Download In particular, the assumptions about the wage

2x2x3 Modified Ricardian (Factor Specific) Model
Unlike in the simple Ricardian model, in the modified (factor specific) model trade is based on
differences in factor endowments and not on differences in technologies (although like in the
simple Ricardian model trade in the factor specific model is also related to differences in supply
conditions and not differences in consumer preferences).
Model Assumptions
Two countries: Home (England) and Foreign (Portugal)
Two goods: Manufactures (cloth) and food (wine)
Three factors of production: Labor (L), Capital (K), Land (T)
Both countries have the same technologies (production functions), the same supplies of nonspecific factor - labor (L), but have different endowments of capital and land. In particular,
England has more capital than Portugal, while Portugal has more land than England.
1
Manufactures are produced using capital and labor (but not land). The output of manufactures
depends on how much capital and labor are used in that sector. This relationship is summarized
by the production function for manufactures:
QM  QM ( K , LM )  K  L1M 
Food is produced using land and labor (but not capital). Similarly, the output of food depends on
how much land and labor are used in that sector.
QF  QF (T , LF )  T  L1F
Labor is a mobile factor which can move freely between sectors, while land and capital are both
specific factor that can be used only in the production of one good. For the economy as a whole,
the labor employed must equal the total supply L:
LM + L F = L
Production Possibilities
To analyze the economy’s production possibilities we need to ask how economy’s output mix
changes as labor is shifted from one sector to the other. Therefore, start with the graphical
representation of production functions for particular sectors and then derive the production
possibility frontier.
2
QM
QK , LM 
LM
Figure 1 . Production function in the manufacturing sector.
3
MPLM
MPLM ( K , LM )
LM
Figure 2. Marginal product of labor in the manufacturing sector
4
QF
PPF
LF
QM
LM
Figure 3. Production possibility frontier.
5
The slope of QM(K,LM) represents the marginal product of labor. However, in contrast to a
simple Ricardian model, if labor input is increased without increasing capital, there will be
diminishing returns: each successive increment of labor will add less to production than the last.
Diminishing returns are reflected in the shape of the production function which gets flatter as
more labor is used.
In contrast to a simple Ricardian model where the production possibility frontier was a straight
line because the opportunity cost was constant now the production possibility frontier is a curve
due to the addition of the other factors of production. The curvature of PPF reflects diminishing
returns to labor in each sector. If we shift one unit of labor from production of food to
production of manufactures this extra input will increase output in that extra sector by the
marginal product of labor in manufactures.
If we shift one unit of labor from production of food to production of manufactures this extra
input will increase output by the marginal product of labor in manufactures MPL M (and lower
the output of food by MPLF). Therefore, if we want to increase the output of manufactures by
one unit we have to increase labor input in production of manufactures by 1/MPLM units of
labor. Hence, to increase output of manufactures by one unit we must decrease the output of
food by MPLF/MPLM units.
6
Thus, the slope of the production possibility frontier reflects the opportunity cost of
manufactures expressed in terms of food. However, unlike in the simple Ricardian model, in the
factor specific model the opportunity cost is not constant. If we decrease output of food then the
value of MPLF will increase and MPLM will decrease. Hence, the opportunity cost of
manufactures expressed in terms of food will rise and the slope of PPF will increase.
Labor Allocation
Until now we have shown how output in each sector is determined given the allocation of labor.
Now let’s see how labor is allocated across sectors.
The demand for labor in each sector depends on the price of output (pM, pF) and the nominal
wage rate (w).
In each sector profit maximizing firms demand labor up to the point where the value produced
by an additional unit of labor equal the cost of labor (wage).
7
Numerical Example.
Suppose that wage rate is $ 4 per worker, the marginal product of labor is 3 gallons of wine
when the firm employs 10 workers, and the price of wine is $ 2 per gallon. Will the firm employ
an additional worker? Compare gains and costs. By employing an additional worker the firm can
earn $ 6 of additional revenue (it can produce 3 more gallons of wine and sells them for $ 2
each). The cost to the firm will be $ 4 paid in the worker’s wage. Thus, the firm can increase its
profit by $ 2. Therefore, the firm will hire an eleventh worker. However, when the firm does that
it reduces the land-labor ratio, and the marginal product of labor falls to 2 gallons. Now, if the
firm were to hire an additional worker it could earn only $ 4 so the firm cannot increase its
profits by employing an additional worker as it would have to pay $ 4 in the worker’s wage.
8
pM MPLM
w
pM MPLM ( K , LM )
LM
L*M
Figure 4. Equilibrium employment given the wage rate.
9
In equilibrium in each industry the value of marginal product of labor must equal the wage rate:
MPLM  PM  w
MPLF  PF  w
Labor market equilibrium requires equalization of the values of marginal products across
industries
(due to mobility of workers between industries).
MPLM  PM  MPLF  PF
10
MPLM
MPLF
w
pM MPLM ( K , LM )
pF MPLF (T , LF )
LF
LM
L*M
L
Figure 5. Equilibrium in the labor market
11
Determination of Prices
Let’s now examine how costs and demand for factors are related to the prices of factors when
producers employ two factors.
In a perfectly competitive economy the price of each good must equal unit cost of production
(perfect competition conditions). The unit cost of production equals the sum of the cost of capital
and labor inputs.
pM  cM  a KM rK  a LM w
p F  cF  aTF rT  a LF w
where: aKM ( w / rK ) and aLM (w / rK ) are unit factor requirements that have been chosen to minimize
unit cost in production of manufactures. Hence, costs cannot be reduced by increasing aKM or
reducing aLM (or vice versa).
Consider the production of the manufacturing good that requires capital and labor as factors of
production (alternatively consider the production of the agricultural good that requires land and
labor as factors of production). The manufacturing good is produced with constant returns to
scale. The production technology may be summarized in terms of a unit isoquant (i.e. a curve
showing all the combinations of capital and labor that can be used to produce one unit of the
manufacturing good).
12
The unit isoquant shows all combinations of capital and labor that can be used to produce one
unit of the manufacturing good. The unit isoquant shows that there is a tradeoff between the
quantity of capital used per unit of output aKM and the quantity of labor per unit of output aLM.
The shape of the unit isoquant reflects the assumption that it becomes increasingly difficult to
substitute capital for labor as the capital-labor ratio increases (and vice versa).
13
aKM
a**KM
a*KM
E’
E

