Question

In a perfectly competitive industry, each firm has a total cost function of TC = 400 + 10q + q2 and a marginal cost curve of MC = 10 + 2q if it produces a positive quantity of output q. If a firm produces zero output it has no costs. The market price is $50. Which statement is true?]

a. Each firm produces 20 units of output; the industry will require entry to reach its long-run equilibrium.

b. Each firm is producing 25 units; as the firm is making short-run profits, the industry is not at its long-run equilibrium.

c. Each firm is producing 25 units; the firm is covering its variable costs, but making a short run loss.

d. Each firm is producing 20 units; the firm will continue producing in the short run, but will consider exiting in the long run as it is not covering its total costs of production.

e. Each firm produces 20 units of output; the market is in its long-run equilibrium.

Answer 1

In order to maximize profit a perfect competitive firm produces that quantity at which P = MC where P = Market Price = 50 and MC = Marginal Cost = d(TC)/dq = 10 + 2q

In Long run equilibrium each perfect competitive firm earns 0 profit because of they earn positive profit then new firm will enters resulting in increase in market supply and thus resulting decrease in price till the point comes when they each started earning 0 profit. Similarly if they earn negative profit then existing firm will exit the market resulting in decrease in market supply and thus resulting increase in price till the point comes when they each started earning 0 profit.

So In Long run equilibrium we have Profit = 0

Now, according to above profit maximizing condition we have P = MC => 50 = 10 + 2q => q = 20

So, each firm will produce 20 units.

Profit = Total Revenue - Total Cost.

Total Revenue = P*q = 50*20 = 1000 and Total Cost = TC = 400 + 10*20 + 20^2 = 400 + 200 + 400 = 1000

=> Profit = 1000 - 1000 = 0.

Thus each firm is earning 0 profit and thus they are in long run equilibrium. Thus option (e) is the correct answer.

Hence, the correct answer is (e) Each firm produces 20 units of output; the market is in its long-run equilibrium.