Question

3. Suppose the firm in monopolistic market faces the following demand function: Q = 5,000 - 125P ; and total cost function TC - 50 +0.00802 a. Write the equation for the inverse demand function. (1 pt) b. Find the marginal revenue function. (1 pt) c. How much output should the manager produce to maximize profit? What price should be charged for the output? (2 pt) d. Calculate the marginal cost function. (2 pt)

Answer 1

a)

Q=5000-125P

On rearranging we get

125P=5000-Q

P=40-0.008Q

Inverse demand function is given by

P=40-0.008Q

b)

Total Revenue=P*Q=(40-0.008Q)*Q=40Q-0.008Q²

Marginal Revenue=MR=dTR/dQ=40-0.016Q

c)

TC=50+0.008Q²

Marginal Cost=MC=dTC/dQ=0.016Q

Set MC=MR for profit maximization

0.016Q=40-0.016Q

0.032Q=40

Q=1250

P=40-0.008Q=40-0.008*1250=$30

Profit maximizing price=$30

Profit maximizing output=1250 units

d)

We have determined in part c that

Marginal Cost=MC=dTC/dQ=0.016Q

e)

At optimal price output combination

Total Revenue=TR=P*Q=30*1250=$37500

Total Cost=TC=50+0.008*Q2=50+0.008*1250²=$12550

Profit=TR-TC=37500-12550=$24950

f)

Firm is making positive economic profit in short run. Other firms will enter the market. Price and hence Profit will come down. Firm will make zero economic profit in long run like a perfect competitive firm.

Firm will make normal profit (zero economic profit) only in long run.