w
rK
a**LM a*LM
aLM
Figure 6. Unit isoquant.
14
In a competitive economy producers will choose the capital-labor ratio that minimizes their
costs.
dCM = 0 = daKMrK + daLMw
Slope
daKM
w

daLM
rK
An infinitesimal change in the capital-labor ratio from the cost minimizing choice must have no
effect on cost.
“HAT ALGEBRA”
Consider what happens when the factor prices w and rK change. There will be two effects:
i) a change in the choice of aKM and aLM
ii) a change in the cost of production.
Let’s differentiate totally the unit production cost
15


dCM  a KM drK  a LM dw   rK daKM  wda LM 
  


0
Let’s write it in a different form (divide both sides by CM)



 
 


 


dC
a
r
dr
a
w
dw
M
Cˆ M 
  KM K  K    LM     KM rˆK   LM wˆ
 CM  
CM
r   CM  
w








 rˆ  
  wˆ 
% change
  KM 
  LM 


rateofgrowth
Where ΘKM – share of capital in total production cost of M, ΘLM – share of labor in total
production cost of M ΘKM + ΘLM = 1.
The cost minimizing labor-capital ratio depends on the ratio of price of labor to price capital:
w
a KM
   
aLM
 rK 
16
The relationship between factor prices and capital-labor ratio in the manufacturing sector that
results from a 1% change in the ratio of factor prices is known as the elasticity of substitution
σM.
M 
d (aKM / aLM ) /(aKM / aLM )
d ( w / rK ) /( w / rK )
d (aKM / aLM ) daKM daLM


 aˆ KM  aˆ LM
(aKM / aLM )
aKM
aLM
d ( w / r ) dw drK


 wˆ  rˆK
(w / r )
w rK
Hence,
aˆ KM  aˆ LM   M ( wˆ  rˆ)
aˆTF  aˆ LF   F ( wˆ  rˆ)
Using hat notation we can rewrite our pricing conditions as:
17
pˆ M   KM rˆK   LM wˆ
pˆ F  TF rˆT   LF wˆ
These equations allow us to derive changes in capital and land rentals given the changes in the
prices of manufactures pM, food pF and labor w.
rˆ K 
1

