to the administrators
than relocate. Furthermore, the towns or administrative units that you would find in some
countries do not offer the residents many alternatives. In Zimbabwe, the one-city concept
adopted in the post-independence era has generally attempted to reduce the variations in
the quality of social services in the low- and the high-density residential areas, gradually
nullifying the critical classification. If you intended to escape the dirty in one highdensity suburb by relocating to another high-density suburb, you may very well face the
same predicament even there.
Tiebout's proposition that people "vote with their feet" to find the community that
provides their optimal bundle of taxes and public goods has played a central role in the
theory of local public finance over the past few decades. Surprisingly, there have been
few direct tests of his premise. Banzhaf and Walsh (2006) use a Tiebout equilibrium
model to derive testable hypotheses about changes in local community demographics.
Their model clearly predicts increased population density in neighborhoods that
experience an exogenous increase in public goods but yields only tentative predictions
about the effect on neighbourhood composition. To test these hypotheses, they use a
difference-in-difference model to identify the effect of initial pollution levels and changes
in local pollution on population and demographic composition. Their results provide
strong empirical support for the notion that households "vote with their feet" in response
to changes in environmental quality, thus providing direct empirical support for the
assumptions underlying the Tiebout model.
3.3 Oakland Model
The model assumes that there are congestion costs associated with the provision of the
public goods. The economy is composed of two goods: Y which is purely private and X
which is a public good. There is no perfect excludability. The economy is composed of N
33
individuals. The sum of the individuals’ consumption cannot exceed total production and
this applies to both commodities.
In the case of private goods this can be represented as:
N
Y
j
 Y ------------------------------------(1)
j 1
Y is the total amount of the private good produced in the economy.
Y j is the jth individual’s consumption of the private good.
The utility of the ith individual can be represented as Ui
Ui  Ui (Yi ; X ) -------------------------------(2)
From expression (2) it follows that:
U i
 0 where i≠j (j=1,2…N)------------(3)
Y j
If the jth person increases his consumption of the private good the utility of the ith
individual is unaffected, that is ruling out externality in consumption. The utility derived
from the consumption of the public good depends on the quantity consumed by the
individual and the total of the public good consumed by all other individuals.
N
Y
j
 Y ------------------------------------(4)
j 1
Each person’s consumption is constrained not to exceed total production as shown in the
above equation. The ith person’s consumption of the public good can be represented by Xi
and the total amount of the public good available is X, implying then that the individual’s
utility function is:
N
U i  U i (Y i ; X i ;  X j ; X ) --------------------------------(5)
j 1
N
Where:
X
j
is the usage of the public good.
j 1
U i
 0 ------------------------------------------------------(6)
X
34
Expression (6) says the more of the public good is available, the more utility individual i
gets as he has access to the commodity.
U i
 X
 0 --------------------------------------------------(7)
j
Expression (7) describes the congestion that accompanies the increased number of users.
In the traditional characterization of public goods, the amount consumed by the
individual cannot exceed the total amount of the public good available. Thus:
X i  X ------------------------------------------------------(8)
The weak inequality implies that exclusion is possible and costless. Given an amount of
the public good available (X), extension of the services of the good to additional
individuals diminishes the enjoyment of the good to those already consuming it, which is
what (7) says. On the other hand given the total usage of the public good, the provision of
additional units enhances the utility of those units already being consumed. In other
words expression (6) suggests that adding units of the public good has a decongestion
effect.
The utility of the individual can therefore be generalized to:
U i  U i (Y i ; X i ; c) -------------------------------------------(9)
N
Where: c represents congestion which is positively related to total usage (  X j ) and
j 1
negatively related to total output of the public good (X).
U i
 0 ----------------------------------------------------(10)
c
If we increase congestion, then the utility of individual i would decline:
c  c( K ; X ) -------------------------------------------------(11)
Where: K is usage of the public good or utilization of the units of the public good.
35
C
 c k  0 ------------------------------------------------(12)
K
If we increase usage then congestion also increases.
Implications of the Oakland Model
If the membership in a community increases, that is if population size rises, then usage
also increases with the possibility that congestion will demand that more of the public
facility be made available.
3.4 Samuelsonian Model
The Samuelsonian model proves that a Pareto efficient allocation will require that the
sum of marginal private benefit, that is the agent’s marginal rate of substitution of the
private good for the public good must just equal the marginal cost of an additional unit of
the public good. In other words where a public good is consumed by two individuals A
and B, then the marginal willingness to pay for the public good should be summed for all
individuals in order to come up with the optimal provision of the public good. The
optimal amount of the public good is determined where:
N
 MRS
i 1
XY
 MC
In an economy with several individuals, the public good should be financed by the
collective contribution of each according to the marginal benefit derived from the public
good. We can use vertical summation to come up with the collective marginal benefit
curve (MBs) as shown in the graph below:
36
X* is the optimal amount of the public good.
3.5 The Political Democracy Explanation: Median Voter Theorem
The evolution of this theorem can be associated with the separate works of Hotelling
(1929) and Black (1948). The Median Voter Theorem says that if voters cast their votes
for the party or candidate closest to their most preferred, feasible amount of public
expenditure, then it turns out that the candidate closest to the median voter always win an
election. This follows from the fact that the candidate who is closest to the median voter’s
preferences would have positioned himself strategically to reduce or minimize the
distance to either extreme of the preferences. On one extreme is the low public
expenditure and on the other is the high public expenditure. The assumption is that each
candidate declares a set of public goods and services that he is going to offer.
A certain group or individual is decisive in determining the mode of government
expenditure. We need to study the preferences of the decisive voter to understand the
growth of government expenditure. The medium voter is a person who has medium
income in the society. The individuals are ranked according to their incomes. For
example:
37
ABC
where A = low income person
B = middle income person
C = high income person
Assume that there is a uniform turnout of voters. The next step is to rank these
individuals in terms of their preferences for the goods provided by the public sector.
Individual A prefers more public goods than individual B and individual B prefers more
public goods than individual C. The person with a medium income also has the medium
preferences with respect to the public goods.
The rank that is in terms of public goods preferences is as follows:
ABC
The factors that determine the level of government expenditure are:
a)
Income of the medium voter (real after tax income) (Ym).
b)
The real price of the service to the medium voter. This depends on benefits
derived from the public expenditure by the medium voter, the cost of
producing the good provided and the medium voter’s share of the cost.
How do we determine the real price faced by the medium voter? We have to establish the
desired level of publicly produced goods by the median voter. The determining factor is
the real price (Pm) faced by the median voter. This real price depends on:
a)
Cost of production of the publicly produced good.
b)
How much benefit does the individual (medium voter) (G*) derive from any
given amount of the publicly produced good (G).
c)
It also depends on the tax share of the medium voter.
The cost of production is given by the following expression:
TC = qNG……………………………………………(13)
where TC = total cost of producing the public good
Q = unit cost of public good
38
N = population
TC = AC.G……………………………………………(14)
qN = Average cost
N = takes account of whether unit costs are dependent on population or not.
 = is a scale effect on unit cost. If  = 0 then we have constant unit costs. If   0
then the unit cost will be scaled up by the number of people for which the good is
produced. If   0 then we have falling unit costs.
Benefits derived by the medium voter are also critical in the determination of the real
price. G* = G if G is a public good. G* is the amount of the public good consumed by the
medium voter.
For a pure private good:
G* = G/N
For intermediate cases:
G* = G.N-
when  = 0, we have a public good,
when  = -1, we have a pure private good.
In general 0 <  < 1, for the mixed goods.
The cost per unit derived by the medium voter is given by TC/G* = qN+
Does the median voter pay this cost? It depends on the tax share of the medium voter. Let
the tax share (cost share) of the medium voter be tm.
Pm = tmqN+……………………………………….(15)
If tm = 1, the medium voter pays the cost per unit of benefit.
0 < tm < 
If tm < 1, then he pays less than the cost per unit of benefit. If tm > 1, it follows that he
pays more than the cost per unit of the benefit.
Given ym, Pm we can come up with the demand for publicly produced goods by the
median voter. Assume a log linear demands function:
log G* = a + b log ym + c log Pm……………………………….(16)
log G* = a + b log ym +c log tm + c log q + c(+) log N……..(17)
39
b = income elasticity of demand for the publicly produced good. If the good is a normal
good b>0.
c = price elasticity of demand for the public good. If the good is not giffen c < 0. When
the tax share (tm) goes up the demand for the publicly produced good goes down.
G* = is the desired level by the medium voter. This might differ from the actual level.
G* = GN- = G/N……………………………………………..(18)
log G* = log G -  log N………………………………………(19)
log G = log G* +  log N……………………………………...(20)
Substituting (17) into (20) we get,
log G = a + b log ym + c log tm + c log q + [c(+) + ] log N..(21)
G is the total amount of the publicly produced good for which the medium voter will
vote.
Empirical estimates by Pommer and Schinider based on 110 Switzerland local councils.
These two gentlemen estimated the following econometric equation:
log E i  a 0  a 1 log Inc i  a 2 log Tax i  a 3 log Pop i  e i where
i = local municipality (authority)
Inci and Taxi are income and tax shares of the medium voter in each municipality.
ln E i  11.9 ln C  1.29 ln c  0.7 ln Tax  0.63 ln Pop
11.9 ln C is the constant.
R 2  0.535
The model explains 53.5% of the variation in government expenditure between different
municipalities. The model assumes that the medium voter knows his tax share. The
medium voter may only know the direct taxes and may not be aware of the indirect taxes
he faces. So they are willing to underestimate their tax shares. This may lead to the
underestimation of the cost of publicly produced goods. This results in what is known as
fiscal illusion. In countries where direct taxes are more than indirect taxes then people
can approximate the cost of public goods better. So a measure of the tax complexity can
be included in the model.
40
Government expenditure as a share of GDP
Given population N
GDP  NY where Y = per capita income.
E = Total Government Expenditure  qN   G
E
qN   G

