Question

Elina runs a firm in a competitive industry. Her cost function is c(y) =200 + 2y², where y is the level of output. If the output price is $40, which statement is true?

a.In the short run the firm will produce an output of 10 units, however in the long run the firm will exit.

b.In the short run the firm will make zero economic profits; in the long run the firm will continue to produce and will make zero economic profits.

c.The firm will shut down in the short run; at a price of $40 the firm will exit in the long run

d.The firm will produce 160 units in the short run; this outcome coincides with the long run equilibrium.

e.The firm will make economic profits in the short run; the firm will exit in the long run.

Answer 1

Given: c(y) = TC = 200 + 2y² and P = $40

Here, MC = dTC/dy = 4y

AC = TC/y = (200/y) + 2y

In short run, the equilibrium for perfectly competitive firm is given by:

P = MC

40 = 4y

y = 40/4

y = 10 units

Now, at y = 10,

TR = P * y = 40 * 10 = $400

TC = 200 + 2(10)² = $400

So, firm is earning normal profits or zero economic profits in the short-run.

In the long-run, at y = 10,

AC = (200/10) + (2*10)

AC = 20 + 20

AC = $40

Thus, P = AC, so the firm will continue to operate in the long-run. Since TR = TC, it will earn zero economic profits in the long-run also.

The answer is: (b) In the short run the firm will make zero economic profits; in the long run the firm will continue to produce and will make zero economic profits.