( pˆ M   LM wˆ )  pˆ M  LM ( pˆ M  wˆ )
 KM
 KM
rˆT 
1

( pˆ F   LF wˆ )  pˆ F  LF ( pˆ F  wˆ )
TF
TF
Now let’s determine the change in the wage rate w by examining the demand and supply for
labor. Demand for labor comes from both sectors in which labor is used, while output is
determined by supply of the specific factor. Hence,
QM 
K
a KM
QF 
T
aTF
18
Therefore,
a
LM  a LM QM   LM
 a KM
a
LF  a LF QF   LF
 aTF

 K


T

Concentrate on the manufacturing sector and notice that the supply of capital is fixed and
employment of labor in production of manufactures can change only through changes in the
capital-labor ratio (unit factor requirements). Using “hat algebra” we have:

1
LˆM  aˆ LM  aˆ KM   M ( wˆ  rˆK )   M ( wˆ 
( pˆ M   LM wˆ ))   M
 KM
  KM

( pˆ M  wˆ )

In the same manner we obtain:

1
Lˆ F  aˆ LF  aˆTF   F ( wˆ  rˆT )   F ( wˆ 
( pˆ F   LF wˆ ))   F
TF
 TF

( pˆ F  wˆ )

19
Now turn to the full employment condition in the labor market. Note that the labor supply is
fixed. If total employment is to remain, an increase in one sector’s employment must be offset
by a decline in the other sector.
dLM  dLF  dL  0
dLM  dLF
This expression can also be transformed into one that uses the hat algebra:
dLM LM dLF LF dL


0
LM 
L
LF 
L
L


Lˆ M
M
Lˆ F
F
M LˆM  F Lˆ F  Lˆ  0
Where M is the share of labor employed in production of manufactures in the economy’s total
labor supply.
Finally, let’s substitute the labor demand equations into the transformed labor market
equilibrium condition:
20
M  M
1
1
( pˆ M  wˆ )  F  F
( pˆ F  wˆ )  0
 KM
TF
1
1
pˆ M  F  F
pˆ F
 KM
TF
1
1
M  M
 F  F
 KM
TF
M  M
wˆ 
Note that the change in the wage rate is a weighted average of the changes in the prices of
manufactures and food.
EFFECTS OF CHANGES IN RELATIVE PRICES
Suppose that the price of manufactures increases relative to that of food, i.e. pˆ M  pˆ F
We can notice that the change in the wage rate will be smaller than the change in p̂M but bigger
than the change in p̂F because the change in the wage rate is a weighted average of the change in
the two goods prices:
pˆ M  wˆ  pˆ F
21
The effect of the allocation of labor is apparent from labor demand equations. Since pˆ M  wˆ ,
LˆM  0 employment in the production of manufactures increases and employment in the
production of food falls, LˆF  0.
The effects on the prices of capital and land may be seen from equations describing changes in
unit costs:
rˆ K  pˆ M 
 LM
( pˆ M  wˆ )  pˆ M

