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ECON 340 HW 5 – These monopolists, find the profit

Question
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
(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

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