Economics

1
PROBLEM SET 1

1. Consider a monopoly market, where consumer demand is given by ?
   ?(?) = 160 − 2?, and the
   monopolist’s marginal cost function is ??(?) = 10 +
   ?
   5
   .
   a) Solve the monopolist’s profit maximization problem to find how much it will produce and what price
   it will set. (Hint: remember to always obtain inverse demand first)
   b) Find producer surplus, consumer surplus, and deadweight loss if there is any.
   c) What profit does the monopolist earn?
2. Consider a market with 16 small price-taking firms, each with total cost function: ??(?) = 2?
   2 + 4? + 1.
   Demand in this market is given by ?
   ? = 20 − ?/2.
   a) Find the market equilibrium: price, quantity, and the surplus that goes to producers and consumers.
   b) Suppose a tax of $6/unit is introduced, charged from each producer when they sell their output.
   Solve for the new equilibrium, including surpluses, government revenue and deadweight loss.
   Next, repeat part b, for each of the 2 interventions below (each taken separately). In each case, find
   what equivalent tax would have achieved the same reduction in market quantity. What would have been
   different with the tax?
   c) Price ceiling of $7
   d) Price floor of $24 (what would a price ceiling of $24 do?)
3. Consider again the parameters of problem 2, part a).
   a) Suppose that the 16 firms decided to “cooperate” with one another by deciding jointly what price
   to set. If they trust each other to adhere to the agreement, what value will they pick for the price?
   Solve for this new outcome – find the price, quantity and relevant surpluses (including DWL).
   b) Now suppose the cartel failed because the firms kept undercutting each other (charging a price
   below that of other firms, thus stealing their customers). But it turns out that the product they sell
   is not easily transported, so they come up with the following idea: divide the region into 16 smaller
   areas, with each firm being assigned to a specific area, encompassing 1/16th of the customers
   (assume there are many more consumers than firms, and they all have the same maximum
   willingness to pay). Solve the new monopoly profit-maximization problem. Do you think this
   agreement would be easier or harder to enforce than the original cartel?
4. Consider a monopoly market, where consumer demand is given by ?
   ?(?) =
   100
   ?2
   , and the monopolist’s cost
   function is ?? = 5? + 5. Solve the monopolist’s profit maximization problem. What price does it set, and
   how much profit does it earn?
5. There are 10 households, each with a demand for electricity of ?
   ? = 50 − ?. A utility company (a natural
   monopoly) produces electricity at a cost of ??(?) = 480 + ?.
   a) If a regulator wants to eliminate deadweight loss, what price will it set? What will happen?
   b) If a regulator wants to ensure that the DWL is minimized, but at the same time, the utility company
   does not lose money, what is the price it will set, and what will be the DWL?
   c) Suppose that the regulator comes up with another plan: each households pays a fixed fee just to
   receive any electricity service, and the per-unit price is set in accordance to a). What will be the fixed
   fee each household will have to pay? Will all households agree to pay this extra fee instead of going
   without electricity? Will there be deadweight loss?