GDP
NY
 E 
ln 
  ln q   ln N  ln G  ln N  ln Y
 GDP 
In this type of model the parameters are elasticities.
Implications of the Median Voter Theorem
The Median Voter Theorem enjoys immense versatility to the extent that it can be applied
to various policy decisions relating to public expenditure, taxation levels, national
defense expenditure levels, and the transfers to the poor and elderly. One obvious
implication of the model is that public policies will tend to be moderate middle-of-theroad policies drawn from the middle of the economic and political spectrum.
41
CHAPTER 4
MECHANISMS FOR REVEALING SOCIAL CHOICE
This section basically looks at the voting rules in relation to how social decisions are
arrived at. These are the mechanisms through which the individuals in society reveal their
preferences for public goods and taxation levels. A benevolent dictator may claim to
know what ‘his people’ prefer and proceed to implement policies that he says are in the
best interest of the citizens whom he has not consulted. We need to establish whether or
not such actions, or policies born from such thought are ‘in the best interest of the
public’. In general a good mechanism for revealing social choice should satisfy Arrow’s
Impossibility Theorem.
4.1 Arrow’s Impossibility Theorem6
Kenneth Arrow argued that it is virtually impossible to construct a Social Welfare
Function (SWF) or social ordering of states of the world that obeys five relatively weak,
but desirable, axioms of choice. He considered five axioms that might reasonably be
required for any collective choice system. These include:
a) Pareto Optimality: This says if everyone prefers state S0 to state S1 then society
should also prefer S0 to S1. In other words if the individuals have a common
opinion on the appropriate expenditure and / or taxation level, then consensus
prevails and the collective decision is uniform.
b) Non-Dictatorship: This says no individual should have full control over the
collective choice process such that that individual’s preferences over alternatives
are always decisive, even when everyone else prefers just the opposite. More
6
The theorem is credited to Nobel Prize Winner Kenneth Arrow, who aptly stated that no system or
mechanism of revealing social choice would ever be perfect and immune from one or the other.
42
precisely, if individual i prefers X to Y (X Pi Y), but everyone else prefers Y to X
i.e Y Pj X  j; j≠i
The importance of non-dictatorship is so as to eliminate the possibility of one
individual manipulating the social choice process.
c) Rationality: This is combined with the axiom of transitivity. It says if society
prefers X to Y, and Y to Z, then it should also prefer X to Z. This is also applicable
in the indifference relationship, that is, if society is indifferent between X and Y,
then it should also be indifferent between X and Z and this is called indifference
transitivity. The earlier being preference transitivity.
d) All preference orderings should be available. This is referred to as the axiom of
unrestricted domain. The axiom says, all the possible combinations of individual
preferences should be comparable. For instance if we have six alternatives, A, B,
C,……,F, then the preference relations between any two alternatives should be
known.
e) Independence of Irrelevant Alternatives: This says in comparing any two
alternatives, the choice as to which is preferable must depend on the individual’s
orderings of only those alternatives that are under comparison. In other words, the
alternatives are independent in the sense that there is no bunching.
Implications of Arrow’s Theorem
It is practically impossible to satisfy five axioms simultaneously because some of the
axioms are not compatible with each other. For instance, it is not possible to have a social
choice mechanism that satisfies axiom (c) unless it is a dictatorship which is a violation
of axiom (b). Each time you try to satisfy some of the axioms you are creating the
possibility of violating other axioms. If you relax the axiom of non-dictatorship, then it is
possible to satisfy the rest of other axioms. Unfortunately there is no guarantee
whatsoever that after that axiom has been relaxed, the other members of the society will
truthfully reveal their preferences to the dictator.
43
4.2.1 Unanimity/Consensus
Unanimity is a situation where decisions should be passed only upon their approval by
the rest of the society’s members. Any one individual has veto and can stop the
implementation of the proposed policy. The advantage of this method is that it prevents
the tyranny of the majority. A policy only passes if it is approved by α% of the
population, and α=100. The general use of this rule is to prevent or hinder the easy
passage of policies.
4.2.2 Simple Majority
This means in a population that has N individuals then a policy will only pass if at least
50% vote in favour of the policy. If, for instance, there are three individuals A, B and C,
then approval would require at least two votes in favour of the policy. There are however
complexities that are often associated with such a rule. For instance, it could lead to a
voting paradox also referred to as the Condorcet Paradox. The Condorcet Paradox is a
situation of indecision that is often a characterization of the simple majority voting rule.
Suppose we have three individuals A, B and C; and three alternatives S0, S1 and S2; then
the table below would illustrate the paradox:
Voter
A
S0
1
Alternatives
S1
2
S2
3
B
3
1
2
C
2
3
1
The absence of a solution based on the simple majority rule in the above example leads to
the Condorcet paradox. The preferences shown above can be described as multi-peaked.
4.2.3 Point Voting
In point voting, each individual is allocated utility points that he has to divide among
alternatives according to the relative strength of preference. The most preferred
alternatives to the individual is given more points such that the alternatives are eventually
44
compared based on the sum of points allocated by the various individuals. Suppose we
have individuals A, B,……,E and three alternatives and we allocate twelve points to each
individual, such that:
Individual/Voter
S0
S1
S2
A
6
4
2
B
2
7
3
C
2
1
9
D
5
3
4
E
2
3
7
TOTAL
17
18
25
The distribution of points reflects the relative strength of preferences that an individual
has for each alternative. The most preferred alternative is the one that has the highest
points. This system however has several administrative and institution limitations, among
them the need to have a highly literate and numerate society. In the above example, S2 is
the preferred alternative.
4.2.4 Borda Count
This system involves ranking alternatives from 1,……….,M; where 1 is the best
alternative and M is the worst. Each individual should then produce a ranking of the
alternatives. The rankings are finally added to give a basis for comparison of the
alternatives. The alternative that has the lowest Borda count is the most preferred.
Suppose we use three alternatives and 5 individuals:
45
Individual/Voter
S0
S1
S2
A
1
2
3
B
1
2
3
C
2
3
1
D
2
3
1
E
2
3
1
TOTAL
8
13
9
The most preferred alternative is S0 because it has the lowest Borda count. The problem
with this rule is that it is sensitive to irrelevant alternatives.
4.2.5 Logrolling
Logrolling is associated with the ideas of Buchanan and Tullock (1962). Literally
logrolling implies exchanging votes or selling votes. Logrolling occurs when legislators
bargain in such a way that they persuade others to vote for their preferred policy in return
for them voting for the others’ preferred policy. The total bargaining or exchange
mechanism should give some net benefit to the legislator. The legislator should exchange
votes until the marginal cost of voting for a policy alternative which is not desired equals
the expected marginal gain from the votes obtained in return for issues that are most
preferred. There are both external and internal costs in exchanging votes. In addition the
logrolling coalitions are often unstable. One logroller could renege or break an earlier
promise. The following simultaneous equations can be used to illustrate the logrolling
decision:

Sˆi  ˆ 0  ˆ1 Di  ˆ 2 Pˆi -------------(1)


tˆi  ˆ0  ˆ1 Di  ˆ2 Pi --------------(2)


S i   0  1 Di   2 Pi   4 tˆi ------(3)


