the monopolist’s optimal quantity and price
1. Suppose a monopolist faces the market demand function P =
a – bQ. Its marginal cost is given by MC = c + eQ. Assume that a > c and 2b
+ e > O.
a) Derive an expression for the monopolist’s optimal
quantity and price in terms of a, b, c, and e.
b) Show that an increase in c (which corresponds to an
upward parallel shift in marginal cost) or a decrease in a (which corresponds
to a leftward parallel shift in demand) must decrease the equilibrium quantity
of output.
c) Show that when e 2:: 0, an increase in a must increase
the equilibrium price.
2. A monopolist serves a market in which the de¬mand is P =
120 – 2Q. It has a fixed cost of 300. Its marginal cost is 10 for the first 15
units (MC = 10 when 0 ≤ Q ≤ 15). If it wants to produce
more than 15 units, it must pay overtime wages to its workers, and its
mar¬ginal cost is then 20. What is the maximum amount of profit the firm can
earn?
3. Suppose that demand and supply curves in the market for
corn are Qd = 20,000 – SOP and QS = 30P. Suppose that the government would like
to see the price at $300 per unit and is prepared to artificially increase
demand by initiating a government purchase program. How much would the
government need to spend to achieve this? What is the total deadweight loss if
the government is successful in its objective?
