Chapter 3: Specific Factors and Income Distribution
Topics:
Specific Factors Model
International Trade in the Specific Factors Model
Income Distribution and the Gains from Trade
The Political Economy of Trade: A Preliminary View

If trade is such a good thing for the economy, why is there opposition to it? The Ricardian
model implies that every individual is the same, so that every individual is made better off by
trade.

However, in reality trade affects the distribution of income of various groups in the
population. Reasons: 1) Resources cannot really move so readily across industries; 2)
Industries differ in the factors of production that they demand. There are political issues;
consider the example of Japanese rice farmers. Can also be issues of perceived national
security or self-sufficiency.

Thus, we need a model that can account for these effects on income distribution.
1. Specific Factors Model
a) Assumptions of the Model
There are two industries, manufactures (M) and food (F). There are 3 factors of
production, rather than just one: labor (L), capital (K), and land (T). L is used in
both industries, while K is used only in manufacturing and T is used only for food
production.
We have production functions for these industries and a labor constraint:
(1) QM = QM(K,LM)
(2) QF = QF(T,LF)
(3)
L = LM + LF
The production functions exhibit convexity. The slope of Qi(K,Li) represents the
marginal product of labor for industry i, the increase in output when there is an
incremental increase in labor supplied.
See Fig. 3-1
We assume that there are diminishing returns to labor, in the sense that the 2nd
derivative is negative – keeping capital (or land) constant, the benefit of an extra
unit of labor diminishes as the amount already supplied increases. This is a key
assumption.
See Fig. 3-2
Using the production possibility frontier concept of Chapter 2, we can transform
the production functions into the economy’s PPF, as seen in Fig. 3-3.
Start in the lower left quadrant. Everything is reversed here, in terms of the usual
directions of the axes. The line reflects equation (3) above, so the slope is –1.
Pick any point on this line, and extend dotted lines both horizontally and
vertically until these intersect the production functions for food and manufactures.
This gives the amounts produced with the L inputs given (we assume that K and T
are fixed). Note that the bottom right quadrant is rotated 90 degrees clockwise,
while the upper left quadrant is a mirror reflection across the vertical axis.
Now, extend dotted lines from the intersected points on the production functions
into the upper right quadrant. The quantities produced for labor inputs (LM,LF)
give the PPF. Note that this is curved, rather than linear as in the Ricardian
model. This reflects the diminishing returns to labor in each sector. The slope of
the PPF measures the trade-off for food production and manufactures, and is
equal to -MPLF/MPLM; as LM rises and LF falls, this ratio increases, so the slope
gets steeper as we move to the right.
b) Prices, Wages, and Labor Allocation
How much labor will be employed in each sector? This depends on the price of
output and the wage rate. Profit-maximizing firms will employ labor up to the
point where the value of the MPL is less than the wage, so:
(4) MPLM * PM = w = MPLF * PF
Since MPL slopes downward (Fig. 3-2), this value function also slopes downward
(we assume for the moment that the price is fixed). The wage is the same in both
industries, since we have free mobility of labor. This generates a demand curve
for labor, as shown in Fig. 3-4. Note that the horizontal axis is reversed for LF.
Rearranging (4), we get:
(5) -PM/PF = -MPLF/MPLM
so that, at the production point, the PPF must be tangent to a line whose slope is
-PM/PF. This is shown in Fig. 3-7.
Now consider a change in the prices of food and manufactures. First, suppose
that both increase by 10%. Well, intuitively, the wage is just going to increase by
10%, as this is just the equivalent of inflation. The allocation of labor across
sectors doesn’t change, as the relative prices haven’t changed. See Fig. 3-6.
However, suppose that there is a change in relative prices (the price of one’s
relatives?); for example, suppose PM increases by 7% and PF remains the same.
Now the demand curve for manufacturing labor shifts upward, as seen in Fig. 3-7.
We see: 1) More labor is used in manufacturing, and 2) The wage increases, but
less than the amount of the change in PM (less since the MPLM falls as LM
increases).
We can also see this by looking at the PPF, as in Fig. 3-8. The production point
shifts from point 1 to point 2, reflecting the change in relative prices.
We can also draw the relative supply curve of labor in relation to the price ratio.
This is shown in Fig. 3-9. The higher the relative price of manufactures, the
greater the relative supply of manufacturing labor. The equilibrium prices and
quantities are given by the intersection of RS and RD.
Who benefits? Workers may or may not be better off; w/PM falls and w/PF rises,
so the effect is ambiguous. Capital owners are happy, since the real wage rate in
terms of manufactures has risen; landowners are unhappy, since the real wage rate
in terms of food production has risen.
2. International Trade in the Specific Factors Model
What is the effect of trade on welfare? Consider that two countries (e.g., Japan and
the U.S.) differ in their relative supply of production input factors. This could occur
for many reasons, including 1) different technologies, and 2) different resources. We
