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MBA 505: Homework Assignment 5
1. (Price Customization with Smooth Demand Curves) A firm faces two micro-markets. The
demand curve in the first one is Q1 = 100 – P1; the demand curve in the second one is Q2 =
170 – 2P2 (both prices are expressed in dollars per unit). The marginal cost of production in
each micro-market is constant and equal to $10 per unit.
a. Suppose that the firm can charge a distinct price in each micro-market. What is the
profit-maximizing price in each micro-market?
b. Suppose that the firm must charge the same price in both markets (i.e., it is
constrained to engage in uniform pricing). What is the profit-maximizing uniform
price? How much is purchased in each market?
c. How does the firm’s profit contribution compare across the two scenarios?
2. (Price Customization with “Stair-Step” Demand Curves) A firm faces a market consisting of
four segments, with characteristics given in the table below
Maximum willingness to pay
(MWTP)
Segment 1
Segment 2
Segment 3
Segment 4
$70 per unit
$60 per unit
$30 per unit
$20 per unit
Units purchased if price is
less than or equal to MWTP
of segment
10
30
100
150
The firm has a marginal cost of $10 per unit
a. Sketch the demand curve for this market.
b. What is the profit-maximizing price if the firm charges a uniform price?
c. Suppose the firm can distinguish customers that come from segments 1 or 2 from
customers that come from segments 3 or 4 (and can build a “fence” that prevents
arbitrage). What are the profit-maximizing customized prices for these two micromarkets?
d. Suppose the firm can distinguish customers that come from each individual segment
(and can build a “fence” that prevents arbitrage). What are the profit-maximizing
customized prices for the four relevant micro-markets?
3. Disney owns the rights to market products (e.g., children’s clothing) that are based on their
much beloved children characters (e.g., Mickey Mouse). The company prefers not to get
involved in the production and marketing details of these products, since there is a large
pool of firms that can perform such standardized, low-margin activities. The purpose of this
problem is to explore the implications contracting between a monopolist of intellectual
property and firm that is awarded a franchise to produce goods based on that intellectual
property.
Suppose that the annual demand curve for a particular product using Disney characters
(children’s pajamas) is known to be given by the equation, Q = 100 – P, where Q is units per
year and P is the price per unit. A typical contractor can produce the product with a
marginal cost equal to $10 per unit (independent of the volume of output produced) and an
avoidable fixed cost of $1,000 per year. There are many contractors with this cost structure.
All of them agree about what demand is going to be and know the cost structure of each
other. The company licenses contractors by imposing an annual licensing fee L that does not
depend on the amount of output the contractor produces.
a. Suppose that Disney solicits bids for this product, under the rule that the contractor
with the highest bid L wins the contract. The winner gets the exclusive rights to
produce and sell the product. What licensing fee would Disney expect to get?
b. Suppose, instead, that Disney considered awarding contracts to two contractors
who would compete with each other. (You might, to be concrete, imagine that the
competition between contractors would be Cournot quantity competition, but this
assumption is not crucial to the story). As before, the set of potential contractors
have identical marginal and fixed costs. Is it likely that Disney will do better under
this arrangement than under the arrangement in part (a)?
4.
(Thinking through how changes in economic fundamentals affect the Cournot reaction
functions and equilibrium) Blount, Inc. is one of two Cournot dupolists in the market for
gizmos. It and its main competitor Fishman Ltd. face a downward-sloping market demand
curve. Each firm has an identical marginal cost that is independent of output. Please indicate
how the following will affect Blount’s and Fishman’ reaction functions, and the Cournot
equilibrium quantities produced by Blount and Fishman.
a. Leading safety experts begin to recommend that all homeowners should replace
their smoke detectors with gizmos.
b. Gizmos are made out of platinum, with each gizmo requiring 1 kg of platinum. The
price of platinum goes up.
c. Blount, Inc.’s general and administrative expenses increase.
d. The end of a recession makes consumers less price sensitive. Suppose that this has
the concrete effect of making the market demand curve steeper at the existing
monopoly price/quantity point.
e. The government imposes an excise tax on gizmos produced by Fishman, but not on
those produced by Blount.
2

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