 KM 
0
rˆT  pˆ F 
 LF
( pˆ F  wˆ )  pˆ F


TF 
0
The overall description of the relation of the goods prices and factor prices is:
rˆK  pˆ M  wˆ  pˆ F  rˆT
The price of capital rises in terms of both goods. Therefore, someone who derives income
entirely from capital would be unambiguously better-off.
The price of land falls relative to both goods. Therefore, someone who derives income entirely
from land would be unambiguously worse-off.
22
Someone deriving income from labor would find that the purchasing power of income increases
in terms of food and falls in terms of manufactures.
These findings can be summarized in the Haberler Theorem:
A CHANGE IN RELATIVE PRICES RAISES THE REAL EARNINGS OF THE FACTOR
USED SPECIFICALLY IN THE INDUSTRY WHOSE OUTPUT PRICE HAS RISEN, AND
REDUCES THE REAL EARNINGS OF THE FACTOR USED SPECIFICALLY IN THE
INDUSTRY WHOSE OUTPUT PRICE HAS FALLEN. THE REAL EARNINGS OF THE
MOBILE FACTOR (LABOR) FALL IN TERMS OF THE GOOD WHOSE PRICE HAS
RISEN AND RISE IN TERMS OF THE GOOD WHOSE PRICE HAS FALLEN.
INTERNATIONAL TRADE
Having studied the economy of one country we are ready to study the effects of international
trade. Differences in factor endowments lead to differences in transformation curves between
countries. When England has more capital than Portugal and Portugal has more land than
England relative price of manufactures (expressed in terms of agricultural goods) under autarky
is higher in Portugal than in England.
23
 pM

