Question

Problem 8:

Consider a monopolistic competitor with TC = 100 - 4Q + Q² . Suppose that the demand for

their version of the product is P = 50 - 3Q .

a) What quantity maximizes their profits?

b) What price do they charge?

c) What profits do they earn in the short run?

d) What will happen to their profits in the long run?

Answer 1

A) a profit maximizing monopolistic competitive firm produces at the point where MR=MC and sets it's profit maximizing price at the point where it's profit maximizing output lies on the demand curve.

Here, TC = 100 - 4Q + Q²

Or, MC = d(TC)/dQ = 2Q - 4

And, demand equation is given as: P = 50 - 3Q

Multiplying both sides by Q we get,

PQ = Total revenue (TR) = 50Q - 3Q²

Or, MR = d(TR)/dQ = 50 - 6Q

Setting MR = MC we get,

50 - 6Q = 2Q - 4

Or, 8Q = 54

Or, Q = 6.75

Therefore, the firm has to produce 6.75 units in order to maximize profit.

B) when Q = 6.75, from demand equation we get, P = 50 - (3*6.75) = $29.75

Answer: $29.75

C) in short run, total revenue = P*Q = $(29.75 * 6.75) = $200.8125

TC = 100 - (4*6.75)+ (6.75)² = $118.5625

Profit = TR - TC = $82.25

D) in long run a monopolistically competitive firm earns zero economic profit, because in Long run other firms will enter the market which will decrease market demand and eventually, at the profit maximizing output level, price will be equal to ATC. That is, TR = TC. This will happen because of the "free entry and exit" characteristics of monopolistic competitive market.