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 + Q(squared).

1. Find the inverse demand function for your firm’s product.
2. Determine the profit-maximizing price and level of production.
3. Calculate your firm’s maximum profits.
4. What long-run adjustments should you expect? Explain

Answer 1

Solution :-

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

Q = 36 - 4P and C(Q) = 4 + 4Q + Q^2

(a) The inverse demand function for the firm's is given by:

Q = 36 - 4P

4P = 36 - Q

P = 36/4 - Q/4

P = 9 - 0.25Q (This is the required inverse demand function)

(b) profit-maximizing price and level of production;

At the profit-maximizing level of production,

MR = MC

MR = P×Q = (9-0.25Q)Q = 9Q - 0.25Q^2 ———(1)

Differentiating equation 1 w. r. t Q

MR = 9-0.50Q

Now the total cost is given as,

C (Q) = 4 + 4Q + Q^2 ————(2)

Differentiating equation 2 w.r.t Q

MC = 4+2Q,

For 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) firm’s maximum profits :-

The maximum profit will be

PQ - C

= 8.5*2 - 4 - 4×2 - 2^2

= $1

Therefore the maximum profit will be $1

(d) long-run adjustments:

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