 pF
A
T
A

p 
p 

  M    M 
 Portugal  pF 
 pF  England
With free trade the relative price of manufactures is the same in two countries which means that
the relative price of manufactures increases in England and falls in Portugal. As a result of the
change in relative prices of manufactures output of manufactures increases in England and falls
in Portugal and output of agricultural goods increases in Portugal and falls in England.
24
QF
QPT
QPA  CPA
C
C
T
QEA  CEA
QET
A
U
UT
QPT QPA  CPA C T QEA  CEA QET
QM
Figure 7. Trade in factor specific model
25
MPLM
MPLF
w
pF
( pM / pF ) MPLM ( K , LM )
MPLF (T , LF )
LF
LM
L*M
L**M
L
Figure 8. The effect of change in relative prices due to opening to international trade in England
26
Trade and Distribution of Income
The Haberler theorem can be used to show how trade affects the real earnings of land, capital
and labor.
Knowing that the relative price of manufactures increases in England and falls in Portugal the
impact of changes in real factor rewards in both countries can be summarized in the following
tables:
England (capital abundant country)
Sector
Employment Output
Manufactures
Food
LM↑
LF↓
QM↑
QF↓
Portugal (land abundant country)
Sector
Employment Output
Manufactures
Food
LM↓
LF↑
QM↓
QF↑
Real wage
MPLM(LM)↓
MPLF(LF)↑
Real wage
MPLM(LM)↑
MPLF(LF)↓
Real reward to specific
factor
MPKM(LM)↑
MPTF(LF)↓
Real reward to specific
factor
MPKM(LM)↓
MPTF(LF)↑
27
Applications of Factor Specific Model in Political Economy of Protectionism
Directly uproductive profit-seeking (DUP) activities and endogenous tariff formation.
In reality tariffs are accompanied by three phenomena:
i) tariff evasion (smuggling) activities in which profit is made by getting around the tariffs
ii) tariff seeking lobbying by pressure groups that expect to profit from protection
iii) revenue seeking lobbying to get a share of revenue disbursement expected to follow the
receipt of the tariff revenue (as tariffs imposed for protectionist reasons, as a result of
tariff seeking lobbying, almost always generate revenue).
When quantitative restrictions are used instead of tariffs, the above three phenomena arise as QR
evasion, QR seeking and premium seeking, respectively.
All those activities are profitable without being directly productive. Economic agents earn
incomes, using real resources, but without contributing directly or indirectly to output (resource
using activities that yield zero output).
28
Many of these activities are attempts to make profit by either getting around governmental
policies (e.g. tariff evasion) or getting governmental policies modified (e.g. by replacing free
trade with a protective tariff).
Krueger (1974) defines “rent seeking activities” as lobbying activities generated by the existence
of policy interventions, such as quantitative restrictions, licenses or restrictions which carry
premiums or windfall profits that accure to the successful lobbyist. Hence, follows the rent
seeking activity.
However, rent seeking activities are not the only category of DUP activities. In addition, there
are DUP activities that reflect lobbying triggered by price instruments (i.e. tariffs lead to
revenues that generate revenue seeking).
There are also DUP activities that seek to impose or influence the policy intervention itself, as
when tariff seeking is considered. DUP activities can involve evading a policy instrument.
A functional classification of DUP activities is presented in the figure below.
29
Policy-interventions related DUPs
Intervention-seeking DUPs
Price interventions
(eg. tariff seeking)
Intervention-triggered DUPs
QR restrictions
(eg. import-quota seeking)
Price intervention triggered lobbying
(eg. revenue seeking)
DUP lobbying
Intervention-evading DUPs
QR intervention triggered lobbying
(rent seeking of Krueger)
Price interventions
(eg. smuggling)
Quantity interventions
(eg. smuggling)
Figure 9. Functional classification of DUP activities.
30
Findlay-Wellisz (1982) Model
The Findlay-Wellisz (1982) model takes one factor as mobile between two sectors each of which
also has a sector-specific factor in addition. They model lobbying for and against a tariff by the
sector-specific factors since in the simple model structure the tariff will raise the real wage of
one such factor and reduce that of the other. Lobbying itself uses up the mobile factor. The
model is solved for the endogenous tariff that results from this set of assumptions.
In the conventional theory of the cost of protection the increased rents to factors engaged in the
protected industry are regarded as transfers to them from consumers or factors employed
elsewhere in the economy, and are therefore not considered as constituting a cost to the society
as a whole in the sense of using scarce resources.
Findlay and Wellisz (1982) incorporate Tullock’s argument into a formal analysis of the welfare
cost of a tariff.
Tullock’s (1967) Argument
Tullock (1967) in his paper entitled “The welfare costs of tariffs, monopolies and theft”,
published in the Western Economic Journal, argues that various interest groups in the society
would actively seek to promote the generation of these rents arising from the imposition of
tariffs while others whose interests are adversely affected would seek to prevent them.
31
Both sides would absorb scarce resources in the conflict over the extent and structure of trade
restrictions, and the social value of these resources should be considered in addition to the
conventional deadweight loss in arriving at estimates of the total welfare cost – protection is
very costly.
Tullock’s example – the analogy with theft: potential victims spend a part of their resources on
safes and locks to protect their resources, while thieves spend a part of their resources on
nitroglycerine and oxyacetylene torches to blow up or cut safes of their potential victims. The
resources spend by both sides constitute a cost to the society associated with the process of
transferring incomes from the law-abiding citizens to the criminals.
The tariff level is determined endogenously in a factor-specific general equilibrium model
extended to incorporate the process of tariff formation emerging from the clash of opposing
interest groups.
The model allows to determine: i) the level of tariff, ii) the lobbying expenditures on “tariff
seeking” and opposition thereto by interest groups, as well as iii) the associated deadweight
losses.
32
MODEL ASSUMPTIONS:
 2 goods: food (F) and manufactures (M)
 3 factors: land specific to food (T), capital specific to manufactures (K), labor (L) employed
in both sectors that can move freely.
 The supply of factors is fixed.
 CRS in both sectors.
 Perfect competition in factor and commodity markets
 International terms of trade are taken as given (small country)
 Both landowners (farmers) and capitalists are organized into pressure groups that can
influence political process. Workers are not organized and do not participate in this game.
Landowners (farmers) want to introduce a tariff on food at the prohibitive level, while capitalists
want to preserve free trade (like in 19th century England). Depending upon the relative strengths
of the two sides some tariff between zero and prohibitive level will emerge in equilibrium.
The social cost of the resources used up in this struggle constitutes a welfare cost in addition to
the familiar deadweight loss associated with tariffs.
33
Production functions:
F = F(LF, T)
M = M(LM, K)
F.O.Cs
p
F
w
LF
M
w
LM
F
r
T
M
q
K
p – domestic price of food in terms of manufactures (normalization pM = 1, pF/pM = p).
34
The domestic price ratio p is connected to the given (determined in the R.O.W) international
terms of trade π by the relation:
p = (1+t) π
where t is an endogenous variable determined by the political process (the struggle of various
pressure groups: landowners and capitalists).
Political process is modeled in a simple way as a reduced form of an earlier framework proposed
by Brock and Magee (1978).
The tariff level is determined as a stable function of resources committed to the political process
by each of the two interest groups. For simplicity, labor is the only factor used by both sides in
the political process:
t=t(LT,LK)
35
t
 0,
LT
t
 0,
LK
 2t
LT
2
 2t
LK 2
 0,
0
LT – labor used by landowners in the political process
LK – labor used by capitalists in the political process
Both LT and LK receive the going wage w.
Full employment (market clearing condition) in the labor market:

