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In: Economics

Suppose a monopolist is can price discriminate between two groups of consumers. Group 1 has demand...

Suppose a monopolist is can price discriminate between two groups of consumers. Group 1 has demand function given by P1 = 100-2Q1 and group 2 has demand function given by P2 = 200-4Q2. Suppose this monopolist has constant marginal cost of $20 and zero fixed cost.

Calculate consumer surplus, producer surplus, and total welfare in this market.

Expert Solution

The monopolist is charging different price from different markets. The monopolist will maximize profit at MR = MC

Equate it to MC

P1 = 100 - 2Q1 = $ 60 per unit

CS1 = (1/2)×(100-60)×20 = $ 400

PS1 = (100-20)×85 = $ 6800

Total surplus =$ 7200

Now calculate for market 2

Equate it to mc

P2 = 200 - 4×22.5 = 110 per unit

CS2 =0.5×(200 -110)×22.5 = $ 1,012.50

PS2 = (110-20)×22.5 = $ 2025

TS = $ 3,037.50

Now calculate the demand when P1 =P2 = P

P = 100 - 2Q1

Or, Q1 = 50 - 0.5P

P = 200 - 4Q2

Or, Q2 = 50 - 0.25P

Add these two equations we get

Q = 100 - 0.75P

P = (100 - Q)/0.75

Now equate it to MC

(100-Q)/0.75 = 20

100 - Q = 15

Qp = 85 units

P = $ 20

Total welfare under perfect competition = (1/2)×(133.33 - 20)×85 = $ 4,816.67

Rahul Sunny answered 2 years ago

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Suppose a monopolist is can price discriminate between two groups of consumers. Group 1 has demand...

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