Question

A competitive firm has a marginal cost equal to: MC(y)=3y, where y is the output level. The intersection of the average cost and the marginal cost happens at output level equal to 4. How much will the firm produce in the long-run at price equal to $9?

Answer 1

Since in the perfectly competitive firm, there are large number of buyers and sellers and they sell identical product and price is determined by industry and not by the firm. So any firm or any buyers can buy or sell any quantity of goods at the market price. It means there is no effect of the individual demand or supply of goods on the market price. It means production decisions cannot affect the market price. There is perfect information about the product to the buyers and sellers.

The profit-maximizing condition of perfectly competitive firm is

P=MC

In the long-run profit-maximizing condition is

P=minimum of (ATC)=MC

As it has been given that a competitive firm has a marginal cost equal to: MC(y)=3y, where y is the output level. The intersection of the average cost and the marginal cost happens at output level equal to 4.

Since at Q=4 units

MC=ATC

MC always cuts ATC at ATC minimum point.

Since if the price is $9, then in the long-run, firm will produce 4 units of output for maximizing output level in the long-run.

Hence in the long-run firm will produce 4 units.