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Econ 101, section3, F06

Schroeter

Project #3

(Due:4:00 p.m., Friday, November 3. All papers must be submitted at the Econ

Help Room, 178 Heady Hall. Papers will NOT be accepted in lecture or at Prof. Schroeter's office or mailbox. I suggest you keep a copyof your project write-up.

BE SURE YOU REVIEW "Guidelines for the preparation of projects" in the

syllabus, before beginning work on this assignment.)

PartI. Tradable pollution permits.

(This is very similar to problem 12 from the "Problems and Applications" section at the end of chapter 10, but with different numbers and a little added explanation and some hints to help you through it.)

There are three industrial firms in HappyValley. Each one pollutes the atmosphere, but their current levels of pollution, and their costs of pollution abatement differ:

Firm / Initial
pollution level / Marginal abatement cost: Cost of abating (reducing) pollution by 1 unit/year
A / 80 units/year / $100
B / 100 / 75
C / 120 / 50

(Note: In lecture, we said that, for each firm, the marginal cost of abatement would typically increase with the amount of abatement undertaken. In this simple problem, marginal abatement costs for a given firm are constant, however. For example, Firm A incurs a cost of $100/unit for the first, second, and every unit of pollution that it abates.)

a. Suppose that there were pollution permits available, each one entitling the holder to pollute one unit per year. Firms would only be allowed to pollute up to the level of their permit holdings. Graph the aggregate demand curve for pollution permits.

(Hint: Start by considering a pollution permit price above $100/permit. At such a price, none of the firms would demand any pollution permits because each firm would find it cheaper to abate pollution than to pay for permission to pollute. As the price of permits falls below $100/permit, however, firm A would demand 80 permits because it would now find it cheaper to pay for the right to pollute than to abate pollution. As the price of pollution permits falls further, firm B and eventually firm C would add their contributions to aggregate demand for pollution permits. The resulting demand curve will have the "stair-step" appearance of the demand curve we encountered in chapter 7 in our development of the concept of consumer surplus.)

b. The government decides that it wants to reduce total pollution from the present level of 300 units/year to 150 units/year. So it issues only 150 permits, initially giving 50 to each firm, but allowing the permits to be traded among firms. Government provision of 150 tradable pollution permits means that the supply of permits is perfectly inelastic at a quantity of 150. Graph the supply of pollution permits on the same graph you drew for part a. What is the equilibrium price of the tradable pollution permits? (See chapter 10's Figure 4b.) Answer the following questions for each of the three firms:

Will the firm buy more than its initial allocation of 50 pollution permits? If so, how many?

Will the firm sell some or all of its initial allocation of permits? If so, how many?

(Hint: For each firm, the level of marginal abatement cost establishes the value of a pollution permit to the firm. Compare each firm's permit value to the equilibrium price of permits to determine if the firm would want to buy permits or sell permits. If the firm's permit value equals the equilibrium price, it would be indifferent about the number of permits it bought or sold, so we'll assume that it would buy or sell the number of permits necessary to clear the market.)

c. What is the total cost (for all three firms combined) of reducing pollution to 150 units/year under the government's tradable pollution permit policy?

(Note: Here I am referring to just the "technological" costs of pollution abatement that are reflected in the numbers in the table at the beginning of the problem. We don't consider any costs of purchasing additional permits because, from society's point of view, these "cancel out." One firm's expenditure for extra permits is another firm's revenue from the sale of its surplus permits.)

d. As an alternative to the tradable pollution permit policy, the government might issue 50 pollution permits to each firm but prohibit trade in the permits. In this case, each firm would simply use its allocation of 50 permits. What would be the total cost (for all three firms combined) of reducing pollution to 150 units/year in this case?

Part II. The cost curves of a firm.

Acme widget company owns "fixed" inputs, collectively called Acme's "factory." To make widgets, Acme hires workers (a "variable" input) to work in the factory. The relationship between the number of workers hired and the number of widgets produced (Acme's production function) is described by the table below.

Labor
(workers/day) / Output
(widgets/day)
0 / 0
1 / 50
2 / 96
3 / 138
4 / 176
5 / 210
6 / 240
7 / 266
8 / 288
9 / 306
10 / 320

Acme's opportunity cost of using its factory is $400/day and the wage it must pay to workers is $150/day.

Construct a table with first and second columns identical to the columns in the table above. Then add six more columns giving fixed cost, variable cost, total cost, average fixed cost, average variable cost, and average total cost for each of the output levels in column 2. Add one more column giving marginal cost estimates for the output ranges 0 to 50, 50 to 96, 96 to 138, etc.

On a single pair of axes, graph average fixed cost, average variable cost, average total cost, and marginal cost as functions of output. (When you graph marginal cost values, plot them versus the quantity given by the midpoint of the corresponding output range. For example, you'll have one marginal cost estimate corresponding to the output range 176 to 210. Plot this value versus an output of 193, halfway between 176 and 210.)

Do the average total cost and marginal cost curves exhibit the relationship you expect? Explain.