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Econ 100C

Fall 2021

PROBLEM SET 6

1. Consider a market with 16 small price-taking firms, each with total cost function:  Demand in this market is given by

a) Assuming the firms act competitively, find market supply and the competitive short run equilibrium. Calculate consumer and producer surplus, as well as firm-level profits.

b) 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).

c) 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 actually a residential service (meaning consumers cannot transport it), and they come up with the following idea: divide the region into 16 smaller areas, with each firm being assigned to a specific area, encompassing 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?

d) Might the outcome from part c) be socially optimal? Explain exactly under what circumstances.

2. Carl likes to maintain his garden with a loud hedge trimmer. His neighbors don’t like the noise and suffer cost  per hour of gardening each week.

Suppose Carl’s marginal benefit from gardening is and his marginal cost is (= net earnings from doing the same work for someone else).

a) Does it make sense that external marginal cost has this functional form  ? What is the socially efficient number of hours for Carl to spend on gardening every week?

b) How many hours does Carl actually spend gardening? Show the external cost and the deadweight loss in the graph.

c) If the city could charge a fee t for every hour of gardening (this would act like an excise tax), what fee should they charge in order to get Carl to the socially efficient level of gardening?

Now suppose Carl’s neighbors also extract some benefits from his care of his garden – they enjoy having a well-kept neighborhood. The benefit they get is $10 per hour of Carl’s gardening. (The costs created by the noise still apply)

d) What is the socially efficient level of gardening, and approximately what fee should the city charge per hour of noisy gardening in order to reach the efficient level?