Question

In: Economics

Suppose that market demand for a good is Q = 480 - 2p. The marginal cost...

Suppose that market demand for a good is Q = 480 - 2p. The marginal cost is MC = 2Q. Calculate the following in the context of a monopoly market. a) Profit maximizing price and quantity. b) Market power. c) Consumer surplus and producer surplus. d) Dead Weight Loss (DWL).

Solutions

Expert Solution

Q = 48 - 2p

2p = 48-Q

p = 24 - 0.5Q

Mc = 2Q

a) Profit maximizing price and quantity is where MR = MC

MR = d(TR)/dQ

TR = P*Q = 24Q - 0.5Q2

MR = 24 -Q

MR = MC

24-Q = 2Q

24 = 3Q

8 =Q

P = 24 -0.5*8 = $20

MC =2*8 = 16

b) Market power = (P-MC)/ P = (20-16)/20 = 4/20 = 0.2 = 20%

c) P = 24 -0.5Q

When Q = 0, P = 24

Consumer surplus = (1/2)*(24-20)*8

= $16

When Q = 0. MC = 0

Producer surplus = (1/2)*(20-0)*8 = $80

d) Dead weight loss = (1/2)*(20-Pc)*(Qc-8)

Pc = price of competitive market

In competitive market,

P = MC

24-0.5Q = 2Q

24 = 2.5Q

Qc = 9.6

Pc = 24-0.5*9.6

= 19.2

Dead weight loss = (1/2)*(20-19.2)*(9.6-8) = $0.64

Rahul Sunny answered 2 years ago

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