ECON 340 Spring 2017 HW#5

1. For each of these monopolists, find the profit maximizing price

(a) QD = 100 ? 4P ; T C(Q) = 10Q

(b) QD = 90 ? 12 P, T C(Q) = 3Q2

(c) QD = P ?4 , T C(Q) = 3Q

2. For each of the following, find the optimal pricing strategy and the quantity that will be sold given the stated form of price discrimination

(a) QD = 30 ? 6P, T C(Q) = Q; First-degree price discrimination

(b) QD

i = 150 ? 3P, T C(Q) = 2Q; Two-part tariff [Note: the i subscript

denotes that this is the demand from an individual consumer]

D

(c) QD

m = 60 ? 2P, Qf = 50 ? P, T C(Q) = 20Q; Third-degree price

discrimination [Note: there are two groups, m and f ]

3

. Suppose that Fortnum’s has four customers: Elizabeth, Charles, Tosha,

and Tim, to which they may sell two products: tea and cakes

. The

marginal cost of a pot of tea is £2 and the marginal cost of plate of

cakes is £1

. Their customers willingness to pay for each product is: Elizabeth

Charles

Tosha

Tim Cakes

8

7

4

10 Tea

10

12

14

4

(a) Suppose Fortnum’s sells cakes and tea separately

. What price would

they charge for each?

(b) Suppose Fortnum’s only sold “Afternoon Tea,” which is a bundle of

cakes and tea

. What price would they charge for Afternoon Tea?

(c) Suppose Fortnum’s offered both Afternoon Tea, as well as selling tea

and cakes individually

. What prices would they set?

4

. Suppose there are two firms producing identical biscuits

. The demand for

bicycles is QD = 200 ? 4P

. Both firms have an identical marginal cost of

producing a biscuit is $5

(a) Suppose both firms complete ala Cournot

. What is the equilibrium

price and quantity for each firm?

(b) Suppose both firms compete ala Bertrand

. What is the equilibrium

price and quantity for each firm?

1 (c) Suppose both firms compete ala Stackelberg

. What is the equilibrium

price and quantity for each firm? 2