Question

Stewie is the only supplier of Cold Hwhip in Quahog, giving him a monopoly. His only customer, Meg, has inverse demand given by p = 8 − q and Stewie as a marginal cost of 4 for each tub of Cold Hwhip.

(a) Find the profit-maximizing uniform price and quantity, as well as Stewie’s profits

(b) Now suppose Brian gets wind of Stewie’s Cold Hwhip and wants to buy some as well. Brian’s inverse demand is p = 20 − q. What is the optimal uniform price for Stewie to charge and what are his profits?

(c) Finally, suppose that Stewie is out of town and can’t monitor which customer is buying his product. Instead he creates two kinds of packages, one containing 4 tubs of Cold Hwhip and one containing 16 tubs of Cold Hwhip, and allows his customers to simply buy one and only one of the kind of package that they prefer. What price should Stewie charge for each package to maximize profits, while enticing Meg to buy the package of 4 and Brian to buy the package of 16?

Answer 1

Answer : For Meg :

p = 8 - q

TR (Total Revenue) = p *q = (8 - q) * q = 8q - q^2

MR (Marginal Revenue) =TR / q = 8 - 2q

MC (Marginal cost) = 4 (given)

For monopolist's the profit maximizing condition is, MR = MC.

=> 8 - 2q = 4

=> 8 - 4 = 2q

=> 4 = 2q

=> q = 4/2

=> q = 2

Now, p = 8 - 2

=> p = $6

For Brian :

p = 20 - q

TR = p * q = (20 - q) * q = 20q - q^2

MR = TR / q = 20 - 2q

MC = 4 (given)

At profit maximizing condition, MR = MC

=> 20 - 2q = 4

=> 20 - 4 = 2q

=> 16 = 2q

=> q = 16/2

=> q = 8

Now, p = 20 - 8

=> p = $12

Therefore, to maximize the profit level Stewie should charge $6 to Meg and $12 to Brian.