ti   0  1 Di   2 Pi   4 Sˆi ------(4)
For issues S and T, Si and ti are the probabilities that legislator i votes for S1 over S0 and
T1 over T0 respectively. Di and Pi are vectors of district and personal characteristics of the
legislator. Ŝ i is the probability that the ith legislator will vote in favour of S1 over S0
46
without the influence of logrolling. tˆi is the probability that the ith legislator votes in
favour of T1 over T0 in the absence of logrolling.
Equations (3) and (4) represent the probabilities that the ith legislator would vote for S1
over S0 and T1 over T0, given that another legislator will also vote for S1 over S0 in return
for the favour done on issue T. Logrolling is evident when  4 and  4 are positive,
which is an indication of behind-the-scenes behaviour.
47
CHAPTER 5
EXTERNALITIES
5.0 Defining an Externality
Pigou (1920) defines an externality as a situation where one person A, in the course of
rendering some service for which payment is made to a second person B, incidentally also
renders a service or disservice to other persons of such a sort that payment cannot be
extracted from the benefiting parties or compensation enforced on behalf of the injured
parties. Heller and Starett say the externality is a scenario where the decision variable of
one economic agent enters into the utility function or production function of another.
Suppose we have one individual A, consuming a set of commodities X= X1,…………,XN.
Then the utility function of the individual A will be UA=UA(X). If society is invaded by an
additional individual B, who apart from consuming the vector of commodities X also
smokes. Then B’s utility function:
UB=UB(X;S)
U B
 0 , implying that smoke gives utility to B.
S
Where: S represents smoke.
If however individual A is hurt by the smoke then A’s utility function becomes:
UA=UA(X;S)
U A
 0 , implying that smoke gives disutility A.
S
5.1 The Optimal Level of Pollution
The economic definition of pollution is dependent upon both some PHYSICAL effect of
waste on the environment and a human reaction to that physical effect. The physical
effect can be biological (e.g. species change, ill-health), chemical (e.g. the effect of acid
rain on building surfaces) or auditory (noise). The human reaction shows up as an
48
expression of distaste, unpleasantness, distress, concern, and anxiety. We summarise the
human reaction as a loss of welfare/utility/satisfaction.
Two possibilities for the economic meaning of pollution. Consider an upstream industry,
which discharges waste to a river, causing loss of dissolved oxygen in the water. In turn,
suppose the oxygen reduction causes a loss of fish stock in the river, incurring financial
and/or recreational losses to anglers downstream. If the anglers are not compensated for
their loss of welfare, the upstream industry will continue its activities as if damage
downstream was irrelevant to them. They are said to create an external cost. An external
cost is also known as a negative externality, and an external diseconomy. If we were
considering a situation where one agent generates a positive level of welfare for a third
party, we would have an instance of an external benefit (positive externality, or external
economy).
An external cost exists when the following two conditions prevail:
An activity by one agent causes a loss of welfare to another agent.
The loss of welfare is uncompensated.
Note that both conditions are essential for an external cost to exist. For example, if the
loss of welfare is accompanied by compensation by the agent causing the externality, the
effect is said to be internalized.
5.2 Optimal Externality
Note that:
The physical presence of pollution does not mean that economic pollution exists.
Even if economic pollution exists it is unlikely to be the case that it should be eliminated.
In figure below, the level of the polluter’s activity, Q, is shown on the horizontal axis.
Costs and benefits in money terms are shown on the vertical axis. MNPB is the ‘marginal
net private benefits’. The polluter will incur costs in undertaking the activity that happens
to give rise to the pollution, and will receive benefits in the form of revenue. The
49
difference between revenue and cost is the private net benefit. MNPB is then the marginal
version of this net benefit, i.e. the extra net benefit from changing the level of activity by
one unit.
MEC is the marginal external cost, i.e the value of the extra damage done by pollution
arising from the activity measured by Q. it shown here as rising with output Q.
We are now in apposition to identify the optimal level of externality. It is where the two
curves intersect, i.e. where MNPB=MEC. Why is this? Since the two curves are marginal
curves, the areas under them are ‘total’ magnitudes. The area under MNPB is the
polluter’s total net private benefit, and the area under MEC is total external cost. On the
assumption that the polluter and sufferer are equally deserving - i.e. we do not wish to
weight the gains or losses of one party more than another’s – the aim of society could be
stated as one of maximizing the sum of benefits minus the sum of costs. If so, we can see
that triangle OXY is the largest area of net benefit obtainable. Hence Q* is the optimal
level of activity. It follows that the level of physical pollution corresponding to this level
of activity is the optimal pollution. Finally, the optimal amount of economic damage
corresponding to the optimal level of pollution Q* is area OYQ* - area B. Area OYQ* is
known as the optimal level of externality.
50
At Q* MNPB = MEC
This result can also be derived formally.
MNPB=P-MC
Where MC is the marginal cost of producing a polluting product.
Hence P-MC = MEC
Or P = MC +MEC
Now, MC + MEC is the sum of the marginal costs of the activity generating the
externality. It is Marginal Social Cost (MSC).
Hence when MNPB = MEC, P = MSC.
Price equals marginal social cost is the condition for Pareto Optimality.
51
5.3 Types of externalities
We can now define some terms in terms of the diagram above.
Area B = the optimal level of externality.
Area A + B= the optimal level of net private benefits for the
polluter
Area A = the optimal level of net social benefits
Area C + D = the level of non-optimal externality which needs to be removed by
regulation of some sort.
Area C = the level of net private benefits that are socially unwarranted.
Q* = the optimal level of economic activity.
Qb = the level of economic activity that generates maximum private benefits.
The figure above thus demonstrates a very important proposition: in the presence of
externality there is a divergence between private and social cost. If that divergence is not
corrected the polluter will continue to operate at a point like Qb in figure above. At Qb,
private benefit is maximized at A+B+C, but external cost is B+C+D. So the net social
benefit = A+B+C-B-C-D = A-D, which is clearly less than A, the net social benefits
when the polluter’s activity is regulated to Q*.
Externality level C + D is said to be Pareto relevant because its removal leads to a Pareto
improvement, i.e. a net gain in social benefits. Externality level B is Pareto irrelevant
because there is no reason to remove it.
Who are the polluters? The typical image is that polluters are firms. But it is also the case
that polluters are individual people – car drivers create noise and cause accidents, people
who play radios in and out of doors cause noise nuisance, and so on. The government can
also be considered as a creator of external effects through poor legislation and rules.
52
5.4 Solutions to the Externality Problem
An externality is a problem because it distorts the efficient functioning of the market
system. There is a good reason why policy-makers may want to deal with the externalities
and prevent market failure. Various strategies have been suggested to handle issues that
involve the interrelationships between economic agents, with the primary purpose of
avoiding the adverse effects on innocent. It is not therefore surprising that the greatest
concern has been on the negative externalities, those that impose harm or damage to third
parties. The externality problem can be solved or eliminated through the use of any of the
following:
1. Command and Control: It involves initiating laws or regulations that ban the
generation of negative externalities. Some of the mechanisms might involve not
only targeting the externality but also targeting the activity causing the
externality. The are adverse effects if such measures are implemented, for
instance, it would be practically impossible for most manufacturing processes no
matter how beneficial their output is, to remain operational without generating
some form of pollution. Such draconian laws can thus have prohibitive effect on
the existence or development of industry in the country. Just consider, for
instance, an extreme example where the Zimbabwean government institutes a law
that exposes the directors of a polluting company to prosecution and threatens to
close firms that engage in environmental pollution. Clearly the fear of the likely
consequences may tilt economic activity away from heavy industry,
notwithstanding the fact that the country cannot thrive without the products of
such activities.
2. Pigouvian Tax: It suggests the use of taxes to achieve efficiency in the presence
of negative externalities and subsidies in the presence of positive externalities.
Pigou argued that when competition rules with social and private net products at
the margin diverging, then it is theoretically possible to put matters right by
imposition of a tax or granting a subsidy. The polluting firm should be taxed
according to the amount of the pollutant emitted. If the firm is producing output X
53
and selling at per unit price Px and emitting S amount of pollutant, then its profit
maximization problem can be stated as:
Max  PX X  CX ( X ; S )
Where: Cx is the cost of production
If a Pigouvian tax of t per unit of pollution is introduced, then the profit
maximization problem becomes:
Max  PX X  CX ( X ; S )  tS
3. Pollution Quota
This is a quantitative restriction which stipulates how much pollutant each firm is
allowed to produce. The firms should improve their production to ensure that they do
not exceed the allocated quota. There are always costs associated with reducing the
pollution levels. For instance firms have to make investment in technology that is
compatible with the permissible pollution levels. There are also penalties for violating
the pollution quota. In an economy where there are two firms 1 and 2; the quota for
firm 1 can be represented by X1 and the quota for firm 2 is represented by X2. The
target maximum emission level, that is the aggregate pollution level expected when
both firms observe the pollution quota is equal to:
X  X1  X 2
The cost of achieving emission or pollution quota X1 for firm 1 can be represented as:
C1 ( X1 )
And the cost for firm 2 of achieving pollution quota X2 is represented by:
C2 ( X 2 )
The total cost of achieving the pollution quotas in the economy then becomes:
C( X )  C1 ( X 1 )  C2 ( X 2 )
It follows that the first-order condition for minimizing emissions is:
C
C 2
C
 1
0
X
X 1 X 2
Rearranging gives:
54
C1
C
 2
X 1
X 2
Each firm should be allowed a pollution quota such that the marginal cost of emission
control is equalized across firms. If one firm had a higher marginal cost of emission
control than the other, society could lower the cost by reducing the firm’s quota and
increasing that of the other firm.
4. Allocating Property Rights
The use of property rights is based on Coase Theorem. This theorem says if property
rights are complete and if parties can negotiate an efficient solution to the externality;
if private parties can bargain without transaction costs over the allocation of
resources; then such bargaining will always solve problems of externalities on its own
and allocate resources efficiently regardless of who owns the property rights.
According to this theorem, an externality is an outcome of the absence of complete
property rights, that is, the existence of common property which normally leads to
what is referred to as ‘Tragedy of the Commons’. The ‘Tragedy of the Commons’
implies that common property is in danger of being overused with the risk that it will
eventually be depleted or dilapidated beyond any possible reclamation. Suppose there
are two firms; 1 and 2. Firm 1 is a victim of pollution produced by firm 2. Firm 1 is
involved in producing commodity Y1 which it sells at price P1. Firm 2 produces Y2
which it sells at P2. The production process for firm 2 also generates smoke or
pollution. Each firm uses only labour as an input such that the firm’s labour demand
is L1 for firm 1 and L2 for firm 2. The price of labour per unit is w.
The solution in the case where Firm 1 has Property Rights
If firm 1 has the property rights then it can seek compensation from firm 2 and firm
1’s profit function will be:
1  P1Y1  wL1  Ps S
Where: Ps is the price charged by firm 1 for each unit of pollution produced by firm 2
and S is the amount of smoke produced by firm 2.
55
The profit function for firm 2 will be:
 2  P2Y2  wL2  Ps S
Thus PsS is the revenue generated by firm 1 from pollution which is equivalent to the
compensation made by firm 2 for polluting.
The solution in the case where Firm 2 has Property Rights
If firm 2 has the property rights, then firm 1 has an opportunity to bribe firm 2 so that
it reduces its pollution levels. The profit functions of the two firms will change
accordingly such that:
1  P1Y1  wL1  Ps (S  S )
Where: S is the amount of smoke initially generated by firm 2, that is before a bribe
is paid by firm 1.
Ps is the payment made by firm 1 per unit of pollution reduction by firm 2.
The profit of firm 2 will be:
 2  P2Y2  wL2  Ps (S  S )

The total payment made by firm 1 for pollution reduction is Ps ( S  S ) . The overall
conclusion is that the pollution level that ultimately prevails is S in both cases.
Whoever has the property rights has the chance to generate revenue from pollution.
The allocation of property rights may therefore have a redistribution effect. The above
can be graphically represented as shown below:
56
The optimal pollution level is where marginal benefit (MB) to the polluter is equal to the
marginal damage to the victim. If firm 1 has the property rights, it can allow firm 2 to
increase the pollution level from e` to e*. At e` marginal benefit to the polluter is greater
than the marginal damage to the victim. This is because at e` firm 2 enjoys a greater
marginal benefit from polluting than the marginal damage endured by firm 1. Therefore
firm 2 can compensate firm 1. If firm 2 (polluter) has the property rights, then it can emit
pollution level e2 unless it is compensated or bribed for reducing pollution levels. Firm 1
will face pollution level e2 unless it accepts to pay the bribe for pollution reduction to
firm 2. Firm 1 will face a marginal damage which is greater than the marginal benefit to
the polluter.
57
CHAPTER 6
PUBLIC SECTOR REFORM IN ZIMBABWE
6.1 The accumulation of Public Sector Distortions
The 1980s economy was dominated by import-substitution and the role of government in
the economy was already quite significant as evidenced by the existence of several public
corporations involved in mining, agriculture, manufacturing, distribution, power supply
and the services sector. The trend of public sector growth was strengthened through
policies such as nationalization and granting more state enterprises monopoly rights. By
1990 there were 39 parastatals. It became clear that the trend could not be sustained as the
system was flawed with restrictive controls and legislation that tended to crowd-out
private sector investment and to deter competition. In the 1990 budget statement, the then
Minister of Finance and Economic Development said:
“The economy is shackled by over twenty-five years of controls and is overly
protected to the point that it has become a high cost and largely uncompetitive as
well as beset with inefficiencies and crippling monopolistic practices.”7
The budget deficit was around 10% of GDP per year for the period 1980-1990. The
expenditure levels of government were very high with education, health and defense
being the major contributors. Subsidies on basic commodities also contributed to the
widening deficit. Between 1980 and 1984, there was massive peasant resettlement. About
52 000 peasants were resettled over that period. To finance its expenditure, the
government in 1983 secured a $375 million loan from the IMF in the form standby credit.
The IMF in 1984 suspended the disbursement because the government was:

Slow in implementing public sector reforms such as cutting expenditure on
development programmes and subsidies.
7

Failing to meet the budget reduction targets

Failing to service its debts
Budget statement 1990, Minister of Finance and Economic Development
58
The World Bank in 1984 went on to finance the Export Revolving Scheme to the tune of
Z$70 million which was conditional upon the government’s promise to reform its public
sector. In 1986 United Nations Industrial Development Organisation (UNIDO) published
a report that revealed that Zimbabwe’s structural problems were in the form of:

High degree of state-owned monopolies in the economy which was the major
hindrance to investment promotion and job creation.

