Question

The inverse demand function for good X is P = 5−0.05Q. The firm’s cost curve is TC(Q) = 10 + Q

Suppose that, instead of the single-pricing, the monopolist can employ two-part pricing.

(1.18) (2 points) What is the profit maximizing level of output?

(1.19) (2 points) What is the fixed fee charged at the profit maximizing level of output?

(1.20) (2 points) What is the price charged at the profit maximizing level of output

Answer 1

(1.18)

In order to maximize profit under two part pricing a firm produces that quantity at which P(Price) = MC(Marginal Cost) and change price equal to marginal cost. Also it will charge entry fee or fixed fee equal to Consumer surplus.

MC = dTC/dQ = 1

P = MC => 5−0.05Q = 1 => Q = 80

Hence it will charge price = 1

Hence,Profit maximizing level of output = 80 units

(1.19)

As discussed above it will charge fixed fee = consumer surplus

Consumer surplus is the area below demand curve and above price line

Y intercept = P = 5 - 0.05*0 = 5

Hence consumer surplus = (1/2)(5 - 1)80 = 160

Hence Fixed Fee = 160

Hence,  the fixed fee charged at the profit maximizing level of output is 160.

(1.20)

As discussed above, In order to maximize profit under two part pricing a firm produces that quantity at which P(Price) = MC(Marginal Cost) and change price equal to marginal cost.

MC = dTC/dQ = 1

Hence, the price charged at the profit maximizing level of output is 1