The Ohio State University
Department of Economics
Prof. James Peck
Midterm Questions and Answers
A monopolist has many potential customers, represented by the interval, [0,1].
[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.
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
(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).
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.
(A) The monopolist can
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