The table below represents the production function for Hawg Wild, a small catering company specializing in barbecued pork. The numbers in the cells represent the number of customers that can be served with various combinations of labor and capital.
(a) Is this production function a short-run or long-run production function? How can you tell?
(b) Suppose that Hawg Wild employs 5 units of capital and 2 workers. How many diners will be served?
(c) Suppose that Hawg Wild employs 5 units of capital and 2 workers, but that the owner, Billy Porcine, is considering adding his nephew to the payroll. What will the marginal product of Billy’s nephew be?
(d) Notice that when Hawg Wild uses 1 unit of capital, the marginal product of the fifth unit of labor is 16. But when Hawg Wild uses 5 units of capital, the marginal product of the fifth unit of labor is 43. Does this production function violate the law of diminishing marginal product of labor? Why or why not?
(e) Suppose that Hawg Wild employs 5 units of capital and 2 workers, but that the owner, Billy Porcine, is considering adding another meat smoker to the kitchen (which will raise the amount of capital input to 6 units). What will the marginal product of the smoker be?
(f) Hawg Wild employs 5 units of capital and 2 workers. Billy is considering the choice between hiring another worker or buying another smoker. If smokers cost $8 and workers $12, then at the margin, what is the most cost-effective choice for Billy to make?