Suppose a Price-Taking Firm Uses a Single Input - Labor

Essay

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 π < π'< π" -- indicating slopes and intercepts.Suppose the profit maximizing plan results in profit π'.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.