A firm has production function f(K; L) = squarerootKL. In the short run, the rm has capital K = 400; this cannot be changed in the near future. The cost of a unit of capital is $20, while the cost of a unit of labor is $30.
a. In the short-run, where capital is xed at K = 400, how much labor does the rm need to employ in order to produce q = 300 output? What is the cost of producing 300 output?
b. Repeat part a for q = 400, q = 500 and q = 600.
c. What is the cost of producing q output in the short-run?
d. What is the marginal cost of producing a 301s unit? A 401st unit? If you are comfortable doing so, you may answer this question by writing down the marginal cost function directly, rather than recalculating total cost for q = 301 and q = 401.
e. Given your answer to part c, draw a graph with the rm's average total cost, average variable cost, and marginal cost (hint: MC = Q(3/20) )