Question

Joyce is operating a sushi restaurant in a small town. She is a monopolist. Her total cost function is C = 50Q − Q2and the demand function is P = 80 − 4Q. Provide a fully labeled diagram and simple calculations to illustrate and quantify how price, quantities, profits and the monopoly efficiency loss would be affected if the firm could implement a Two-Part Tariff.

Answer 1

Solution:

$$MC=C{\prime}=50-2Q$$

$$MC=p$$

$$50-2Q=80-4Q$$

$$2Q=30$$

$$Q=15; p=20$$

Then $Pr=TR-TC$

$$TR=p \times Q=300$$

$$TC=50Q-Q^2=50\times 15 - 15^2=750-225=525$$

$$Pr=300-525=-225$$

Now the company is operating at a loss. If the firm could implement a Two-Part Tarif:

p=40; Q=10.

$$TR=40 \times10=400$$

$$TC=50\times10 - 10^2=400$$

Get the breakeven point.