A firm has a production function given by Q = K0.2L0.8. Suppose that each unit of capital cost is r and each unit of labor cost is w.
First, we focus on the producer behavior.
Solve the cost minimization problem and derive the optimal labor and capital, given a production level Q.
Derive the equation that represents the firm’s expansion path.
(Extra credit bonus question) Let CL(Q) denote the long-run cost function. This can be expressed as CL(Q) = Ccoef(r, w)Q. Note that Ccoef(r, w) only depends on r and w. Calculate Ccoef(r, w).
Next, introduce the market. The demand function is given by Q = 40 – 4P. Fix c = Ccoef(r, w) in (d), (e) and (f). Thus, the cost function is given by C(Q) = cQ, i.e., the marginal cost is c.
Suppose the market is perfectly competitive. Calculate the profit-maximizing price and quantity.
Suppose the market is monopolistic. Calculate the profit-maximizing price and quantity.
Following (e), suppose the market is monopolistic. Calculate the total surplus (TS).
(Extra Credit Bonus Question) Following (e) and (f), suppose the market is monopolistic. Instead of using the fixed marginal cost at c, use Ccoef(r, w) for the marginal cost. Calculate how many times the effect of 1% increasing in w on TS is compared to 1% increasing in r. (Evaluate the effect as a percentage.)