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.
1. Under no price-discrimination
"TR= P\\times Q = 300Q \u2013 Q2; MR = 300 \u2013 2Q"
Set MR = MC; 300 – 2Q = 2Q ; Q = 75.
Hence, Q* = 75
Replace Q*=75 to market demand equation;
"P^* = 300 \u2013 75 = 225."
Hence,"P^* = 225"
"CS =\\frac{1}{2} \\times (300 \u2013 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
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