 


 

L

L

L

L
L
F
M
T
K
 

   

 
 production   lobbying 
36
Assume for the moment that the resources allocated to the political process (lobbying) are taken
as given, and study the properties of the model.
Define the labor available for production as:
LA = LF + LM = L – (LT + LK)
Notice that F, M (outputs) and r,q,w (factor rewards) are determined as functions of p and L A
alone with the following properties:
F
F
 0,
 0,
p
L A
M
M
 0,
 0,
p
L A
r
r
 0,
 0,
p
L A
q
q
 0,
 0,
p
L A
w
w
 0,
0
p
L A
37
Output of food increases in the relative price of food and in total amount of labor available for
production.
Output of manufactures decreases in the relative price of food and increases in total amount of
labor available for production.
Reward of landowners increases with the relative price of food and the number of people
employed in production.
Reward of capitalists decreases in the relative price of food and increases in the number of
people employed in production.
Wage expressed in terms of manufactures increases when the relative price of food goes up and
decreases in the number of people employed.
Free trade vs. protectionism
Under free trade and in the absence of any political pressure LT = 0. The income of landowners
expressed in terms of manufactures would be πr(π,L)T.
The net benefit from engaging in the political process for landowners, given the actions taken by
capitalists, would be equal the income under tariff and engaging resources in political process –
cost of hiring people engaged in political process – income under free trade and no involvement
in political process:
38
NT  pLT , LK r  pLT , LK , L  LK  LT T  w pLT , LK L  LT  LK LT  r  , LT
The first order condition for maximizing NT (given LK) with respect to LT is:

p r  LT p LT r  prT  LT w p w LT p 


1


 1 



w
r

p
p

L
r

L
L
w

L
w

p
p

L

T
T 
T
T
T 


The interpretation of this condition is as follows. The marginal contribution of LT in raising land
rents (prT) should be equal to the marginal cost of LT.
An increase in LT has three separate effects on the income from land. It increases p, which
induces and increase in r (both of which raise the income of landowners) but at the same time
(given p) and increase in LT reduces r (less people employed means lower productivity of land).
It is, however, assumed that the negative effect is small relative to the positive effect so the
entire term on the LHS is positive (this condition is necessary for any expenditure in political
activity to be effective at all).
The marginal cost of LT is greater than w (both expressions on the RHS are positive).
39
It tˆ denotes the optimal tariff (possibly prohibitive) obtained by the landowners in the absence of
any defensive measures by capitalists, L̂T the amount of labor used by landowners to achieve
this, q the resulting rental per unit of capital then the net benefit to the manufacturers of entering
the political activity to protect their incomes would be:
N K  q pLT , LK , L  LK  LT K  w pLT , LK , L  LT  LK LK  qˆ  (1  tˆ),1  LˆT K
The first order conditions for maximizing NK with respect to LK, taking LT as given yields:
 p q LK p
LK q  qK  LK w
p w LK p 


1





w
q

p
p

L
q

L
L
w

L
w

p
p

L
K
K  K
K
K 


The interpretation is very similar to the previous F.O.C. for landowners. The marginal return
from employing LK amount of labor to raise income of capitalists equals its marginal cost. The
product of two negative terms of the LHS is positive, while the second term is negative. Again,
we assume that it is worthwhile for capitalists to engage in the political process to defend their
incomes.
40
The first order conditions for landowners and capitalists can be interpreted as “reaction
functions” showing the optimal response by each group given the actions of the other. These
functions allow us to find optimal political inputs for both groups LT *, LK * . Given these inputs we
can find the equilibrium net benefits from engaging in the political process. The value of t* and
all other eight variables can be determined by the set of first nine equations.
The welfare cost of the endogenous tariff can be illustrated graphically.
41
F
C
B
C’
Ufreetrade
B’
Uprotectionism
A
p*=(1+t*)π
Figure 10. Welfare costs of protectionism.
M
42