The size of the public sector was exerting a crowding-out effect on private capital

The economy was heading towards stagnation in terms of investment,
employment and growth
6.2 The Beginning of effective Public Sector Reform
In 1991 the government announced reform package Economic Structural Adjustment
Programme (ESAP) which was to take effect over the period 1991-1995. The program
intended to reform the public sector by reducing expenditure on social services and
channeling resources towards capital formation in the material production sectors such as
agriculture, mining and manufacturing. The main targets of the reform programme were:

Reducing the budget deficit from 10% of GDP to 5% by 1994/5

Reducing the size of the civil service significantly. The none-education civil
service was to be reduced by 25% which was equivalent to 23 000 employees by
the end of 1995. The progress on this aspect was quite significant in the early
years of the reform, with 11 000 retrenchments already effected by 1993. The
government could not sufficiently rationalize the civil service and duplication of
activities remained.

Phasing-out subsidies to the parastatals

The subsequent privatization of the state-owned organizations. The government
though under pressure from the World Bank and the IMF did not want absolute
privatization but preferred commercialization and the resistance was in the light of
the high profitability of some parastatals such as Air Zimbabwe, Posts and
Telecommunications Corporation (PTC), and ZESA. A compromise was
eventually struck between the Zimbabwean government and the financiers of the
59
ESAP, paving way for the phasing out of subsidies and gradual privatization. In
1991, the government announced a timetable for reducing subsidies to parastatals
from Z$629 million in 1990-91 to Z$40 by the end of the program. The
government however maintained some targeted subsidies especially on maize
meal.

Introducing cost recovery measures for education and health provision and these
were charging user fees. Government set up social dimension fund (SDF) with an
initial allocation of Z$20 million to cater for those who could not afford payment
for basic services.

Reducing the number of government departments
6.3 Performance of the Zimbabwean Economy During the
Economic Structural Adjustment Programme
Selected figures in table below are in millions of Zimbabwean dollars
INDICATOR
Real GDP at constant 1990 prices
Balance of Payments
Export Earnings
Imports
Employment in formal sector (000)
Rate of unemployment (%)
Budget deficit
Budget deficit as % of GDP
Inflation
Interest rates
Exchange rates USD:Z$
1991
22682
-386.6
5544.9
7443.1
1244
20%
-1597
7%
16
19%
5.05
1992
20634
-617.2
7333.6
11232.3
1236.2
21.80%
-1709
8%
14
35,5%
5.48
1993
20908
1359.3
10164.2
11798.4
1240.3
28%
-3696
18%
12
27%
6.94
1994
22333
2198.7
15365.2
18270.6
1263.3
28%
-3721
17%
10
30%
8.39
1995
22365
1819.6
18359
23048
1239.6
31%
-5792
26%
10
30%
9.31
During the period that Zimbabwe experimented with the Economic Structural Adjustment
Programme:

Real GDP declined from Z$22,628.0 million in 1991 down to Z$22,356.0 million
in 1995.

Balance of Payments shifted from a negative Z$386.6 million in 1991 to a
positive Z$1,819.6 million in 1995.
60

Export earnings grew from Z$5,544.9 million in 1991 to Z$18,359.0 million in
1995.

Unemployment rose from 20% in 1991 to a massive 31% in 1995.

Interest rates shot up from 18.5% in 1991 to 29.83% per annum in 1995.

The budget deficit increased from 7% in 1991 to 26% in 1995 despite the fact
that reducing this economic indicator was central to the objectives of E.S.A.P.

Inflation averaged above 10%

The Zimbabwean dollar depreciated by over 84% against the US Dollar during
the period.
6.4 Tax Reform in Zimbabwe
The objective of tax reform was to raise more revenue in order to keep the budget at
sustainable levels. Several taxes and levies were introduced, some of which include
drought levy which faced criticism from the country’s labour-force. The levy was
intended to raise funds for drought relief but remained in place well after the drought
period. The tobacco levy was introduced at 5% of sales and it was announced over the
1996/97 financial year. The taxing on fringe benefits was introduced over the same
period, for example the company car tax. Several tax exemption structures were
abandoned, thus broadening the tax base. The pension funds, which were previously taxfree, now fell under the wrath of the tax man. More recently (2004) the Value-Added Tax
replaced Sales Tax with the hope of reducing tax evasion. The Customs Department was
merged with the Department of Taxes to form the Zimbabwe Revenue Authority
(ZIMRA). In 1997 government proposed to raise sales tax from 15% to 17.5% but the
move was reversed after widespread resistance.
6.5 Evaluation of the Progress of Public Sector Reform
There has been a number of threats to debt reduction policies, for instance the droughts
have imposed the need to import maize. During the 1991/92 drought the government
imported 1.9 million tones of grain to give relief to 6 million people. Earlier in the
season, government through the Grain Marketing Board had exported 0.6 million tones
despite the pending grain shortage, thus depriving the government of over Z$1 billion.
61
The government revenue in 1991-92 was 12.6% short of the budget forecast and over
89% of firms operated below full capacity. The total national debt rose from US$2.6
billion in 1990 to US$4 billion by 1994. The parastatals had an accumulated debt of Z$2
billion in 1993/94, with the GMB contributing over half of the total. Over expenditure by
some government ministries continued until the government introduced the ‘Stop
Payment’ clause in the 1994/5 budget. The ‘Stop Payment’ clause barred ministries or
departments from paying suppliers once the department’s budget limit has been reached.
The system enhanced fiscal discipline but had drastic effects especially on the health
sector when suppliers of foodstuffs and drugs retaliated by withholding their products. In
1994 the government initiated a decentralization exercise meant to empower local
authorities and offload the burden of service delivery that was on central government.
Direct grants to local authorities were phased out whilst several posts in the
administrative structures of government were abolished. Parastatals also introduced
similar measures. For instance, by 1993 Zisco Steel had retrenched 817 workers and
Dairibord retrenched 33% of its workforce, almost 1 100 men. Workers in the public
sector were allowed Voluntary Early Retirement (VER). In 1996, the privatization
exercise intensified, and several sectors previously dominated by parastatals were
liberalized. For example, Cotton Marketing Board (CMB) had its monopoly on buying
cotton withdrawn.
In 1998 there were three companies already involved in buying cotton, and CMB was
subsequently privatized and transformed into Cottco, with government shareholding
dropping from 100% to 25%. Dairibord and Commercial
Bank of Zimbabwe (CBZ)
also off-loaded part of government shareholding over the same period. Two methods
were often used in the privatization exercise:

Floating of shares: This involved initial share offer prior to listing on the local
bourse.

Sale-by-Tender: This is where the government invites investors to bid for the
purchase of its stake. This method of disposing government shareholding has in
some instances sparked controversy. In 1996 the government undertook to sell
51% of its shares in Hwange Thermal Power Station to a Malaysian company
62
YTL in a deal which many have been cited as evidence of abuse of the open
tender system at the expense of the highest bidders.
63
CHAPTER 7
TAXATION
7.1 Defining Incidence of a Tax
7.1.1 Statutory Incidence of a Tax
Statutory incidence indicates who is legally responsible for the tax and legal
responsibility implies the obligation to collect and remit the tax to government. If the
government imposes a sales tax of 15% to be collected at the retail level, then the
statutory incidence is on the retailer whose responsibility it is to collect and remit the tax
on behalf of the government. Statutory incidence lies on the retailer in the above case.
7.1.2 Economic Incidence of a Tax
This is the change in the distribution of private real income brought about by the tax. In
other words economic incidence is the economic burden created by the tax on economic
agents. For instance if a unit tax which is a commodity tax of $10 is introduced on a
commodity that is originally priced at $80, and the elasticities of demand and supply are
such that the seller is able to transfer the full amount of the tax to the consumer in the
form of increased price, then the after-tax price would be $90. Clearly the statutory
incidence will be on the seller, yet the economic incidence is undoubtedly on the buyer.
Statutory incidence tells us essentially nothing about who is bearing the tax burden.
7.1.2 Tax Shifting
This refers to the extent to which statutory and economic incidence diverge.
Tax Shifting = Statutory incidence on seller – Economic Incidence on seller
In the example discussed earlier, the tax shifted is $10, implying that the seller has wholly
shifted the tax to the buyer.
64
7.2 Ricardian Equivalence Hypothesis
The Ricardian Equivalence Hypothesis was popularized by Barro (1974). The hypothesis
says, under the following set of assumption:

Intergenerational altruism,

Perfect capital markets, and

Lump sum taxation,
the government bonds are not net wealth or net worth. Bonds provide scope for
government to increase expenditure in the current period but they impose an obligation
on the government to raise more revenue in future inorder to honour maturing bonds.
Implications of the Hypothesis:

Every bond-financed deficit must be met by some future tax increase and the
living economic agents are able to foresee such tax increases and these agents
would care enough to adjust their present consumption accordingly.

A reduction in taxes is likely to create deficits in the current period and the
economic agents would expect future taxes to be high as government attempts to
eliminate the past deficits and this is the basis if the debt-neutrality argument. The
debt-neutrality argument claims that interest rates do not respond directly to
government debt or in response to changes in government expenditure.
7.3 The Canons of a Good Tax System
The following are the key features of a desirable tax regime:
1. Administrative simplicity: It is important that the costs of tax collection be as
low as possible. The US Internal Revenue Service (IRS) in 1990 estimated that it
was spending about US$0.51 to collect each US$100 in taxes, giving a ratio of
administrative costs to revenue of about 0.5%. Economic agents also incur costs
in the form of resources spent on tax preparation and professional advice which
are referred to as compliance costs. According to Shemrod and Sorum(1983) such
costs were estimated in 1984 to be 29 hours for tax preparation and $53 for
65
professional advice applicable on an average US household. If you combine the
hours and the $53, then the total resource cost involving tax compliance becomes
$364, applying a value of $10.70 for each hour). If the above cost per household
is multiplied by 97 million tax-paying units in the US, then the total resource cost
becomes US$35.3 billion, translating to about 9% of total income tax revenue.
Even the tax systems that appear efficient and fair may be undesirable because
they are excessively complicated and expensive to administer. The difficulties
involved in valuing certain economic activities create huge administrative costs
that make it infeasible to apply tax on such activities. If the government
proceeded to impose taxes on such activities, notwithstanding the administrative
difficulties and complexities, then most of the revenue would go towards the
administrative cost, thus defeating the revenue objective. This probably explains
why the informal sector has largely remained untaxed in Zimbabwe. The activities
are not well recorded, making it both difficult and expensive to trace the
transactions. The costs that would be incurred if government were to enforce the
taxation of the informal sector, far outweighs the intended benefits.
2. Efficiency: This implies the excess burden should be minimized.
3. Buoyancy: The buoyancy of a tax system is the responsiveness of tax revenue to
changes in income (Y). High buoyancy is a desirable attribute of a tax system
because apart from augmenting the revenue productivity, it also enhances the
overall fiscal operations in mitigating the undesirable cyclical movements thereby
acting as an automatic fiscal stabilizer. The global buoyancy of a tax system is
measured by the proportional change in the tax revenue with respect to the
proportional change in national income and is expressed as:
BT ,Y 
T Y
. ---------------------(1)
Y T
Where: T is the tax revenue
Y is the national income or GDP
In an economy with n taxes, then we can summarize:
66
T  T1  T2  ..........  Tn
The global buoyancy of a tax system can then be expressed as:
T 
T 
T 
BT ,Y   1 BT ,Y    2 BT ,Y   .........   n BT ,Y  ------------(2)
T 
T 
T 
Where: BTi ,Y is the buoyancy of tax i, with i=1,2,……,n
The individual buoyancy for each tax can be calculated as:
BTi ,Y 
Ti Y
. -----------------------------------------------------(3)
Y Ti
Substituting (3) into (2) will give:
 T  T Y
 T  T Y
BT ,Y   1  1 .  ............   n  n . ---------------------(4)
 T  Y T1
 T  Y Tn
In empirical research buoyancy is obtained using the following linear equation:
T    Y   ------------------------------------------------------(5)
Where: α is a constant
β is the marginal rate of taxation
T

