Download Specific Factors Model

Specific Factors
Model
Outline
1. Objective
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2. Assumptions
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3.
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Production possibilities.
4. How much labour will be used in each sector?
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5. Factor price equalization within a country
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6. Factor price equalization between countries
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7. Uncertainty
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Model
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Case 1
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Case 2
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1. Objectives
-Study International trade effects on income distribution inside a
country.
-Study efficiency and distribution effects of factor mobility : Factors
can not move immediately and costless from one sector to another as
theory assumes. At the same time the different proportion of factors
needed to produce each good implies that trade benefits some sectors
in the economy while prejudicing others.
For this reason we will focus the study of specific factor model on the
factor price equalization within countries and between countries.
-Study political support for reform under certainty (according to factor
ownership) and under uncertainty (according to expected mobility and
gains).
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2. Assumptions
• 2 goods j: manufactures and food.
• 3 production factors: labour (L), capital (K) and land (T).
• Labour is a mobile factor, while capital and land are specific factors
designated to the production of manufactures and food respectively.
• For given levels of the specific factors each good has decreasing
returns to scale on labour.
• Production functions are: QM  QM K , LM  for manufactures
QF  QF T , LF 
for food
• K and T are the economy supply of capital and land.
• The economy supply of labour is: L  LM  LF
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3. Production possibilities.
As specific factors are fixed for each good’s production, the output will
depend on the distribution of labour between the two goods production.
The marginal product of labour is decreasing.
Manufactures production function
Marginal product of labour
MPLM
QM
LM
The same can be represented for food sector.
LM
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4. How much labour will be used in each sector?
It will depend on the goods prices, as well as the wage level. The wage
is determined by the demand of labour of both production sectors.
The demand for labour in each sector is given by the maximization
problem of producers which implies that the value of an additional unit
of work equals it’s cost:
MPL j * p j  w
where:
MPL j is the marginal product of labour in production of good j.
p j is the price of good j.
w is the wage level.
This is that the value of marginal product of labour equals the wage level.
For given levels of pM and pF the value of marginal productivity of labour in
the production of both goods can be represented by a downward sloping
curve.
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Income distribution
Represents the income of
labour.
MPLM
Represents the income of
capital (“surplus” of the
employer).
+
A
wA
Represent the total product
LA
L
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As we assume that labour moves freely between sectors, wage level will
be equal for a worker in manufactures and in food production.
MVPLM
Demand for
labour in
manufactures.
Demand for
labour in
food.
MVPLF
E
wE
LE
Labour used in
manufactures: LM
Labour used in food: LF
Total labour supply
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5. Factor price equalization within a country
5.A. Efficiency issues
MVPLM
wM
MVPLF
BM
E
wF
BF
Situation B is inefficient as:
MVPBM  MVPBF
If we move one worker from food sector to manufactures, then the
production that is destroyed in the food sector is lower than the added in
manufactures. There is a gain for the society until point E is reached.
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Why there are barriers that keep the situation B?
• There are sectors that resist to move from B to E: both workers
from manufacture sector and land owners from food sector are not
willing to reduce their income.
• Better organized workers in unions get better wages.
• There is a social conflict as there are two social classes that do want
the change: workers from food sector and capital owners from
manufacture sector.
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5.B. Adjustment to shocks and changes in purchasing power
Which is the effect in purchasing power of a manufacture prices increase?
Income of K increases (surplus larger) and income of T decreases. These
factors are “specific” : they suffer a strong “Stolper-Samuelson” effect.
The value of marginal product of mobile labour increases in the
manufacture sector and the nominal wage increases in both sectors.
MVPLM
MVPLF
D
wD
wC
wE
C
E
LM
LF
L’M
L’F
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As prices in the food sector remained equal, the purchasing power of
workers in terms of food has increased, but what happens with the
purchasing power in terms of manufactures?
If all the variation in price of manufactured products is transferred to
wages then the wage level should be wD, higher than wC. Thus at WC,
the purchasing power of wages in terms of manufactures has
decreased.
Total effect in purchasing power is uncertain, as it also depends on the
consumption goods basket ( see point 7: Uncertainty).
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6. Factor price equalization between countries
MVPLM
MVPLF
L Europe
By trading with the rest of the world, European workers will see their
welfare reduced when factor price equalization takes place. At the same
time in the rest of the world capitalists (owners of scarce factor there)
will be worse too as they will reduce part of their profits.
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Wages decrease in Europe and increase
in the rest of the world.
Trade
Investment remuneration increase in
Europe and decreases in the rest of the
world.
