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assume that a monopolist faces a demand curve Q =200 - 10P, and marginal cost of...

assume that a monopolist faces a demand curve Q =200 - 10P, and marginal cost of $15. Compared with the perfectly competitive market's price, assuming the same demand function and costs hold true, what is the Monopolist's mark up? What is the deadweight loss from Monopoly pricing

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Answer #1

Q = 200 - 10P

10P = 200 - Q

P = 20 - 0.1Q

Monopolist maximizes profit by equating Marginal revenue (MR) with Marginal cost (MC).

Total revenue (TR) = P x Q = 20Q - 0.1Q2

MR = dTR/dQ = 20 - 0.2Q

Equating with MC,

20 - 0.2Q = 15

0.2Q = 5

Q = 25

P = 20 - (0.1 x 25) = 25 - 2.5 = $22.5

Mark-up (Over cost) = (P - MC) / MC = $(22.5 - 15) / $15 = $7.5 / $15 = 0.5 (= 50%)

In perfect competition, profit is maximized by equating Price with MC.

20 - 0.1Q = 15

0.1Q = 5

Q = 50

P = MC = $15

Deadweight loss = (1/2) x Difference in price x Difference in quantity = (1/2) x $(22.5 - 15) x (50 - 25)

= (1/2) x $7.5 x 25 = $187.5

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