Y
Thus BT ,Y 
The term
T Y
Y 
.     -------------------------------------------------(6)
Y T
T 
Y
is obtained by averaging Y and T over the sample period.
T
An alternative way of estimating the buoyancy is to express equation (3) in exponential
terms such that it becomes:
T  Y   -----------------------------------------------------------(7)
Then transforming expression (7) into the double-logarithmic form gives:
log Tt  log ˆ  ˆ log Yt   t ---------------------------------------(8)
In this case ˆ becomes the ordinary least squares estimate of buoyancy. The empirical
results have shown that personal income tax and corporate tax are generally buoyant
(Osoro, 1993; Munti, 2003; Sulimani, 2005).
67
4. Equity: This is one of the most complicated canons to evaluate because it takes several
dimensions:

Equal Proportional sacrifice: This suggests that a tax should cause each individual
to give up the same percentage of his total utility. For instance if tax-payer A has
higher income that allows him to attain 200 units in utility, while tax-payer B has
lower income that allows him only 100 units of utility, then the higher income
tax-payer should suffer 20 units of disutility as a result of the tax if tax-payer B
bears 10 units of disutility and this example each tax-payer is contributing 10% of
his earnings. This approach seems to suggest that equity can best be achieved
through the use of proportional taxation.

Equal Marginal sacrifice: This approach suggests that each tax-payer should bear
an equal marginal decrease in the utility of his income from the payment of a tax.
For instance, if the marginal tax dollar paid by A causes him 5 units of disutility,
whilst that paid by B renders him 15 units of disutility, then A should pay more
taxes and B should pay less until their marginal disutilities are equal. This
approach therefore advocates for a highly progressive tax structure.
Progressivity of a Tax
This is a measure of how much the tax obligations of a high income individual differ
from those of a low income individual. There are two commonly used measures of
progressivity:
a) The V1 Measure:
T1 T0

I1 I 0
V1 
I1  I 0
Where: T0 and T1 are the tax liabilities at income levels I0 and I1 respectively,
with I0 < I1
A tax system with a higher V1 is said to be more progressive.
b) The V2 Measure: Is the elasticity of tax revenue with respect to income.
68
 T1  T0 


T0 

V2 
 I1  I 0 


 I0 
where: all variables are as before
A tax system is more progressive if the elasticity of tax revenue with respect to
income is higher.
Benefit Principle
This approach directly relates the revenue and expenditure sides of the budget. The
approach assumes that individuals enter into a quid pro quo8 arrangement with the
government. This implies that the individual voluntarily exchanges purchasing power in
the form of taxes for the acquisition of government economic goods, otherwise referred
to as public goods. The individual consumer pays directly for those public goods from
which they derive utility. Equity in this context is not based on the level of sacrifice but
instead on the dual facts that:

the exchange of the purchasing power for the public good is voluntary as would
be the case in the market sector.

the payments are made in accordance with the benefits that are received. The
benefits in turn may be priced, either in terms of the governmental cost of
providing the service, or in accordance with the value of the service to the
purchaser, or a combination of these considerations.
7.4 Optimal Taxation
The theory of optimal taxation attempts to answer questions such as:

How progressive should an income tax scheme be?

How should tax rates vary across commodities?

Should the government use income tax or commodity tax?, and

What is the equivalence relationship between the two taxes?
Latin term meaning ‘something given in exchange for something else’, or ‘a willing buyer, willing seller
transaction’.
8
69
Assumptions of the Optimal Taxation Analysis

We assume that the objective of the government is to minimize the excess burden
generated by the tax system.

The government intends to raise a set revenue target represented by R.
7.5 Optimal Taxation and the Revenue-Productivity of a Tax
System
Tax revenue (R) is basically dependent on two factors:
1. The number of tax-paying units or the tax base (B)
2. The tax rate (t)
The relationship of tax revenue with the variables stated above can be summarized in the
following function:
R  f B; t 
The tax base is in turn dependent on the tax rate as shown in the relationship below:
B  Bt 
If for instance we increase the tax rate in the economy, we should expect a shrink in the
tax base due to tax evasion and the resultant disincentive to work effort. The Laffer curve
is probably the most ideal tool for illustrating the relationship.
7.5.1 The Laffer Curve and Revenue Productivity of Tax
The Laffer curve is named after Professor Arthur Laffer9 who argued that a tax rate (t) of
0% would lead to a revenue (R) level of zero, calculated as:
R = tB = 0;
since t = 0%
He suggested that, as taxes increased from fairly low levels, tax revenue received by the
government would also increase. However, as tax rates rose, there would come a point
9
Arthur Laffer was an advisor to US President Ronald Reagan in the early 1980s. A former film actor,
Reagan is popular for having initiated a series of tax cuts, forming a set of policies that became known as
Reaganomics.
70
where people would not regard it as worth working so hard. This lack of incentives would
lead to a fall in income and therefore a fall in tax revenue. The logical end-point is with
tax rates at 100% where no one would bother to work and so tax revenue would become
zero. The tax base (B) shrinks to zero such that:
R = tB
With t = 100% and B = 0
Laffer argued that, under certain circumstances, government could achieve higher
revenue levels by lowering the tax rate. His conceptualization is based on the fact that
there are always two tax rates that yield the same amount of revenue, one at a lower level
of economic activity and the other at a higher level, the only exception being at the
optimal tax rate. This statement is consistent with Rolle’s Theorem10.
The Laffer curve shows the relationship between tax rates and tax revenue collected by
governments. The graph below shows the Laffer Curve.
T* represents the optimum tax rate where the maximum amount of tax revenue can be
collected. Laffer and other right-wing economists used the curve to argue that taxes were
currently too high and should therefore be reduced to encourage incentives and harder
10
Rolle’s Theorem says; “If
a curve crosses an abscissa or axis twice, then there must be a
point between the crossings where the tangent to the curve is parallel to the axis.”
71
work (a supply-side policy).
The curve suggests that, as taxes increase from low levels, tax revenue collected by the
government also increases. It also shows that tax rates increasing after a certain point (T*)
would cause people not to work as hard or not at all, thereby reducing tax revenue.
Eventually, if tax rates reached 100% (the far right of the curve), then all people would
choose not to work because everything they earned would go to the government.
Governments would like to be at point T*, because it is the point at which they collect
maximum amount of tax revenue while people continue to work hard.
The basic idea behind the relationship between tax rates and tax revenues is that changes
in tax rates have two effects on revenues: the arithmetic effect and the economic effect.
The arithmetic effect is simply that if tax rates are lowered, tax revenues (per dollar of tax
base) will be lowered by the amount of the decrease in the rate. The reverse is true for an
increase in tax rates. The economic effect, however, recognizes the positive impact that
lower tax rates have on work, output, and employment--and thereby the tax base--by
providing incentives to increase these activities. Raising tax rates has the opposite
economic effect by penalizing participation in the taxed activities. The arithmetic effect
always works in the opposite direction from the economic effect. Therefore, when the
economic and the arithmetic effects of tax-rate changes are combined, the consequences
of the change in tax rates on total tax revenues are no longer quite so obvious.
Figure 1 is a graphic illustration of the concept of the Laffer Curve--not the exact levels
of taxation corresponding to specific levels of revenues. At a tax rate of 0 percent, the
government would collect no tax revenues, no matter how large the tax base. Likewise, at
a tax rate of 100 percent, the government would also collect no tax revenues because no
one would willingly work for an after-tax wage of zero (i.e., there would be no tax base).
Between these two extremes there are two tax rates that will collect the same amount of
revenue: a high tax rate on a small tax base and a low tax rate on a large tax base.
72
The Laffer Curve itself does not say whether a tax cut will raise or lower revenues.
Revenue responses to a tax rate change will depend upon the tax system in place, the time
period being considered, the ease of movement into underground activities, the level of
tax rates already in place, the prevalence of legal and accounting-driven tax loopholes,
and the proclivities of the productive factors11. If the existing tax rate is too high--in the
"prohibitive range" shown above--then a tax-rate cut would result in increased tax
revenues. The economic effect of the tax cut would outweigh the arithmetic effect of the
tax cut.
Moving from total tax revenues to budgets, there is one expenditure effect in addition to
the two effects that tax-rate changes have on revenues. Because tax cuts create an
incentive to increase output, employment, and production, they also help balance the
11 Laffer A. B. (2004) “The Laffer Curve: Past, Present, and Future”, Supply-side Investment Research, 6 January 2004.
73
budget by reducing means-tested government expenditures. A faster-growing economy
means lower unemployment and higher incomes, resulting in reduced unemployment
benefits and other social welfare programs.
7.6 Optimal Income Taxation: Atkinson and Feldstein Model
The model considers a social welfare function of the form:
1

v
W    U iv  for v ≤ 1
 alli 
Where: W is social welfare
Ui is the utility of the ith individual
v is the value that different individuals attach to an extra unit of utility. It can be
considered to be an inequality aversion parameter.
If v = 1, society’s welfare is a simple sum of all individuals’ utility.
When v < 1 as is normally the case, it can be shown that a given increment to the utility
of a low utility individual adds more to the social welfare than if awarded to a high utility
individual.
A numeric illustration
Suppose that we have two individuals 1 and 2, who currently enjoy utilities:
U1 = 2 and U2 = 4 respectively. If v = 0.5, the social welfare becomes:

W  20.5  40.5

1
0.5
 11.65
If 2 utils are added to the lower utility individual, then the social welfare becomes:

W  40.5  40.5

1
0.5
 16
If 2 utils are added to the higher utility individual, then the social welfare becomes:

W  20.5  60.5

1
0.5
 14.93
The conclusion then in terms the tax policy is that a tax system should be in such a way
as to grant incentives to the lower income, and therefore the lower utility groups. This
74
presupposes a highly progressive tax system. Such a system would grant tax concessions
or exemptions to the poor whilst at the same time penalizing the wealthy.
7.7 Optimal Commodity Taxation: The Ramsey Rule
Most literature on optimal commodity taxation is based on the assumption that
government has a given level of revenue to be raised which must be financed solely by
commodity taxes. The key task is then to set the tax levels for the various commodities in
such a way that the cost of raising the required revenue to society is minimised.
Assumptions of the Ramsey Analysis

There is a single household in the economy, so that there are no distributional or
equity considerations in the setting of tax rates and this assumption allows the tax
system to be evaluated only in terms of efficiency or minimum distortion

There are n commodities and a single form of labour which is the only input in
production.

