Chapter 26) A monopoly faces an inverse demand curve, p(y) = 100 – 2y, and has c

Question

Chapter 26) A monopoly faces an inverse demand curve, p(y) = 100 – 2y, and has constant marginal costs of 20. Show your work.

What is its profit maximizing level of output?

What is its profit maximizing price?

What is the socially optimal price for this firm?

What is the socially optimal level of output for this firm?

What is the deadweight loss due to the monopolistic behavior of this firm?

Suppose this monopolist could operate as a perfectly discriminating monopolist and sell each unit of output at the highest price it would fetch. What would the deadweight loss be in this case? How do you know?

Explanation / Answer

P = 100 - 2y

MC = 20

(1) Profit is maximized when Marginal revenue (MR) equals MC.

Total revenue (TR) = p x y = 100y - 2y2

MR = dTR / dy = 100 - 4y

Equating with MC,

100 - 4y = 20

4y = 80

y = 20

(2) When y = 20,

P = 100 - (2 x 20) = 100 - 40 = 60

(3)

Socially optimum outcome is hen Price is set to MC, therefore socially optimal price is equal to 20.

(4)

When P = 20, we have

20 = 100 - 2y

2y = 80

y = 40 (Socially optimal output)

(5)

Deadweight loss = (1/2) x Difference in price x Difference in output

= (1/2) x (60 - 20) x (40 - 20) = (1/2) x 40 x 20

= 400

NOTE: As per Chegg answering guidelines, first 5 parts are answered.

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