Question

Suppose in the short run a perfectly competitive firm has the total cost function: TC(Q)=675 + 3q2 where q is the firm's quantity of output. If the market price is P=240, how much profit will this firm earn if it maximizes its profit?

b) how much profit will this firm make?

c) Given your answer to b), what will happen to the market price as we move from the short run

to the long run?

d) What is the break-even price for this market?

Answer 1

A profit maximizing perfectly competitive firm produces at the point where market price = MC.

Given that, TC = 675 + 3q²

Or, MC = d(TC)/dq = 0 + 6q = 6q

Therefore, at profit maximizing point, 6q = 240

Or, q = 40

Therefore, profit maximizing quantity is 40 units.

Total revenue = price * quantity = $(240 * 40) = $9600

Total cost = 675 + 3(40)² = $5475

Profit = TR - TC = $(9600 - 5475) = $4125

Therefore, when the firm maximizes it's profit, it's profit is $4125.

B) The firm makes a profit of $4125.

C) As we move from the short run to the long run, the super normal profit earned by this perfectly competitive firm will attract other firms to the industry. Therefore, market supply will increase and as a result, equilibrium market price will decrease. Price will decrease until it is equal to minimum ATC, so that in long run equilibrium, each firm earns zero economic profit.

D) At break even point, TR = TC. Or, Price = ATC. This happens when price = minimum ATC for a perfectly competitive firm. Because, when ATC is at it's minimum, price = MC = ATC.

Given that, TC = 675 + 3q²

Or, ATC = (TC/q) = (675/q) + 3q

When ATC is minimized, d(ATC)/dq = 0

Or, -(675/q²) + 3 = 0

Or, (675/q²) = 3

Or, q² = 225

Or, q = 15

When q = 15, ATC = (675/15)+(3*15) = $(45+45) = $90

Therefore, break even price for this market is $90