Question

As the manager of a monopoly, you face potential government regulation. Your inverse demand is P= 25-1Q, and your costs are C(Q)= 5 Q.

a. Determine the monopoly price and output

b. Determine the socially efficient price and output

c. What is the maximum amount your firm should be willing to spend on lobbying efforts to prevent the price from being regulated at the socially optimal level?

Answer 1

a. Solution: Monopoly price: $15; Monopoly output = 10

Working:

Revenue = Price * Quantity = (25-1Q) * 5Q = 25Q - Q^2

First derivative, MR = 25-2Q

Now C(Q)= 5 Q, it gives Marginal Cost = d(C(Q))/dQ = 5

At profit maximization, Marginal Revenue = Marginal Cost

Thus, 25 - 2Q = 5

It gives Q = 10

P = 25 - Q = 15

　

b. Solution: Socially efficient price: $5 ; Socially efficient output: 20

Working:

Inverse demand = 25 - Q

At social efficiency, MSB = MC, thus 25 - Q = MC

It gives Q = 20

P = 25 - Q = 25 -20 = 5

　

c. Solution: $50

Working: In order to prevent the price from being regulated at the socially optimal level, the firm would be willing to spend on lobbying efforts at:

= Monopoly revenue - Socially optimal revenue

= [15 X 10] - [20 X 5]

= 50