Question

A monopolist has the following information, where Q is the quantity of goods and

P is the price:

Market Demand: P = 300 -Q

Marginal Cost: MC = 2Q

Total Cost: TC = 2 +Q~2

No price discrimination: calculate Q", P*, CS, PS, DWL

Perfect price discrimination: calculate Q", P*, CS, PS, DWL

Second-degree price discrimination: calculate $275, $250, $225, $200 for

each first, second, third, forth of 25 units block.

Answer 1

1. Under no price-discrimination

$TR= P\times Q = 300Q – Q2; MR = 300 – 2Q$

Set MR = MC; 300 – 2Q = 2Q ; Q = 75.

Hence, Q* = 75

Replace Q*=75 to market demand equation;

$P^* = 300 – 75 = 225.$

Hence,$P^* = 225$

$CS =\frac{1}{2} \times (300 – 225)\times 75 = 2812.5$

$PS = \frac{1}{2}\times 150\times 75 + (225-150) \times75 =1125$

$DWL = \frac{1}{2} \times(225-150) \times (100-75) = 937.5$

2. Under perfect price-discrimination

P = MC; 300 – Q = 2Q; Q=100. Hence, Q* = 100

Replace Q* = 100 to market demand equation;

P* = 300 – 100 = 200. Hence, P*=200

CS = 0

PS =$\frac{1}{2} \times 300 \times100 = 15000$

DWL = 0

3. Under second degree price-discrimination:

$TR = 275\times25 + 250\times25 + 225\times25 + 200\times25 = 6,875 + 6,250 + 5,625 + 5,000 = 23,750$

$TC = 2 + 100\times100 = \$10,002$

Profit = 23,750 - 10,002 = 13,748

CS = sum of violet triangle =$\frac{1}{2} \times(300-275) \times 25 \times 4 = 1250$

DWL = 0

PS = Profit = 13,748