Question

A monopolist’s cost function yields constant average and marginal costs, with AC = MC = 5. The firm faces a market demand curve given by P = 29 – Q.
a) Calculate the marginal revenue curve, MR, for the monopoly.
b) Solve for the monopolist’s profit maximizing output and price and calculate the Lerner’s index and the profit of the monopolist. Show the profit maximizing decision of the monopolist and the profits earned diagrammatically.
c) What would be the socially optimal output and price? (Hint: this would be the output and price if the industry were perfectly competitive. That is, the profit maximizing rule would be P =MC)
d) Show diagrammatically the social cost of a monopoly.{Extra Credit: Calculate the social cost of monopoly.}

Answer 1

Answer:

a. Marginal Revenue = 5  

b. Maximum profit = $144

c. Q optimum = 12 ; P optimum = $17

d. Social cost = $72

Explanation:

Step 1. Given information.

• MC=AC=5

• P=29-Q

Step 2. Formulas needed to solve the exercise.

• Total Revenue=TR=P*Q=(29-Q)*Q=29Q-Q2  

• Marginal Revenue=dTR/dQ=29-2Q

Step 3. Calculation.

Set MR=MC for profit maximization  

29-2Q=5  

2Q=29-5

Q=12 -----profit maximizing output

P=29-Q=29-12=$17 -------profit maximizing price

Total Profit=(P-AC)*Q=(17-5)*12=$144 ------Maximum Profit

Lerner's Index=(P-MC)/P=(17-5)/17=0.7059

TAKE A LOOK TO THE ATTACHED IMAGE

Profit is shown by rectangular shaded area.

Socially optimal price P=MC=$5 --------Socially optimal price

We know P=29-Q, Set P=5

5=29-Q

Q=24 ---------Socially optimal output

Social Cost is equal to dead weight loss. It is shown by triangular area DWL

Social Cost=1/2*(17-5)*(24-12) =$72