All markets are perfectly competitive
With the wage rate (W), the competitive assumption ensures that the pretax price of
commodity i is determined as:
Pi  CiW for i=1,2,……..,n----------------------(1)
Where: Pi is the pretax price of commodity i
Ci is the coefficient describing the labour input required to produce on unit of
commodity i
W is the wage rate
The post-tax price (qi) of commodity i is equal to:
qi  Pi  ti ----------------------------------------(2)
Where: ti is the amount of tax on commodity i, which is applied as a specific tax.
75
If X1 is the amount of consumption for good i, then the revenue requirement of the
government can be stated as:
n
R   ti X i --------------------------------------(3)
i 1
Where: R is the revenue target set by the government.
The preferences of the single household are represented by an indirect utility function
which takes the form:
U  V (q1; q2 ;...........; qn ;W ; I ) ----------------(4)
Where: I is the lump-sum income
The total income (Y) is the sum of lump-sum income and wage income.
The optimal commodity taxation problem can then be summarized as:
Maxt1 ,t 2 ,...., t nV q1 , q2 ,........,W , I 
n
Subject to: R   ti X i --------------------------(5)
i 1
Forming Lagrangean problem from the above gives:
n

L  V (q1 , q2 ,..........., qn , W , I )    ti X i  R  --------- (6)
 i 1

The first-order conditions for the choice of tax rate on commodity i stated as:
n

L V
X 

   X k   ti i  =0 ---------------------------(7)
tk tk
tk 
i 1

Where:
V V

-----------------------------------------------------(8)
qk tk
X i X i

------------------------------------------------------(9)
qk tk
Expressions (8) and (9) hold due to the use of a specific tax.
From (7) it follows that:
n

V
X 
   X k   ti i  ------------------------------------(10)
tk
qk 
i 1

A similar condition to equation (10) must hold for all n commodities.
From Roy’s identity, it follows that:
76
V
V

X k  X k ---------------------------------------(11)
qk
I
With α being the marginal utility of income.
Substituting (11) into (10) gives:

n

i 1
X k    X k   ti
X i 
 ------------------------------------------(12)
qk 
If you rearrange equation (12), you get:
 n X i 
  
 ti
  
 X k -----------------------------------------(13)
  
 i 1 qk 
By Slutsky equation, we obtain:
X i
X k
 sik  X k
-------------------------------------------------(14)
qk
I
Where: sik 
X k
qi

u
X i
qk
u
sik  ski is the compensated cross-price term
u means holding utility constant
Substituting (14) into (13) will give:

n
 t s
i 1
i
ik
 Xk
X i 
  
 

 X k ---------------------------------(15)
I 
  
Rearranging (15) produces:
n
t s
i 1
i ik
n
X i
 
  1   X k   ti
X k --------------------------------(16)
I
 
i 1
Further rearranging the above expression gives:
  n X i 
t
s


X
  ti

i ik
k 1 
 ------------------------------------(17)
i 1
  i 1 I 
n
  n X i 
Let   1    ti

  i 1 I 
Then expression (17) reduces to:
n
t s
i 1
i ik
 X k ---------------------------------------------------------(18)
77
Diving (18) by Xk gives:
n
t s
i 1
i ik
Xk
  -----------------------------------------------------------(19)
With  being a constant, by virtue of it not containing any k subscript within it.
Equation (19) is the popular Ramsey rule.
The numerator in expression (19) approximates the total change in the compensated
demand for Xk following an introduction of a set of taxes, that is [t1,t2,….,tn]
Condition (19) says the reduction in the compensated demand for each good should be
proportionately the same relative to the pre-tax position. The single household economy
proposed in the Ramsey framework is, however, an unrealistic description of a typical
economy. Obviously it leads to an outcome that would be unacceptable on the equity
criteria. The rule remains relevant in providing a framework that can be generalized to
more relevant settings. The restrictive assumptions underlying the derivations of the rule
cannot be understated as they significantly weaken its generality.
The Inverse Elasticity Rule
Suppose that  rr is the elasticity of demand for commodity r, and d is a constant; then
the tax rate on commodity r can be determined as:
tr 
d
 rr
---------------------------------------------------------------------------(20)
The inverse elasticity rule, as stated above, says those goods whose demand is least
unresponsive to price changes will broadly be bearing higher taxes to minimize
distortions. That is, the higher the elasticity of demand the lower should be the tax rate.
This implies that necessities such as food items, housing will broadly be heavily taxed
because they are inelastic. Luxury goods will pay less tax because of their high elasticity
of demand. This rule does not consider the equity or social welfare issues since it focuses
on only one household. The Ramsey rule forms the basis of imposing higher taxes on
habit-forming commodities such as alcohol and cigarettes. Mirrlees (1971) treats the lefthand side of equation (19) as an index of discouragement, that is the extent to which a tax
on commodity k discourages the consumption of that commodity. He thus interprets the
78
rule as indicating that the discouragement index should be proportionately the same for
all goods.
7.8 Equivalence of Income Tax and Commodity Tax
The thrust of this topic is to consider the possibility of substitutability between income
taxation and commodity taxation, that is whether a government can retain the same
revenue level after replacing income tax with commodity tax or vice versa.
Assumptions of the analysis

There in only one household/consumer in the economy.

Government uses either income tax or commodity tax at any point in time and not
both.

The decisions of the consumer, who are also the income-earner, are intertemporal.
The intertemporal utility function of the consumer can be stated as:
U  U C1;C2 
Where: C1 is the consumption in period 1
C2 is the consumption in period 2
Then the objective of the consumer is to max utility over the whole period (period 1 and
period 2) which can be stated as:
MaxUC1;C2 
Subject to: C1 
C2
Y
 Y1  2
1 r
1 r
Where: Y1 is the income earned in period 1
Y2 is the income earned in period 2
r is the discount rate.
It can be proved that a commodity tax at rate tc can be replaced by an income tax at rate t
which yields exactly the same revenue.
Option A: Commodity tax
If a commodity tax is applied, then only the consumption side is affected such that the
after-tax outcome will be:
79
1  tc C1  1  tc C2  Y1 
1 r
Y2
------------------------(1)
1 r
Option B: Income tax
C1 
1  t Y2 --------------------------(2)
C2
 1  t Y1 
1 r
1 r
Dividing equation (1) by 1  t c  gives:
C1 
C2
Y
Y2
 1 
----------------------(3)
1  r 1  tc 1  r 1  tc 
Equating the right-hand sides of (2) and (3) we get:
1  t Y1  1  t Y2 
1 r
Factoring out Y1 
Y1
Y2

-------------(4)
1  tc 1  r 1  tc 
Y2
from expression (4) results in:
1 r
Y 
Y  1 


 ---------------(5)
 Y1  2 1  t    Y1  2 
1 r 
1  r  1  tc 


If follows from (5) that:
1  t  
1
--------------------------------------------(6)
1  tc
Making t the subject of the formula we get:
t
tc
-------------------------------------------------(7)
1  tc
Equation (7) proves that a commodity tax at rate tc will achieve exactly the same
revenues as an income tax at rate t. Therefore commodity tax and income tax are
equivalent provided the rates relating to the two are set at levels that comply with
equation (7).
Example:
A commodity tax at rate of 20% can be replaced by an equivalent income tax calculated
as:
t
tc
0.2

 16%
1  tc 1  0.2
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7.9 Incidence of Taxes:
7.9.1 Tax incidence in Partial Equilibrium
Where the tax is shared between the producers and the consumers.
Assume a unit tax is levied on the producer ($t) on each unit.
Pc  Pf  t
Incidence for the consumer is a price increase from P0 to Pc. Incidence for the producer
falls from P0 to Pf.
Let q be the consumer price and P be the producer price: q  P  t
The demand and supply functions can therefore be represented as follows:
D(q) and D(P)
In equilibrium: D(q)  D(P)
Incidence means how much consumer price will be affected by the tax and how much the
producer price will be affected by the tax.
Q(q )  Q(q  t )
What is the effect of the tax (t) on the consumer price? Find the derivative of
D(q)  D(P) with respect to t.
Q q Q P
We applied the chain rule here as follows:



q t P t
81
P  q  t 


 P  q  1


t


Q q Q  q 


  1
q t P  t

Divide both sides by
P.q
Q
Q Pq Q Q Pq  q 




  1
q Q t 

P 
Q

 t





  = price elasticity of demand.
 = price elasticity of supply.
Moving the right hand side to the left hand side, we get:
q
(    P    q )   q
t
q
q

t   P  q
Conclusions

If  = 0 we have a perfectly inelastic supply curve. As shown the burden falls
fully on the producer,
q
 0.
t
82

If    , the producer again pays all the tax.
In both cases above the market price is not affected
83

If    , q

If   0 
t
 1 . Here the consumer pays the full tax.
q
 1 . Here the full tax burden also falls on the consumer.
t
This analysis ignores economy wide repercussions. We know that
84
q Pt
q P

1
t
t
P q

1
t
t
This shows the effect of tax on the producer price.
7.9.2 General Equilibrium Analysis and the Harberger Model
It may be inadequate to analyse one particular market when the sector is large enough to
influence other sector in the economy. A tax on any given sector has direct effects on the
particular sector as well as roundabout effects on the other sectors. General Equilibrium
Analysis (GEA) then becomes important as it takes into account the ways in which
various markets are interrelated. GEA is often computer-aided, in which case it becomes
known as Computable General Equilibrium Analysis (CGEA). One of the widely used
GEA models in the area of taxation is the Harberger Model which is discussed below.
7.9.2.1 Harberger’s Two Sector Model
Assumptions

The economy has two sectors. Sector 1 is the corporate sector producing good X.
Sector two is the non-corporate sector producing good Y.

