Question

You are the manager of a monopolistically competitive firm, and your demand and cost functions are given by Q = 36 – 4P and C(Q) = 4 + 4Q + Q².

a. Find the inverse demand function for your firm’s product.

P = - Q


b. Determine the profit-maximizing price and level of production.

Instruction: Price should be rounded to the nearest penny (two decimal places).

Price: $

Quantity:


c. Calculate your firm’s maximum profits.

Instruction: Your response should appear to the nearest penny (two decimal places).

$


d. What long-run adjustments should you expect? Explain.

Neither entry nor exit will occur.

Entry will occur until profits are zero.

Exit will occur until profits rise sufficiently high.

Answer 1

The firm operates in a monopolistically competitive market and faces a demand and cost functions

Q = 36 – 4P and C(Q) = 4 + 4Q + Q2.

a. The inverse demand function for your firm’s product is given by

Q = 36 - 4P

4P = 36 - Q

P = 36/4 - Q/4

P = 9 - 0.25Q.

This is the inverse demand curve.

b. At the profit-maximizing level of production, MR = MC

9 - 0.5Q = 4 + 2Q

5 = 2.5Q

Q = 2 units and P = 8.5

Hence the Price is $8.5 per unit and Quantity is 2 units.

c. The profits are Revenue - costs

PQ - C

= 8.5*2 - 4 - 4*2 - 2*2.

= $1

Profit is $1.

d. In the long-run adjustments we expect Entry will occur until profits are zero.