(Problem on the Heckscher-Ohlin Model) Suppose there are two goods in the econom

Question

(Problem on the Heckscher-Ohlin Model) Suppose there are two goods in the economy, food and cloth, which can be produced using capital and labor. Suppose there is no factor substitution between capital and labor. Thus all the unit input requirements are fixed at aKC=2; aLC=2, aKF=3; aLF=1. Assume that the economy is endowed with 2000 units of labor and 3000 units of capital.

a) What is the range for the relative price of cloth such that the economy produces both cloth and food? Which good is produced if the relative price is outside of this range?

For parts b through f, assume that the price range is such that both goods are produced.

b)Write down the unit cost of producing one yard of cloth and one calorie of food as a function of the price of capital, r, and labor, w. In a competitive market, those costs will be equal to the prices of cloth and food. Solve for the factor prices r and w.

c. What happens to those factor prices when the price of cloth rises? Who gains and who loses from this change in the price of cloth? Why? Do those changes conform to the changes described for the case with factor substitution?

d. Now assume that the economy's supply of capital increases from 3000 to 4000. Derive the new production possibility frontier.

e. How much cloth and food will the economy produce after this increase in its capital supply?

f. Describe how the allocation of capital and labor between the cloth and food sectors changes. Do these changes conform with the changes described for the case with factor substitution?

Explanation / Answer

Given the following constraints-

aKC=2; aLC=2, aKF=3; aLF=1. And L = 2000, K = 3000

First calculate opportunity cost for both cloth and food.

Here each unit of cloth and food is produced given below-

Capital

labor

cloth

2

2

food

3

1

2Qc + Qf ? 2,000 (labor constraint)

2Qc + 3Qf ? 3,000 (Capital constraint)

Solving, these two constraints

Qf ? 2,000-2Qc

Qf?1000-2/3Qc

This gives two budget constraints for food production.

If the price of cloth falls below 2/3 then the economy should specialize in food production. If the price of cloth rises above 2, then specialization of cloth will occur.

b.

Qc = 2K+2L

Pc= 2r +2w

Qf = 3k +L

Pf = 3r + w

Solve for factor prices

w = Pf -3r

Pc = 2r +2(Pf-3r) = 2r+2Pf -6r = 2Pf-4r

r = (2Pf-Pc) / 4

w = (3Pc – 2Pf) /4

c.

an increase in price of cloth will cause the rental rate of capital to fall. And wage rate of labor would be rise.

d.

New capital constraint is given

2Qc +3Qf?4000

Solving for Qf

Qf?1,333-2/3Qc

Thus the minimum price of cloth is also unchanged at 2/3 units of food. The new production possibilities frontier will intercept the x axis at 2,000 instead of 1500.

Capital

labor

cloth

2

2

food

3

1

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