Question

Pinnacle Inc. produces industrial pins. Its production function is ? = ?? 1/2 ? 1/2 , for ? ≥ 0 and ? ≥ 0, where ? denotes units of capital input, ? denotes units of labor input, and ? denotes units of output. The price of a unit of capital input is ? and the price of a unit of labor input is ?.

a. Find Pinnacle’s ??? and ??? functions.

b. Find Pinnacle’s ??? function.

c. Find Pinnacle’s long run (contingent) demand functions for labor input and capital input. (Hint: These will be functions of the target output level, ?, and the input prices, ? and ?.)

d. Find Pinnacle’s long run total cost function. (Hint: This will be a function of the target output level, ?, and the input prices, ? and ?.)

e. Pinnacle currently produces in the U.S., where ? = 2, ? = 100, and ? = 25. What is Pinnacle’s per-unit cost of a pin?

f. Suppose that Pinnacle has an opportunity to move production to Mexico, where ? = 1 and ? = 100. For which values of ? in Mexico would moving production to Mexico reduce the per-unit cost of pin production?

Answer 1