The Ohio State University
Department of Economics
Econ. 805
Prof. James Peck
Winter 2000
Midterm Examination
Directions
:
Answer all questions, show all work, and label all diagrams.
(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: (v-c)/2
"
t
"
(v-c).
(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,