2 A monopoly faces an inverse demand curve P A Q in market

2. A monopoly faces an inverse demand curve, P = A -Q in market A. The total cost function is C(R) = 2Q+ 2401, and the opportunity cost of doing business in market A is normalized to 0. (a) (10) If the firm is unregulated and producing Q = 49 units, then what is A? (b) (10) If the regulator\'s objective is to maximize social welfare, what price will she ask the firm to charge? At this price, will the firm participate in this market? [Note: Use A from part (a)]. (c) (10) Suppose instead the regulator tries to minimize the deadweight loss, while en- couraging the firm to participate in the market. What would the price be in this case? Does such regulation have any value for social welfare?

Solution

a) When Q = 49, the unregulated monopoly produces where MR = MC. Here MR = A - 2Q. MC is constant at $2. Find the value of A

A - 2Q = 2

A - 2*49 = 2

This gives A = 100

b) Social welfare is maximum when there is allocative efficiency implying that P = MC

100 - Q = 2

Q* = 98 and Price P = $2 per unit. This is not sustainable because the fixed cost of monopoly which is $2401 is not covered. Hence monopoly will not produce at this price.

c) To minimize the deadweight loss and still have the monopoly operating, the most the government can do is to charge a price equal to average cost.

P = AC

100 - Q = (2Q + 2401)/Q

100Q - Q^2 = 2Q + 2401

This becomes a quadratic equation Q^2 - 98Q + 2401 = 0

This gives Q = 49 and price is 100 - 49 = $51

This is the monopoly\'s outcome and hence there is no value for this regulation on social welfare because it is ineffective for the monopoly to reduce the deadweight loss it creates.