Detail

In this case, we are given numerical data about a firm in a perfectly competitive industry.

We know that the firm can sell 1000 units at a price of $3 per unit, giving it a total revenue of $3,000. We also know that its total cost is $6,000 and its fixed costs is $2,000. We're told that marginal cost is $3 but we could have guessed that since the price is $3 and profit maximization means it will produce where MC = P.

Since total revenue is $3,000 and total cost is $6,000 there is no question the firm should shut down in the long run. Even though we've said that some firms will stay in business in the long run this is the best guess on a question such as this when profits are negative. What about the short run?

We learned that a firm should shut down in the short run if P < AVC; however, we aren't told variable costs in this question. Nevertheless, we have enough information to determine what they are. If total cost is $6,000 and fixed cost is $2,000 the difference must be variable costs, which are $4,000. Since total revenue is below even variable cost, the firm should shut down in the short run too. A firm that shuts down in the short run can be assumed not to be around in the long run anyway, at least for the purposes of a test.

3. A firm in a perfectly competitive industry finds itself in the following position: output =1000 units, market price = $3, total cost = $6,000, fixed cost = $2,000, marginal cost = $3. If the firm behaves as a profit maximizer, it should:

should reduce output in the short run, but should increase output in the long run. Since the firm is producing where P=MC it shouldn't reduce output; however, it should shut down in the short run, and since profit is negative it will shut down in the long run.
should shut down in the long run, but continue producing output in the short run. As we said above, even in the short run P < AVC, so the firm should shut down in both short and long run.
should shut down in the long run, and shut down in the short run.
should increase output in the short run, but reduce output in the long run. It never makes sense to change output when P=MC. If the firm increased output the MC of the extra units would be greater than price and the firm would be worse off.
should shut down in the short run, but continue producing output in the long run. As we said above, a firm that shuts down in the short run can be assumed not to be around in the long run, at least for the purposes of a test.