Question

Question 2 (35 points): (3rd Degree Price Discrimination) Let there be a monopolist firm and two groups of consumers. Suppose that marginal cost is defined by MC- 2. The demand that each consumer receives is given by 1 50- P 2Q2- 200 - P2 i) (4 points) Consider the monopolist engages in first degree price discrimina- tion only in market 2. Compute the monopoly profit in this market. ii) (4 points) Which group has a more inelastic demand curve? Why?

Please answer clearly and explain. Thank you!

Answer 1

(i)

With first degree price discrimination, Price = MC and profit equals entire consumer surplus (CS).

2Q2 = 200 - p2

p2 = 200 - 2Q2

Equating with MC,

200 - 2Q2 = 2

2Q2 = 198

Q2 = 99

P = MC = 2

When Q2 = 0, p2 = 200 (Vertical intercept of demand curve)

Profit = CS = Area between demand curve and price = (1/2) x (200 - 2) x 99 = (1/2) x 198 x 99 = 9,801

(ii)

With third-degree discrimination, profit is maximized when MR1 = MC and MR2 = MC.

In market 1,

Q1 = 50 - p1

p1 = 50 - Q1

Total revenue (TR1) = p1 x Q1 = 50Q1 - Q1²

MR1 = dTR1/dQ1 = 50 - 2Q1

50 - 2Q1 = 2

2Q1 = 48

Q1 = 24

p1 = 50 - 24 = 26

Elasticity of demand = (dQ1/dp1) x (p1/Q1) = -1 x (26/24) = -1.08

In market 2,

2Q2 = 500 - p2

Q2 = 250 - 0.5p2

p2 = 200 - 2Q2

TR2 = p2 x Q2 = 200Q2 - 2Q2²

MR2 = dTR2/dQ2 = 200 - 4Q2

200 - 4Q2 = 2

4Q2 = 198

Q2 = 49.5

p2 = 200 - (2 x 49.5) = 200 - 99 = 101

Elasticity of demand = (dQ2/dp2) x (p2/Q2) = -0.5 x (101/49.5) = -1.02

Since absolute value of elasticity is lower in market 2 (1.02 < 1.08), demand is more inelastic in market 2.