Question

Consider a monopolistic competitor with TC= 100-4Q+Q^2.  Suppose that the demand for their version of the product is P= 50-3Q.

1. What quantity maximizes their profits?
2. What price do they charge?
3. What profits do they earn in the short run?
4. What will happen to their profits in the long run?

Answer 1

A) Total revenue ( TR) = P Q

= (50 - 3Q) * Q = 50Q - 3Q^2

Marginal revenue ( MR) = dTR / dQ = 50 - 6Q

TC= 100-4Q+Q^2.

MC = dTC / dQ = -4 + 2Q

At Profit maximization MR = MC

50 - 6Q = -4 + 2Q

8Q = 54 implies Q = 6.75

B) P= 50-3Q.

= 50 - 3*6.75 = 29.75

C) profit = 29.75* 6.75 - ( 100 - 4( 6.75) + ( 6.75)^2)

= 82.25

D) profits in the long run will be zero.

Since there is free entry and exit of firms which means new firms enter the market when profit is Positive and existing firms exit the market when there are losses. So the economic profit is zero in the long run.