Consider a monopolist who face the following market demand curve: Q. 100 - 0.5 p

Question

Consider a monopolist who face the following market demand curve: Q. 100 - 0.5 p, 0 lessthanorequalto p lessthanorequalto 200 = 0, p > 200. The monopolist's cost function is TC(Q) - 20 Q + Q^2 1.1 What is the profit maximized uniform price? 1.2 Calculate the profit at the price obtained in 1.1 abovo. 1.3 Explain how the potential welfare of this market is distributed under uniform price. 1.3 What would be the profit maximized level of output if the firm price discriminates in the first degree? 1.4 Calculate the profit level at the output obtained in 1.3 above. 1.5 Explain how the potential welfare of this market is distributed under perfect price discrimination.

Explanation / Answer

Q = 100-0.5P

P = 200-2Q

TR = PQ = 200Q-2Q2

MR = 200-4Q

TC = 20Q+Q2

MC = 20+2Q

1.1

The monopolist will produce where MR = MC

200-4Q = 20+2Q

180=6Q

Q = 30

P = 200-2*30 = $140

1.2

profit = TR-TC

=140x30 -20x30-900

Profit = $2700

1.3

Consumer surplus = 0.5 x(P at Q=0 - P) x Q

=0.5x (200-140) x30

=900

Producer surplus = 0.5xPxQ

=0.5x140x30

=2100

1.3

AT first degree the firm produces output at all level till P = MC

200-2Q = 20+2Q

180 =4Q

Q = 45

1.4

AT first degree price discrimination all surplus is producer surplus/profit is area below demand curve and above marginal cost

= (Demand price at Q=0- supply price at Q=0) x 45 quantity

= (200-0) x 45 = 9000

1.5

The consumer gets zero surplus all 9000 surplus is enjoyed by producer.

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