1.Suppose that The Acme Widget Co. uses capital (K) and labor (E) are used to produce widgets, and that the production function for widgets is given by Q=K^(1/3)E^(1/2). Suppose that r=$1 and w=$4, where r is the price of capital and w is the wage rate. Finally, suppose also that the price of widgets, p, is $8.
a.Suppose K=8 in the short run, plot this firm’s short-run labor demand curve.
b.Given that w=4, how many workers should this firm hire in the short run?
c.What are the firm’s profits in the short run?
d.Now find the optimal quantity of labor and capital in the long-run.
e.What are the firm’s profits in the long-run?
f.Finally, suppose that the price of labor increases so that w=6. What is the firm’snew optimal quantity of labor and capital (in the long run)?
g.Are capital and labor gross substitutes or gross complements? Explain.