The capital requirement for producing 1 unit of cloth is 2, while 2 units of labor are needed for the same job. Likewise, for food, the unit capital requirement is 3, and the unit labor requirement is 1.

The economy is endowed with 3000 units of capital and 2000 units of labor.

a. Draw the PPF and solve for the equilibrium amount of production.

b. 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?

c. Let the price range is such that both goods are produced. Write down the cost of producing one unit of cloth and one unit of food as a function of the price of capital, r, and labor, w. In a competitive market, those costs will equal the prices of cloth and food.

Solve for r and w.

d. What happens to w and r when the price of cloth rises?

e. Assume there is an increase in capital from 3000 to 4000 units. Derive the new PPF.

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

g. Describe how the allocation of capital and labor between the cloth and food sectors changes.