Question

As the manager of a monopoly, you face potential government regulation. Your inverse demand is P = 50 - 1Q, and your costs are C(Q) = 18Q.

a. Determine the monopoly price and output.

Monopoly price: $

Monopoly output: units

b. Determine the socially efficient price and output.

Socially efficient price: $

Socially efficient output: units

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

1. Monopoly Price is 34

Monopoly output is 16

2. Socially optimum price is 18

Socially optimum output is 32

3. The maximum amount that the firm is willing to spend on lobbying efforts to prevent the price from being regulated at the socially optimum level is $256

Explanation:

Given,

P (AR) = 50 – Q

Total Revenue (TR) = P*Q = 50Q – Q²

Marginal Revenue (MR) = dTR/dQ

MR = 50 – 2Q

Total Cost = C(Q) = 18Q

Marginal Cost (MC) = dC(Q)/dQ

MC = 18

At equilibrium, MR = MC

50 – 2Q = 18

32 = 2Q

Q = 16

Put the value of Q in the price equation

P = 50 -16

P = 34

Therefore,

Monopoly Price = 34 &

Monopoly Quantity = 16

Now, at socially optimum point firm charges price equals to Marginal Cost

50 – Q = 18

Q = 32

Put the value of Q in the price equation

P = 50 – 32 = 18

Therefore,

Socially optimum price = 18 &

Socially optimum quantity = 32

Profit equation (Total Revenue – Total cost) of the firm is as follows

Π = 50Q – Q² – 18Q

When firm is producing monopoly output, the total profits are

Π = 50*16 -16² – 18*16

= 800- 256- 288 = 256

When firm is producing socially optimum output, the total profits are

Π = 50*32 - 32² – 18*32

= 1600 – 1024 – 576 = 0

Therefore, the maximum amount that the firm is willing to spend on lobbying efforts to prevent the price from being regulated at the socially optimum level is $256 because this is the extra amount that the firm is getting if it is not charging socially optimum price and not producing socially optimum output.