There are two factors of production both in fixed supply (L0, K0).

The prices for the goods being produced and the factors being used in production
are: Px, Py w, and r.

There is full utilization of the factors of production.

There is constant returns to scale in both sectors
85
We need both the demand side and the supply side price formation. These are going to be
discussed in turn in the next sections.
Supply Side
This is described by the cost function (this is the technology).
C x (w, r)  average cost in sector X which depends on factor prices.
C y ( w , r )  average cost of sector Y which depends on factor prices.
We can now come up with the total cost for each of these two sectors.
TC x  C x (w, r)  X  total cost in sector X.
TC y  C y ( w , r )  Y  total cost in sector Y.
We are going to denote the amount of labour used to produce one unit of X by C LX. In the
same way the amount of labour used to produce one unit of Y is CLY. Using this
information we can now come up with total demand for labour from both sectors.
C LX  X  C LY  Y  L 0 …………………………………[1]
This equation is telling us about the amount of labour used in sector X and the amount of
labour used in sector Y which give total demand for labour for both sectors. In the same
way we can come up with total demand for capital for both sectors.
C KX  X  C KY  Y  K 0 ………………………………..[2]
Demand Side
CLX, CLY, CKX, and CKY are all functions of factor prices. They are not constant. If the
factor prices change then these coefficients will change. So the demand functions that we
have are Marshallian demand functions.
X  X(Px , Py , M ) where M=income…………………….[3]
86
Y  Y(Px , Py , M ) ……………………………………….[4]
M  wL 0  rK 0
If we replace this income by the minimum expenditure given Px, Py,  required to attain a
certain level of utility, the compensated demand is a function of prices and utility.
X(Px , Py , )  X[Px , Py , e(Px , Py , )]
Price Formation
Given our assumption of perfect competition and the profit maximizing behaviour, price
is equal to marginal cost which in turn is equal to the average cost due our assumption of
constant returns to scale. The prices are given by the following functions:
Px  Cx (w, r) …………………………………………..[5]
Py  C y ( w , r ) …………………………………………..[6]
This is the whole Harbeger’s model with 6 equations and 6 variables. It is not possible to
solve this model because all the six equations are dependent on each other. The six
variables in this model are Px, Py, w, r, X, and Y.
From Walras Law one equation is therefore redundant. Total expenditure is equal to total
cost.
Px X  Py Y  C x X  C y Y
87
If [5] holds, Px X  C x X therefore, Px  C x . It therefore follows that Py  C y . This
means that equation 6 is redundant. So we will not be able to solve for the level of prices
and quantities in this model, but we can solve for the relative prices of goods, factors and
quantities.
Conclusions
a) From the demand side we can derive




 y X x Y  q D (P x  P y )

Where X 

X
Y
and Y 
X
Y
 y and  x are income elasticities of demand for good Y and good X respectively.
q D aggregate elasticity of substitution in demand.
If  y   x  1 we are assuming that the demand functions are homothetic. This
implies that when income changes the proportion of good X and good Y consumed
does not change. The diagram below also assumes that q D  0 .
88
The demand function below shows the relationship between the relative prices and
relative quantities.
X
Y


Px  P y 




Px

Py


X Y  q D (P x  P y )
X Y  0 
X

Y
PX
PY
b) We can also derive the relationship between factor prices and commodity prices.
From competitive pricing we have the following:
C x  Px and C y  Py




P x  P y   * ( w  r ) where
*  a measure of factor intensity.
 Lx ,  Ly  the share of labour in the production of goods X and Y respectively.
 Kx ,  Ky  the share of capital in the production of goods X and Y respectively.
*   Lx   Ly   Ky   Kx
 Lx 
w  C Lx
 the share of labour in the total value added (value of output).
Px
 Kx 
r  C Kx
 share of capital in the total value added.
Px
89
If *  0   Lx   Ly  sector X is labour intensive and vice versa. If we assume
that the corporate sector is labour intensive we will have the following
diagrammatic representation.
w
r
True for *  0 , otherwise
the slope is negative
Px
Py
0
The following two expressions are also true:


w r  0 
c)

w

r

Px  Py  0 
Px

Py
From the factor market equilibrium we derive the third equation as follows
0



 * ( X  Y )  ( w  r )(a x q x  a y q y )




q x , q y  are elasticities of factor substitution in the sectors.
*   Lx   Kx where  Lx 
Lx
K
,and  Kx  x
L0
K0
are the amount of labour used
in sector X divided by total labour in the economy and the amount of capital used
in sector X divided by total capital in the economy.
If  Lx  0.6 we can not safely say this is labour intensive because  Kx may be
0.8. In this case sector X will be capital intensive. If *  0 then the corporate
90
sector (X) is labour intensive. In the absence of distortions these two measures of
factor intensity [(b) and (c)] are the same.


Assume that the corporate sector is labour intensive [ *  0 and X  Y  0 ]
X
Y
*  0
0
w
r
d) The equilibrium in this model can be determined diagrammatically but it is not our
intention to show that in this book. However the crucial parameters in determining
equilibrium in this model and the effect of policy on that equilibrium are as follows:

income elasticities ( x ,  y ) .

elasticity of substitution in demand (q D ) .

factor intensity in the two sectors measured in value terms ( ij ) and also in
physical terms ( ij ) .

elasticity of substitution in both sectors (q x , q y ) .
Effects of a corporate tax
Assume a corporate tax raises the cost of capital in the corporate sector.
91
What happens with the relative prices
w
? If there is an increase in the price of only one
r
factor there will be the substitution effect. In the corporate sector demand for capital falls
and the demand for labour rises. In the non-corporate sector there is no substitution
effect.
Output effect
The marginal cost in the corporate sector is given by C x (w, r) . If the cost of capital
increases  MC x  Px 
Px
 this leads to a fall in the demand for corporate
Py
output  output will fall. The demand for capital will rise and that of labour will fall due
to substitution effect. In the corporate sector demand for capital will fall unambiguously
due to both effects.
In the non-corporate sector assuming that q D  0,
Px
 and demand for the nonPy
corporate sector’s output increases and demand for both capital and labour will go up. If
the capital labour ratio is constant in both sectors net capital will equal zero in the whole
model. Whether there is a net increase or decrease in the demand for capital depends on
the relative factor intensities. If we assume that the K/L ratio in the corporate sector is
two(2) while the same ratio in the non-corporate sector is one(1), 10K and 5L is ejected
from the corporate sector. Therefore 5K and 5L can be absorbed by the non-corporate
sector. This leaves 5K units of capital unabsorbed. This means that there is excess capital.
So the rental cost of capital (r) will fall and the wage rate (w) will rise. So the r/w ratio
will fall. Both factors may bear the burden of taxation but capital bears the greater
proportion of the burden. The authenticity of this model is subject to empirical testing.
Modifications of the simple general equilibrium model
1. The range of taxes can be extended to include commodity taxes in each sector and
commodity taxes in both goods.
2. Allow for the existence of other distortionary taxes in the economy.
3. We can consider a non-infinitesmal corporate tax.
92
4. Factors may not be instantaneously mobile between sectors. Returns to factors
may differ in the two sectors.
5. Differences in tastes between different consumers can be allowed for and this can
result in different demand functions.
6. Market imperfections can be incorporated into the model.
What we have been doing up to now is a static incidence analysis, for example, if we
introduce tax what happens to the equilibrium? The next section introduces dynamic
equilibrium.
Dynamic Equilibrium
In the static analysis we have seen that capital shoulders the greater burden of the tax. We
can also look at the effect of tax on capital formation. The argument here is that capital
taxation lowers the return to capital, savings will be lowered, there will be lower capital
formation, there will be lower steady state capital labour ratio, there will also be lower
productivity and hence lower wages.
Alternatively, if Labour productivity falls  wages fall  capital stock falls  marginal
productivity of capital increases  the return to capital rises.
The marginal productivity of capital will be higher if the return to capital increases. The
dynamic incidence is to lower the wage capital rental ratio. The crucial assumption
implied by this analysis is that capital formation is related to savings or that savings are
dependent on capital rental. But how long a time is involved in this analysis? This is an
empirical question. It can be 10-15 years.
93
7.10 Threats to Government Revenue Generation in Zimbabwe
over Recent Years
The generation and collection of tax revenue in Zimbabwe has faced several challenges in
the last few years. Some of these threats and challenges include:

The growing informal sector activities that are not easy to track and tax.

The replacement of large-scale commercial farming activities which were subject
to tax with an indigenous-dominated subsistence farming sector which does not
contribute to tax revenue.

The widespread unemployment that has significantly reduced the income tax base.

The decline in international aid from multilateral institutions and other donor
agencies. The donor activities complemented government initiatives and reduced
its burden on the provision of social services. The swift retreat by the nongovernmental organisations has left a vacuum on service provision, thus raising
the revenue requirements of the government.

The poor performance of manufacturing firms which has further threatened the
corporate tax base. The poor macroeconomic environment accompanied by the
economic sanctions imposed by European Union and the Commonwealth since
year 2000 have combined to threaten the viability of existing firms, with many
company closures having been recorded up to 2006.

The weak administrative framework that has made it difficult to assess the effects
or revenue implications of the transition to value-added tax.

The hyperinflation that has been experienced in the last few years has
significantly reduced the purchasing power of government revenue due to the time
lag in tax collection.