focus on the latter possibility.
a) Resources and Relative Supply
What happens if a country experiences an increase (or decrease) in the supply of
some resource? Assume an increase in K. Fig. 3-10 shows how, since an increase in
K raises the MPLM, the demand for labor (determined by the value of the marginal
product of labor) shifts out.
Since labor is pulled out of the manufacturing sector (and is also more productive),
manufacturing output will rise. Food output will fall (although this is mediated by the
higher average productivity for LF). Thus K increasing (T increasing) means that the
relative supply of labor shifts to the right (left).
b) Trade and Relative Prices
Suppose Japan and the U.S. have the same labor, but that KJ > KA, but that TA > TJ.
This is shown in Fig. 3-11. The RSJ is to the right of the RSA. When the two
economies trade, the resulting RSWORLD is between the two national curves. The
intersection of the RSWORLD and RDWORLD determines world relative prices (we have
assumed that relative demand is the same in both countries, so RDWORLD = RDA =
RDJ). Trade here increases the relative price of manufactures in Japan and the
relative price of food in the U.S.
c) The Pattern of Trade
Without trade, a country’s output of a good must equal its consumption. However,
trade makes it possible for a country’s consumption (DM or DF) to diverge from the
mix produced (QM or QF). However, the country still faces a budget constraint: The
value of production must equal the value of consumption:
(6) PM*DM + PF*DF = PM*QM + PF*QF
or
(7)
DF – QF = (PM/PF)*(QM-DM)
The latter equation says that food imports must equal the relative price of
manufactures times manufacturing exports.
Fig. 3-12 illustrates some salient features: 1) The slope of the budget constraint is the
negative of the relative price of manufactures, since one less unit of M means PM/PF
extra units of food, and 2) The budget constraint must be tangent to the PPF at the
point of production given the relative prices. Thus, the country can always afford to
consume what it produces.
In the trading equilibrium (Fig. 3-13), we see that Japan becomes an exporter of
manufactures and an importer of food. The reverse is true for the U.S. (in this 2country world economy), and the imports/exports match up exactly.
3. Income Distribution and the Gains from Trade
We saw that trade leads to a rise in PM/PF for Japan. So Japanese owners of capital
are better off, and Japanese landowners are worse off (reversed for U.S). Trade
benefits (hurts) the factor that is specific to the export (import) sector of each country.
The effect on the mobile factor (L) is ambiguous.
What about the effect on social welfare? This is not easy to compare, since the utility
of different types (e.g., landowners and capital owners) may vary in sensitivity to
consumption. However, as we shall see, the pie is bigger with trade, so in principle
everyone could potentially be made better off. 3 steps in the story:
1. Without trade, the economy’s consumption must lie exactly on the
PPF. For example, we have point 2 in Fig. 13-14.
2. A trading economy can actually consume more of both goods than
otherwise. Parts of the budget constraint lies outside the PPF. In the
triangular region to the northeast of point 2 and below the budget
constraint, more of both goods is consumed than at point 2. (Note that
at an initial choice of point 1, trade provides no such benefit).
3. While this shows gains for the economy as a whole, in principle this
could be distributed among the population so that everyone is better
off.
4. The Political Economy of Trade: A Preliminary View
However, in the real world, the presence of winners and losers from trade is the
main reason why trade is restricted. What should a government do in terms of
trade policy, and what is it likely to do in practice?
a) Optimal Trade Policy
Generally, the central planner is presumed to maximize the welfare of the
population as a whole. If this is just a utilitarian summation, we should have
completely free trade. However, in the Rawlsian view, groups that are poor need
special treatment. This is legitimate, but there are still 3 main reasons why
economists do not typically stress the issue of income distribution:
i. All changes in the national economy have income distribution effects.
This is not a special case, and red tape can be the enemy of “economic
progress”.
ii. It makes more sense to compensate those people hurt by trade (from
the bigger pie) than to cut off choice-increasing trade.
iii. Those industries that stand to lose from trade are usually wellrepresented by lobbyists. Here economists are a proxy for those
groups with little voice.
So, overall, it is more important to stress the gains than to dwell on the possible
losses of some group(s).
b) Income Distribution and Trade Politics
Special interests are usually more effective politically than the overall population
that stands to benefit. Why?
Consider for example the sugar industry. Restrictions on imported sugar cost the
U.S. economy about $2 billion per year, while only helping the sugar industry to
the tune of $1 billion per year. Seems like a bad policy, right? And sugar is
hardly vital to our national security.
But this only costs each consumer $8 per year (and most people don’t even know
about this). People don’t typically get too excited about $8 per year.
On the other hand, a sugar producer has a much bigger vested interest (thousands
of dollars at stake), and so it is worthwhile to organize lobbying groups, etc.
Welcome to the real world.