Consider the two-factor Heckscher-Ohlin model discussed in class. Home country has 4,000 hours of capital (K) and 2,000 hours of labor (L). Suppose that in Home country, 4 hours of capital are required to produce one yard of cloth; 4 hours of labor are required to produce one yard of cloth; 8 hours of capital are required to produce one calorie of food; and 2 hours of labor are required to produce one calorie of food. Assume the production technology is given by a Leontief technology where factor substitution is not freely allowed.

A) Derive constraints on capital and labor separately.

B) Draw the production possibility frontier on a diagram. On both x-intercept and y-intercept, calculate the exact number associated with those two points.

C) Calculate the x- and y-coordinates for the point where capital and labor constraints intersect.

D) 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?

E) For the remaining questions, assume the price range is such that both goods are produces. 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.

F) 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?

G) Now assume the economy's supply of machine-hours increases from 4,000 to 6,000. Derive the new production possibility frontier.

H) How much cloth and food will the economy produce after this increase in its capital supply? Suppose all resources are used at the production point.