Factor mobility: abundant factor in one country moves to where it is
scarce. Then the two factors capital and labour will move in opposite
directions: capital moves from the North to the South and labour moves
from the South to the North.
However, factor mobility is not possible, goods make the work of
factor price equalization but full price equality won’t happen.
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Migration can increase unemployment, which happens because it
destroys output in the home country and does not increase it in the
host country (where minimum wage laws or unemployment benefits
operate).
In the host country, marginal product can sometimes decrease fast
because firms are not well equipped to hire more workers; cities are
not equipped in terms of housing, electricity and water supply,
environmental management, etc.
Both, no migration or too much migration are counterproductive for
the economy.
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7. Uncertainty
How does uncertainty determine the support to policy reforms?
(Fernandez and Rodrik, 1991)
FERNANDEZ, Raquel and RODRIK, Dany (1991) "Resistance to Reform: Status-Quo Bias in the Presence of Individual-Specific
Uncertainty" American Economic Review 81, 5 (Dec.) 1146-1155
The presence of individual-specific uncertainty can distort aggregate
preferences. Policy reforms are more likely to be adopted the more
individuals are in favor of it.
However, reforms are not adopted even though:
• Individuals are risk neutral.
• A majority could vote for it ex post.
• The previous two conditions are common knowledge.
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Model
• 2 sectors: winner (W) and loser (L).
• Distribution of people among sectors: gains for W and losses for L.
• After a reform some agents will move from L to W, but a priori they
don’t know who is going to be a lucky mover.
• The reforms bring aggregate gains anyway (expected gains of W >
expected losses of L and realized gains of W’ > realized losses of L’).
Case 1:
Initially: L>W (60 % L and 40 % W).
After reform: L’<W’ (40% L’ and 60 % W’).
Group L will decrease it’s income in 20% and W will increase it in the
same amount. Then, the after-reform variation of income is:
- 0.08 + 0.12 = 0.04.
Final gain of the reform is positive in aggregate, ex post. Will there be
a majority voting for it? (ex ante support)
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To get the reform done 50% of the votes are needed:
Winners
0,2
- 0,2
Losers
Ex post
0.4 0,5 0.6
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Ex ante L
Expected gains of group L:
 0.4
0.2
* 0.2 
* 0.2  0
0.6
0.6
Group L will not vote for the reform ex ante, then the reform will
not take place. It is necessary to distinguish a priori winners and
losers in order to get the reform done.
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If the reform is imposed, then there are net gains:
-0.40.2 + 0.60.2 = - 0.08 + 0.12 = 0.04.
The uncertainty about the final effects makes people vote against
the reform. If a dictator impose the reform, this will take place and
net gains will take place in aggregate and for a majority (here
60%). A majority (60% here) will support the new regime,
provided a way is found to get there.
Status quo bias works in two ways:
1. A reform that ex ante seems to deteriorate the situation of a
majority will not be approved even if ex-post it would find majority
support and bring aggregate gains.
2. A reform that ex-ante seems to bring gains to a majority (or to all)
can be rejected in a second vote, if it does not improve the situation
of a majority ex-post, even if it brings aggregate gains ex-post as
well as ex-ante (see case 2) .
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Case 2
Initially: 10% sure winners, 90% unsure, but 0.2/0.9
will gain a lot (0,3) and 0.7/0.9 will lose a bit (0,067) :
W>L (100 % are W in expected value).
Finally: 70 % L and 30% W.
Reform is voted when expected gains are positive for everybody,
even when after the reform group L has lost.
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Ex post
Ex ante
0,3
-
0,015
0,067
0,7
Net effect ex-post :
0.9 1
 0.067 * 0.7  0.3* 0.3  0.0431
Minority’s gain > majority’s loss : aggregate gain, but rejected in second
majority vote due to 70% of losers !
However, the expected total gain was positive:
0.9 * 0.015  0.1* 0.3  0.0432
and the ex-post losers had an expected gain ex-ante :
N.B.  0.7 * 0.067  0.2 * 0.3  0.052  0.066  0.015
0.9
0.9
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The reform takes place, but once it is adopted it has negative effects
for many people (70% lose 0.067). Initially these voters vote against
their interest. If there is a second chance they will reject the reform.
If there was risk aversion, L would initially reject the reform because
they have big probability of being among the 70% that loses.
For beneficial reforms (case 1), uncertainty is the problem, not risk
aversion. Since no new information is revealed, when a reform has
been rejected a majority will keep rejecting it.
On the importance of redistribution (or compensation principle) see
also the insurance argument developed in Rodrick, D. (1998)
"Why do more open economies have bigger governments?"
Journal of Political Economy, 106, 5 997-1032
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