Question

suppose a monopolist sells to two types of customers: type A and type B. (For simplicity, suppose there is only one type A customer and one type B customer. Type A's inverse demand is described by pa = 200-2Qa. Type B's inverse demand is described by Pb= 200-4Qb. The monopolist's marginal cost is zero. suppose the monopolist can not price discriminate. find the optimal price, quantity, and profit.​

Answer 1

Pa = 200-2Qa

Pb= 200-4Qb

MC = 0

Optimal profit is where MC = MR, so MR = 0

If there is no price discrimination Pa = Pb = P

For customer type A

P = 200-2Qa

Total Revenue TR = Price (P) x Quantity (Q)

P = 200Qa – 2Qa^2

MR = dTR/dQa = 200 – 4Qa

But MR = 0

200 – 4Qa = 0

4Qa = 200

Qa = 50

For customer type B

P = 200-4Qb

Total Revenue TR = Price (P) x Quantity (Q)

P = 200Qb – 4Qb^2

MR = dTR/dQb = 200 – 8Qb

But MR = 0

200 – 8Qb = 0

8Qb = 200

Qb = 25

So Quantity to be sold to customer type A = 50 and customer type B = 25

So Total Quantity = 75

Price P = 200 – 4(25)

Price (P) = 100

Total Revenue = Price x Quantity

= 75 x 100

= 7,500

And since there is no additional cost on these quantities Profit = 7,500