7) Suppose there are two types of people. Type 1 has the inverse demand function

Question

7) Suppose there are two types of people. Type 1 has the inverse demand function p1(y1) = 10 y1 (with MR = 10 2y1 and the second type has the inverse demand function p2(y2) = 5 y2 (with MR = 5 2y2. 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 = 0(T C = 0). a)What quantity and price is offered to each type? What is the profit b) Suppose that a monopolist cannot discriminate. Then they face the inverse demand p = 15/2y/2 (With MR = 15/2y) in this case what would be the common price and quantity sold? What would be the new profit?How do the two cases differ? c) Draw these graphically.

Explanation / Answer

a) IN type 1. , we do MR =M

MR = 10 - 2y1 = 0

y1 = 5 . and P1 = 10-y1 => 10 - 5 = 5

so, the quantity offered in type 1 is 5 units and price is $5.

since TC= 0. then total reveue is total profit .

profit = $25

in TYPE 2. we do MR= mC
MR = 5-2y2= 0

so, y2 = 2.5 and p2 = 2.5

so, the quantity is offered in type 2 is 2.5 untis and price is $2.5

profits = 2.5 *2.5 = $6.25

when there is no discriminatiing. , we do MR=MC
MR = 15/2 - y

15/2 -y = 0

Y = 7.5

P = 15/2 - y/2 = > 7.5 - 3.75 = $3.75

so, the common price is $3.75 and quantity sold = 7.5

profit = 7.5* 3.75 = $28.125

The profits has been decreases when there is no price discrimination.

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