The production function for Hamburger Heaven (HH) is q=10KL. Given that the marignal product of labor, MPL = 10K, marginal product of capital, MPK = 10L, and marginal rate of technical substitution (MRTS = MPL MPK ). As a manager, your job is determine the long-run and short-run costs, given that wage rate w = $10 and rental rate r = $15. Suppose in the short run, the capital of grills used by HH is ?xed at 4, answer part a and b.
a. How much labor HH should employ to produce 100 units of output? How much does it cost in the short run?
b. How much labor HH should employ to produce 200 output? How much does it cost?
Now consider in the long run, and both K and L are variable inputs, answer the following questions.
c. What is the cost-minimizing combination of labor and capital HH should use to produce 100 units of output in the long run? How much does it cost in the long run?
d. What is the cost-minimizing combination of labor and capital HH should use to produce 200 output? How much does it cost?
e. Given the calculation from the short-run and long-run scenario, what makes the long-run costs are less than (or equal to) the short-run?