Suppose a price-taking firm uses a single input – labor – to produce an output x. The production technology has diminishing marginal product of labor throughout.
a. On a graph with labor hours on the horizontal and output on the vertical axis, illustrate the production frontier for this firm.
b. For a given wage rate w and output price p, illustrate three isoprofit curves corresponding to profit levels < ’< ” — indicating slopes and intercepts. Suppose the profit maximizing plan results in profit ’. Then use isoprofit to illustrate the profit maximizing production plan for the firm and show how w and p are related to the marginal product of labor at that plan.
c. Where on your graph do all cost-minimizing production plans lie?
d. On a graph with output on the horizontal and dollars on the vertical axis, illustrate the shape of the cost curve for the firm (holding fixed w). Then suppose that, in addition to labor costs, the firm has to pay a recurring (long run) fixed cost F. Where does the long run cost curve lie in relation to the initial (short run) cost curve you drew?
e. On a separate graph, illustrate the short run marginal and average cost curves. Then, on the same graph illustrate the long run marginal and average cost curves in the presence of the recurring fixed cost.
f. Indicate where in your graph you can locate the short and long run supply curves for this firm.
g. Call the industry in which our firm operates industry A. There is a second industry B that produces a different good y. Suppose that firms in industry B are identical to firms in industry A in the sense that they face the same production technology, the same prices w and p, and the same recurring fixed cost F. The only difference between industry A and industry B is that the market demand in industry A is shallower than the market demand in industry B – i.e. consumers in industry A are more responsive to price changes than consumers in industry B. Consider firm 1 operating in industry A and firm 2 operating in industry B. When both industries are in long-run equilibrium, do firms 1 and 2 produce the same level of output and sell that output at the same price? Explain.
h. Suppose that all firms in these two industries rely exclusively on minimum wage workers. Now the government raises the minimum wage. We notice that, as a result of this increase in the minimum wage, each individual firm in both industries produces less in the new long run equilibrium. If the total number of firms across both industries A and B (together) remained the same, what happened to the number of firms in industry A and what happened to the number of firms in industry B?
b. At the profit maximizing production plan A,
c. All production plans that lie on the production frontier are cost-minimizing.
g. Yes, because the long run equilibrium price is determined by the lowest point of the marginal firm’s long run AC curve — which is the same for firms in both industries.
h. The number went down in industry A and up in industry B — because the quantity demanded falls more in industry A than in industry B. Firms therefore exit industry A and enter industry B.