The proposed Common Market for Eastern and Southern Africa (COMESA) Free
Trade Area may also further reduce the revenue through the scraping of import
duties.
94
CHAPTER 8
TAX EVASION
8.0 Defining of Tax Evasion
Tax evasion is defined as the intentional failure to declare taxable income-generating or
economic activities. Tax evasion should be distinguished from tax avoidance, where the
later is the reorganization of economic activities, possibly at some cost inorder to lower
the tax payment. Tax avoidance would involve altering your economic behaviour in such
a way as to limit your tax liability. If, for instance, you realised that tobacco is subject to
some ‘tobacco levy’ and decided to grow less of it in favour of some other crops, then
that can be considered as tax avoidance. The Zimbabwe Revenue Authority (ZIMRA)
cannot, within the scope of the law, sue you for having diverted your effort from one
activity to the other. Tax avoidance is perfectly legal, but tax evasion is not. In the case of
Commissioner vs. Newman, Judge Learned Hand clearly outlines the legality of tax
avoidance:
“…there is nothing sinister in so arranging one’s affairs so as to keep taxes as
low as possible. Everybody does so, rich or poor; and all do right, for nobody
owes any public duty to pay more than the law demands. To demand more in the
name of morals is mere cant.” (Commission vs. Newman, 1947).
Clearly tax avoidance may be regarded as immoral in some circles. Unfortunately
perception cannot form the basis of a valid lawsuit! Tax evasion, being illegal, it is not
possible to obtain official statistics on it. The measurement of tax evasion or unreported
economic activities is fraught with difficulties and uncertainty. Rey (1965), using Italian
data, estimated that evasion was equivalent to about 52% of actual revenue yield, which
is quite significant. The tax authorities should design policies that should minimize tax
evasion at the least cost.
95
8.1 Analysis of Tax Evasion
The decision to evade taxation fits naturally in the framework of choice under risk. Since
not all tax evaders are caught by the tax authorities, risk arises since an individual who
evades stands a chance of succeeding with evasion and hence increase his wealth, or a
chance of being caught and punished. The individual can thus be viewed as choosing the
extent of tax evasion subject to the probability of being caught and punished. The tax
evader is assumed to be a rational economic agent contemplating an economic crime and
making a decision under uncertainty. The agent is also assumed to have full knowledge of
the probabilities of detection, conviction and the levels of punishment that accompanies
such an offence. The rational economic agent is expected to choose the level of
compliance or evasion that will yield the greatest expected utility. The decision of
whether or not to evade is then guided by the following expression:
EV  1  px  pxF
Where: EV is the expected value or expected benefit of evasion
p is the probability of being audited or detected
x is the amount of undeclared taxes
F is the penalty rate (on undeclared taxes) plus one.
Example:
Suppose a Zimbabwean taxpayer has an income of $20 000 and is planning to underpay
$500 in taxes. The probability that the Zimbabwe Revenue Authority (ZIMRA) will audit
an intelligent/rational evader does not exceed 5%. The maximum penalty applicable for
civil fraud and negligence is 50% of the tax owed. The potential act of tax evasion is
viewed as a gamble with (1-p)% chance of winning $x and a p% chance of losing $xF.
The expected benefit can then be calculated as:
EV  1  0.05500  0.055001.5  $437.50
The positive expected value implies that the evasion game is worth playing. That is, the
individual is tempted to evade since it is a worthy bet.
96
Graphical analysis of Tax Evasion
p is the probability of detection.
R* is the optimal tax evasion. The marginal cost of evasion (MC) increases when the
marginal penalty and/or the probability of detection are increased. The marginal benefit
(MB) of evasion only increases when the marginal tax rate (t) has been increased.
Government has the following options to reduce or eliminate evasion:

To reduce the marginal tax rate so that the marginal benefit shifts downwards.

Increases the probability of an audit (p) so that marginal cost is evasion increases.
This can be achieved in practice by increasing the frequency of tax audits.

Increasing the marginal penalty by raising the fines on evaders.
The marginal cost should be everywhere above the marginal benefit as shown below:
97
The optimal level of tax evasion in the above case is zero since all levels of evasion are
characterised by higher marginal cost compared to marginal benefit. All policies meant to
contain tax evasion should thus acknowledge that apart from being a deliberate act to
contravene law, the act of evasion is motivated by economic rationality with the evader
having to evaluate the potential costs and benefits of their actions.
98
CHAPTER 9
APPRAISAL OF PUBLIC SECTOR PROJECTS
9.0 Introduction
One of the most important aspects of Public Sector Economics is the evaluation of public
projects. This is done inorder to determine whether or not it is worthy pursuing any
particular project. This can best be achieved by producing estimates of benefits and costs
associated with the projects that have been identified. Most capital projects typically
generate benefits over an extended period in the future. Some projects also involve costs
that extend into the future. This raises the need to devise an appropriate discount rate that
will facilitate intertemporal analysis, enabling the net benefits to be expressed in
monetary terms, taking the form of cost-benefit flows. Net benefit implies that the
benefits of any capital project are subtracted from the costs associated with that project in
a given time period. In the next few sections we are going to discuss the alternative
measures that are used in evaluating and ranking capital projects. We shall also discuss
why the social discount rate diverges from the private discount rate.
9.1 Social Discount Rate: Why should it diverge from the Private
Discount Rate?
The aggregation of costs and benefits over time demands that there be a discounting
factor to cater for the time-value of money and other factors that make the current
monetary values different from the future monetary values. In other words the costs
incurred at the level of $x in the current period cannot be regarded as equivalent to costs
of $x in some future period. The same would apply for the benefits. Logically, there is a
99
compelling need to give less value to future monetary values12. Time has influence on
value. If, for instance, you choose to invest in a specific capital project, other choices or
alternatives are forgone. This provides a case for charging interest for borrowed funds.
The expectation of inflation further cements the need to compensate lenders.
Unfortunately the discount rate used for private sector decisions may not be appropriate
for the public sector. Market prices may not reflect social evaluations of a public
undertaking. The problem of finding the correct social rate of discount is further
complicated by the market imperfections, as may exist when shadow prices are
considered. The social discount rate should be expected to be different from the private
rate partly because public decisions are made taking into consideration intergenerational
altruism. That is, the present society is assumed to have a collective responsibility for the
future societies. Thus the debts created in the current period will continue to haunt future
generations. Similarly, the capital investments made by the present generations are likely
to create benefits into the infinite time horizon. A good example is the stream of incomes
or benefits from Tokwe-Mukosi dam when completed. We would expect the project to
benefit the Lowveld sugar estates, the neighbouring communities and the nation over the
several hundreds of years to come. This provides a case for having lower discount rates
applied on public projects compared to the private projects.
Furthermore, private sector lending to government is for most purposes regarded as riskfree. In this context government borrowing should attract lower interest rate, taking into
consideration the exclusion of the risk premium on the interest rate. Whether public
sector projects should be discounted at a lower rate than private sector projects is a highly
contentious issue and one that has spawned an enormous literature13.
Readers who have difficulties appreciating this conventional line of thought should read the ‘Grounds for
Interest’. Some of the good arguments are based on the old theories of Bohm-Bawerk.
13
Grout P. A. (2002) “Public and Private Sector Discount Rates in Public-Private Partnerships”, CMPO
Working Paper Series No. 03/059, University of Bristol, September 2002
12
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9.2 Alternative Methods of Evaluating Capital Projects
There are several measures, most of which are borrowed from private sector project
appraisal, that have been applied on evaluating capital projects in the public sector. Each
of the measures, however, has its own weaknesses. In general, an acceptable measure
should posses the following key features:

It should incorporate the value of time.

It should reflect all future cost-benefit flows.

It should incorporate risk into the calculation of the value.
9.2.1 Payback (Period) Method
The payback method is probably the least sophisticated technique of performing costbenefit analysis. The payback method simply determines how many periods into the
future it takes for a capital project to repay the initial investment. The shorter the payback
period the more preferable it is from the point of view of financing. If, for instance, we
consider two potential projects, A and B, given the following cost-benefit flow streams
for each:
Project A
Project B
Year
Cost-Benefit Flow
Cost-Benefit Flow
0
-$1,000
-$1,000
1
$400
$200
2
$300
$400
3
$250
$500
4
$150
$200
In the above example, we notice that project A has a payback period of four years and
project B has payback period of B has payback period of three years. One weakness of the
payback method is that it does not take into consideration the time value of money.
Furthermore, the payback method does not take into consideration the benefits accruing
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after the payback period, no matter how significant they are. This creates bias against
those projects with delayed, but prolonged future benefits.
9.2.2 Discounted Payback Method
The discounted payback method is a development of the payback method. It attempts to
rectify one of the shortcomings of the payback method by incorporating the time value of
money. The cost-benefit flows are discounted to reflect the value of time. For example, if
the appropriate discount rate is 10%, the net benefit stream for projects A and B can be
recalculated to reflect this new piece of information. The present value (the value of some
future amount in today's dollars given a discount rate) is calculated using the following
formula:
 1 
PV  FV 

1  r 
t
Where: PV represents present value
FV is the future value and
r is the discount rate expressed as a percentage.
t is the time period
9.2.3 Net Present Value (NPV).
This method involves discounting the all future cost-benefit flows so that they take into
consideration the time value of money. The calculation of the NPV then follows the
formula:
T
NPV  
t 0
1
B  C 
1  r  t t
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Where: Bt represents benefits in period t.
C t represents costs in period t.
r is the discount rate.
If a project has net present value which is positive, using discount rate r, then such a
project is worth implementation since there exist some potential welfare improvement.
NPV > 0 (Project is worthwhile, government should consider financing)
NPV < 0 (Project is not worthwhile, and the government consider otherwise because the
returns from the project do not justify the costs). The net present value method provides a
criterion that can be applied on ranking alternative projects. This can be applied such that
those projects with higher NPV are ranked higher for purposes of financing.
Example
Suppose $1000 is available to initiate either project A or B. The net cash flows are
represented in the table below:
Project A
Project B
Year
Cost-Benefit Flow
Cost-Benefit Flow
0
-$1,000
-$1,000
1
$400
$200
2
$300
$400
3
$250
$500
4
$150
$200
Which of the two projects should be implemented if the NPV method is used the basis of
evaluation?
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Solution
YEAR
PROJECT A
PROJECT B
0
-1000
400
300
250
150
-1,000
200
400
500
200
100
300
1
2
3
4
NPV
From the above it immediately follows that both projects are viable. However B should
be adopted because it has higher NPV than A.
9.2.4 Benefit-Cost Ratio (BCR)
The benefit-cost ratio also provides a clue to the welfare effects of a capital project. The
BCR is calculated as:
T
 B 1  r 
t
BCR 
t
t 0
T
 C 1  r 
t
t
t 0
Where everything is just as before.
If then:
BCR > 1 (It is necessary to finance the project)
BCR < 1 (It is not worthwhile financing the project, returns will not off-set the costs)
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9.2.5 Internal Rate of Return Method (IRR)
The internal rate of return method is applied by identifying the discount rate which gives
a net present value of zero. The internal rate (i*) is defined as that discount rate which
yields NPV = 0, such that:
T
IRR  
t 0
Bt  C t
1  i 
* t
The decision criterion then hinges on the size of i* relative to the market rate of interest
(i). If i* > i, then the project should be pursued.
9.3 Conclusion
The literature on cost-benefit analysis for public projects has largely remained
inconclusive with difficulties observed in the measurement of benefits further weakening
the validity of all proposed appraisal techniques or measures. Apart from the appraisal
techniques described above, the modern trends have seen public projects also taking into
account the environmental impact assessments inorder to ascertain the possible adverse
effects on the natural and cultural resources. The cultural resources may be nonrecoverable once they are destroyed.
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