emand 8) (10 points) Suppose there are two types of people. Type 1 has the inver

Question

emand 8) (10 points) Suppose there are two types of people. Type 1 has the inverse d function pi(vi) 200- (with MR 200-2n and the second type has the inverse demand function m(yn) = 100-12 (with MR = 100-Zy2. Suppose that the firm can charge a different price to each group (third-degree price discrimination) and that the firm faces the same marginal cost for each type MC = 20, with total cost given by (TC = 20( +9)). a)What quantity and price is offered to each type? What is the profit b) Suppose that a monopolist cannot discriminate. Define y (n + 3) Then they face the inverse demand p 150-y/2 (With MR-150-y) in this case what would be the common price and quantity sold? What would be the new profit? c)Explain in words how the two cases differ and why

Explanation / Answer

a) IN type 1.

MR=MC, => 200-2y1 = 20 so , y1 = 90

p1 = 200-90= $110

IN type 2.

MR=MC , => 100-2y2 = 20 . or y2 = 40

p2 = 100-40= $60

profits = TR in type 1 + TR in type 2 - TC

Profits = 9900 + 2400 - ( 20(130)

profits = 12300 - 2600 = $9700

b) When it cannot discriminate.

MR=MC => 150-y =20 or y= 130

p= 150-65 = $85

profits = (130*85) - (20(130)

profits = 11050 - 2600= $8450

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