Question

Consider a perfectly competitive market for fish, with the (unrealistic) assumption that fishing is non-random and so the individual firm Tim's Fresh Fish has a short-run total cost given by STC(q)=0.4q², where q is pounds of fish per day. The competitive market price is $8 per pound.

(a) What is the short-run marginal cost (SMC(q)) of this firm?
(b) What quantity should this firm catch and sell to the market each day to maximize profit?

Answer 1

The short-run marginal cost for Tim's Fresh Fish is 0.8q. To maximize profit, Tim's Fresh Fish should catch and sell 10 pounds of fish per day, where the marginal cost is equal to the market price of $8.

Step-by-step explanation:

A perfectly competitive firm in a market for fish faces a market price of $8 per pound. To determine the short-run marginal cost (SMC) of the individual firm Tim's Fresh Fish, we need to find the first derivative of the short-run total cost (STC) function. Taking the derivative of STC(q) = 0.4q², we get SMC(q) = 0.8q. So, the short-run marginal cost for Tim's Fresh Fish is 0.8q.

To maximize profit, a perfectly competitive firm sets its quantity where marginal cost (MC) equals the market price. In this case, MC = SMC = $8. Therefore, Tim's Fresh Fish should catch and sell a quantity of fish per day where SMC is equal to $8, which is 10 pounds of fish.