With no factor substitution,

Factor Abundancy of the Home country: K=3000 L=2000

Factor Abundancy of the Foreign country: K=3000 L=3000

Factor intensity in clothing industry: aKC = 2 & aLC = 2

Factor intensity in food industry: aKF = 3 & aLF = 1

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

b. What is the labor-abundant country? How much food and cloth is produced in each country before trade (in autarky)? Solve by drawing the pre-trade PPF for each country.

For parts (c) through (f), assume the price range is such that both goods are produced in the home country. Evaluate each question for the home country only.

c. Write down the unit cost of producing one yard of cloth and one calorie of food as a function of the price of one machine-hour, r, and one work-hour, 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.

d. 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?

e. Now assume the home economy’s supply of machine-hours increases from 3,000 to 4,000. Derive the new production possibility frontier.

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

g. Describe how the allocation of machine-hours and work-hours between the cloth and food sectors changes. Do those changes conform with the changes described for the case with factor substitution?