## (solution) Econ 428: Problem Set #5 Peter Newberry December 3, 2015 Due

Econ 428: Problem Set #5

Peter Newberry December 3, 2015

Due Date: Thursday December 10th, by 5 PM. You can hand it in in class or to my office. Try your best at each problem. Problems sets will be graded on effort as well as correctness. Write clearly.
Show all your work and label graphs!

If you choose to work in groups, each student must hand in their own problem set.

1 Coase Theorem

1.1 Problem #1

Suppose there is a local power plant which emits pollution. The marginal benefit to citizens of the firm abating pollution is given by:

MB(A) = 60 ? 2A
where A is the amount of abatement. The marginal cost of abatement for the firm is:

MC(A) = 5 + 3A

1. What is the efficient level of abatement? What is the total cost to the firm and the total benefit of abating at this level?
2. If the firm has the right to pollute, what level of abatement would they choose? What is the total cost to the firm and the total benefit of abating at this level?
3. Assume firm has the right to pollute. Suppose firms and citizens can negotiate at no cost. Give an example of an agreement that would result in the efficient solution.
4. If the citizens have the right to clean air, what level of abatement would they choose? What is the total cost to the firm and the total benefit of abating at this level?
5. Assume citizens have the right to clean air. Suppose firms and citizens can negotiate at no cost. Give an example of an agreement that would result in the efficient solution.
6. Give an example of a bargaining cost that would result in no agreement being made (I?m looking for a number).

1

1.2 Problem #2

Suppose there are two neighboring cities. One is an industrial city and the other is agricultural. There is a power plant that serves the industrial city. The power plant emits pollution that harms the agricultural city. The marginal benefit of the electricity produced in the industrial city is given by:

and the marginal cost is constant at:

MB(Q) = 150 ? 10Q MC = 10

The marginal damage of the pollution on the agricultural city is a function of the quantity of electricity and is given by:

2

Measuring Demand

1. 2. 3. 4.

What is the efficient level of electricity produced? What is the total welfare in the industrial city? What is the total damage done to the agricultural city?

If the industrial city has the right to pollute, how much electricity would they produce? What is the total welfare in the industrial city? What is the total damage done to the agricultural city?

Assume the industrial city has the right to pollute and that there are no costs of negotiation. Can the two cities negotiate a deal? Give an example of a deal that can be reached.

Assume there is a \$100 fee to negotiation for both parties (\$200 total). Can the two cities negotiate a deal?

Suppose demand for farms is given by:

MEC(Q) = 4Q

x = H(Px,z)

where Px is the price of a farm and z is the level of water quality. The level of water quality effects how valuable a farm is. Assume that the market for farms is competitive, so that the price of a farm Px is equal to \$100,000 no matter what the level of water quality is. The inverse demand curve for farms is given by:

Px = 500?10x+x?log(z) where Px is in thousands of dollars, and x is in hundreds of farms.

1. Solve for the demand for farms as a function of the air quality and call it x(z). That is, solve for x in terms of z when Px = 100.
2. What is the consumer surplus as a function of z? (hint: consumer surplus will be given by: CS = (500?Px )?x(z)

2
3. Find the demand curve for water quality. A graph is sufficient. You can do this by calculating ?CS

?z for a number of values of z. Using excel would be easiest, but if you choose to do it by hand, calculate

it for values z = 1 through z = 10. Alternatively, you can take the derivative of CS with respect to z and graph it.

2

Econ 428: Problem Set #5

Peter Newberry

December 3, 2015

Due Date: Thursday December 10th, by 5 PM. You can hand it in in class or to my o?ce.

Try your best at each problem. Problems sets will be graded on e?ort as well as correctness.

Write clearly.

Show all your work and label graphs!

If you choose to work in groups, each student must hand in their own problem set. 1 Coase Theorem 1.1 Problem #1 Suppose there is a local power plant which emits pollution. The marginal bene?t to citizens of the ?rm

abating pollution is given by:

M B(A) = 60 ? 2A

where A is the amount of abatement. The marginal cost of abatement for the ?rm is:

M C(A) = 5 + 3A

1. What is the e?cient level of abatement? What is the total cost to the ?rm and the total bene?t of

abating at this level?

2. If the ?rm has the right to pollute, what level of abatement would they choose? What is the total cost

to the ?rm and the total bene?t of abating at this level?

3. Assume ?rm has the right to pollute. Suppose ?rms and citizens can negotiate at no cost. Give an

example of an agreement that would result in the e?cient solution.

4. If the citizens have the right to clean air, what level of abatement would they choose? What is the

total cost to the ?rm and the total bene?t of abating at this level?

5. Assume citizens have the right to clean air. Suppose ?rms and citizens can negotiate at no cost. Give

an example of an agreement that would result in the e?cient solution.

6. Give an example of a bargaining cost that would result in no agreement being made (I?m looking for

a number). 1 1.2 Problem #2 Suppose there are two neighboring cities. One is an industrial city and the other is agricultural. There is

a power plant that serves the industrial city. The power plant emits pollution that harms the agricultural

city. The marginal bene?t of the electricity produced in the industrial city is given by:

M B(Q) = 150 ? 10Q

and the marginal cost is constant at:

M C = 10

The marginal damage of the pollution on the agricultural city is a function of the quantity of electricity and

is given by:

M EC(Q) = 4Q

1. What is the e?cient level of electricity produced? What is the total welfare in the industrial city?

What is the total damage done to the agricultural city?

2. If the industrial city has the right to pollute, how much electricity would they produce? What is the

total welfare in the industrial city? What is the total damage done to the agricultural city?

3. Assume the industrial city has the right to pollute and that there are no costs of negotiation. Can the

two cities negotiate a deal? Give an example of a deal that can be reached.

4. Assume there is a \$100 fee to negotiation for both parties (\$200 total). Can the two cities negotiate a

deal? 2 Measuring Demand Suppose demand for farms is given by:

x = H(Px , z)

where Px is the price of a farm and z is the level of water quality. The level of water quality e?ects how

valuable a farm is. Assume that the market for farms is competitive, so that the price of a farm Px is equal

to \$100,000 no matter what the level of water quality is. The inverse demand curve for farms is given by:

Px = 500 ? 10x + x ? log(z)

where Px is in thousands of dollars, and x is in hundreds of farms.

1. Solve for the demand for farms as a function of the air quality and call it x(z). That is, solve for x in

terms of z when Px = 100.

2. What is the consumer surplus as a function of z? (hint: consumer surplus will be given by: CS =

(500?Px )?x(z)

2 3. Find the demand curve for water quality. A graph is su?cient. You can do this by calculating ?CS

?z

for a number of values of z. Using excel would be easiest, but if you choose to do it by hand, calculate

it for values z = 1 through z = 10. Alternatively, you can take the derivative of CS with respect to z

and graph it. 2

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