Consider a monopolist who is faced with the market demand curve P = 10 - Q. Its total cost is given by 2Q.

a. If the monopolist has to use one price, what would be profit maximizing price?

b. If the monopolist can use two part tariff, what would be the entrance (to the market) fee and the price for each unit of the good?

c. What is the difference between (a) and (b) from the perspectives of consumers, monopolists, and the society as a whole.

Answer:

(a) P = 10 - Q

TR = P * Q = 10Q - Q²

MR = 10 - 2Q

MC = 2

For equilibrium the condition is MR = MC

10- 2Q = 2

=> 2Q = 8

=> Q = 8/2 =4

P = 10 - 4 = $6

Profit = TR - TC = P*Q - 2Q = $6*4 = 2*4 = $16

(b) First equate P = MC

=> 10 - Q = 2

=> Q = 8

P = 10 - 8 = $2

Consumer Surplus = 0.5[ ($10 - $2) * 8] = $32

Because we don't have enough information about the number of consumers, we can only make guesses at the cover charge.

For example, suppose there are 20 consumers. If the seller sets the cover charge at $1.5 per person and there are 10 consumers willing to enter, then the firm can earn total profits of $30.

(c) Both will benefit.