1. Are the following statements true, false? Please give an explanation.
(a) A monopolist producing at a price and quantity where the elasticity of demand is -0.5 is not maximizing profits.
(b) Since monopolies raise prices above the efficient level, the government should always break up the monopolistic firms or foster entry into the market.
(c) Unlike in a perfectly competitive market, imposing a price ceiling on a monopolist may increase output.
2. A monopoly faces market demand Q = 30 - P and has a cost function
C(q) = 1/2 q2
(a) Find the profit maximizing price and quantity and the resulting profit to the monopoly.
(b) Find the price elasticity of the demand Edp at the price and quantity found in (a).
(c) What is the equilibrium price?
(d) Assume that the government puts a price ceiling on the monopolist at P = 18. How much output will the monopolist produce? What will be the profit of the monopolist?
(e) Assume that the government put a price ceiling on the monopolist in order to maximize the total (i.e. consumer plus producer) surplus. What price ceiling should it choose? How much output will the monopolist produce at this price ceiling?
(f) Now assume that in addition to the $130 fee, the government puts on the monopolist the same price ceiling as in part (e). Will the monopolist choose to produce in this case?
(g) Suppose the government decides to impose a tax of $3 per unit on the monopolist. Find the resulting output, price, government revenue and monopolist's profit. Show on a diagram the consumer surplus, the producer surplus, government revenue and deadweight loss.
(h) Assume the monopolist acquired a second factory with a cost function C2(q) = 6q, but it still could use the first factory with
the cost function C1(q) = 1/2 q2
Find the new profit maximizingprice and calculate the amount of output produced in each of the two factories.
3. Suppose that North Pole Enterprises makes ice sculptors in the NorthPole and ships them to the United States, where they are sold in theperfectly-competitive icesculpture market for a fixed price of 100 dollars.
The primary input in North Pole Enterprises production is ice.
Unfortunately, NPE doesn't own any rich ice-producing land in theNorth Pole, and hence must purchase ice from one of the many firmsthat produce ice. The market for ice is perfectly competitive, with a
supply curve given by
S(r) = r,
where r is the price of ice. Since NPE is the only demander of ice produced in the North Pole, it acts as a monopsonist.
Its productionfunction for sculptures is given by:
F(x) = 2√x
Where x is the amount of ice it uses.
(a) How much ice does NPE use?
(b) What is the price of ice?