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The Ohio State University
Department of Economics
Econ. 805
Prof. James Peck
Winter 2000
Midterm Questions and Answers
(1)
25 points
A monopolist has many potential customers, represented by the interval, [0,1].
For
customer
x
!
[0,1], consuming one unit of the product provides a benefit of v, but the customer must pay a
transportation cost of tx to purchase the product, where t is a positive parameter.
The monopolist
has a constant marginal cost, c, and no fixed costs.
Assume that customers are uniformly distributed across the interval, [0,1], according to the
density function, f(x) = 1.
In other words, if everyone in the interval [0,x] purchases, the monopolist
sells x units of the product.
Also assume the following:
assumption 1: (vc)/2
"
t
"
(vc).
(A) Suppose that the monopolist must charge a constant price, p, but that it can also offer to pay a
“transportation subsidy” to its customers, as a function of their location, denoted by s(x).
That is,
a customer at “location” x that pays the price, p, and incurs the transportation cost, tx, also receives
a payment from the monopolist, s(x).
Therefore, her utility would be (v  p  tx + s(x)) if she
purchases the product, and zero if she does not purchase.
What are the profit maximizing values
of p, s(x), and monopoly profits?
(Hint: think of price discrimination)
(B) Suppose that the monopolist must charge a constant price, p, with no transportation subsidy.
Therefore, a customer at location x would receive utility of (v  p  tx) if she purchases the product,
and zero if she does not purchase.
Calculate the profit maximizing value of p, the total quantity
sold, and monopoly profits.
ANSWER:
(A) The monopolist can
perfectly
price discriminate, charging everyone their full
willingness to pay.
The highest net payment, p  s(x), that consumer x is willing to make is v  tx.
The monopolist can extract this payment by setting p  s(x) = v  tx.
The simplest way is to set p=v
and s(x) = tx.
The additional profits received from consumer x is: v  tx  c.
Since v  c > t
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