Gains From Trade with Economies of Scale
by Steven Suranovic ©1997-2004
The main reason why the presence of economies of scale can generate trade gains is because the
reallocation of resources can raise world productive efficiency. To see how we present a simple
example using a model similar to the Ricardian model.
Suppose there are two countries, the US and France, producing two goods, clothing and steel, using one factor of production, labor. Assume the production technology is identical in both countries and can be described with the following production functions.
Production of Clothing:
QC = quantity of clothing produced in the U.S.
LC = amount of labor applied to clothing production in the U.S.
aLC = unit-labor requirement in clothing production in the U.S. and France ( hours of labor necessary to produce one rack of clothing)
and where all starred variables are defined in the same way but refer to the process in France. Note that since production technology is assumed the same in both countries, we use the same unit-labor requirement in the US and the French production function.
Production of Steel: The production of steel is assumed to exhibit economies of scale in production.
QS = quantity of steel produced in the U.S.
LS = amount of labor applied to steel production in the U.S.
aLS(QS) = unit-labor requirement in steel production in the U.S. ( hours of labor necessary to produce one ton of steel). Note, it is assumed that the unit labor requirement is a function of the level of steel output in the domestic industry. More specifically we will assume that the unit-labor requirement falls as industry output rises.
Resource Constraint: The production decision is how to allocate labor between the two industries. We assume that labor is homogeneous and freely mobile between industries. The labor constraints are given below.
where L is the labor endowment in the US and L* is the endowment in France. When the resource constraint holds with equality it implies that the resource is fully employed.
Demand: We will assume that the US and France have identical demands for the two products.
A Numerical Example
We proceed much as Ricardo did in presenting the argument of the gains from specialization in one's comparative advantage good. First we will construct an autarky equilibrium in this model assuming that the two countries are identical in every respect. Then we will show how an improvement in world productive efficiency can arise if one of the two countries produces all of the steel that is demanded in the world.
Suppose the exogenous variables in the two countries take the values in the following table.
Let the unit-labor requirement for steel be read off of the
adjoining graph. The graph shows that when 50 tons of
steel are produced by the economy, the unit-labor
requirement is 1 hour of labor per ton of steel. However,
when 120 tons of steel are produced, the unit-labor
requirement falls to ½ hour of labor per ton of steel.
An Autarky Equilibrium
The US and France, assumed to be identical in all respects, will share identical autarky equilibria. Suppose the equilibria are such that production of steel in each country is 50 tons. Since at 50 tons of output, the unit-labor requirement is 1, it means that the total amount of labor used in steel production is 50 hours. That leaves 50 hours of labor to be allocated to the production of clothing, which with a unit-labor requirement of 1 also, means that total output of clothing is 50 racks. The autarky production and consumption levels are summarized below.
The problem with these initial autarky equilibria is that because demands and supplies are identical in the two countries, the prices of the goods would also be identical. With identical prices, there would be no incentive to trade if trade suddenly became free between the two countries.
Gains from Specialization
Despite the lack of incentive to trade in the original autarky equilibria, we can show, nevertheless, that trade could be advantageous for both countries. All that is necessary is for one of the two countries to produce all of the good with economies of scale and let the other country specialize in the other good.
For example, suppose we let France produce 120 tons of steel. This is greater than the 100 tons of world output of steel in the autarky equilibria. Since the unit-labor requirement of steel is ½ when 120 tons of steel are produced by one country, the total labor can be found by plugging these numbers into the production function. That is, since QS* = LS*/aLS, QS* = 120 and aLS = ½, it must be that LS* = 60. In autarky it took 100 hours of labor for two countries to produce 100 tons of steel. Now it would take France 60 hours to produce 120 tons. That means more output with less labor.
If France allocates its remaining 40 hours of labor to clothing production and if the US specializes in clothing production, then production levels in each country and world totals after the reallocation of labor would be as shown in the following table.
The important result here is that it is possible to find a reallocation of labor across industries such that world output of both goods rises. Or in other words, there is an increase in world productive efficiency.
If output of both goods rises then surely it must be possible to find a terms of trade such that both countries would gain from trade. For example, if France were to export 60 tons of steel and import 30 racks of clothing then each country would consume 70 units of clothing (20 more than in autarky) and 60 tons of steel (10 more than in autarky).
The final conclusion of this numerical example is that when there are economies of scale in production then free trade, after an appropriate reallocation of labor, can improve national welfare for both countries relative to autarky. The welfare improvement arises because by concentrating production in the economies of scale industry in one country, advantage can be taken of the productive efficiency improvements.
International Trade Theory and Policy Lecture Notes: ©1997-2004 Steven M. Suranovic