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Econ 371 (001)

Winter Session, Term 2, 2016

M. Vaney

Problem Set 2

Due: This assignment is due at the end of lecture, Friday March 18, 2016.

All work must be shown. Answer ALL questions. At least one question will be graded.

1. A researcher is interested in determining the factors that in?

uence the demand for

housing. The researcher obtains a data-set that consists of 6 observations of price and

quantity:

(p,q)

(3; 6) (4; 9)

(6; 3) (4; 4)

(5; 6) (5; 2)

(a) Plot the data points. Estimate a linear demand q = q(p) = A

plot.

bP; based on this

(b) A colleague looks at the data-set and notes that some of the data points are

measured in neighborhood X while other data points come from neighborhood

Y . The colleague also has data on the air quality (A) in the two neighborhoods

and this data is added to the data-set:

X: AX = 3 Y:AY = 4

(5; 2)

(6; 3)

(4; 4)

(5; 6)

(3; 6)

(4; 9)

The colleague notes that the two neighborhoods are very similar apart from the

measure of air quality (similar distance to downtown, similar amenities). Estimate

linear demand for housing as a function of price and air quality: q = q(p; A). (You

can estimate two di?erent linear demand functions, q(p; A = 3) and q(p; A = 4).

(c) If the price of housing is P = 4:5; estimate the willingness-to-pay for a change in

air quality from A = 3 to A = 4.

2. The Travel Cost Method is used to derive annual demand for visits to a national

park and the associated bene?ts of the park. The following data is collected for three

di?erent zones (of varying distance from the park):

Zone

A

B

C

Travel Distance (km)

10

30

80

Travel Time (hours)

0.5

1.0

2.0

opp. cost of time (\$/hr)

30

25

10

# Visits per person

30

20

10

Distance and times in the table account for travel both to and from the park. Vehicle

operating costs are \$0:50/km (gas, insurance, depreciation). Assume that each individual travels alone (vehicle costs are not shared). In addition to time and travel costs,

there is a \$10 admission fee required to enter the park.

1

(a) Complete the following table of Total Costs per visit:

Zone

A

B

C

# Visits per person

30

20

10

Total Cost per visit (\$)

Use this information to derive the inverse demand curve for Visits to the National

Park.

(b) Calculate the Consumer Surplus received by a representative individual from each

of the three zones.

(c) Suppose the populations in each of the three zones are as follows:

Zone

A

B

C

Population

100

300

200

Calculate the Total Bene?ts generated from the park.

(d) Derive the market demand curve for the national park (number of visitors per

year as a function of the admission price).

3. Two ?rms are responsible for all emissions of a particular pollutant. The Marginal

Damages function (damages as a function of the total level of pollutants) is described

1

by the function M D = 2 E. Abatement costs for the two ?rms are as follows:

Firm

A

B

MAC

100 EA

80 2EB

(a) If there are no regulations limiting emissions of the ?rms, determine the level of

0

0

emissions of each ?rm, EA ; EB and the total level of emissions, E 0 .

(b) Determine the Total damages in the unregulated environment.

(c) A regulator wishes to have total Emissions at E = 80. A ? and trade?program

cap

^

^

is put into place. Each ?rm is allocated emission rights/permits: EA = EB = 40.

A market allows ?rms to exchange permits at a price PE . Which ?rm will sell

permits? Find that ?rms supply function for permits. Determine the demand

function for permits of the other ?rm.

(d) Determine the equilibrium price of permits and the quantity of permits exchanged.

(e) Calculate the bene?ts or costs of the permit program to each ?rm. Does one ?rm

bene?t from the (equal) allocation of permits?

4. A chemical plant and a food processor are both located along the same river. The

Chemical plant is located upstream of the food processor. Both ?rms make use of

the river. The chemical plant uses the river as a waste sink (release of by-products).

2

The food processor uses the river as an input (fresh water). The M AC curve of the

Chemical plant is M AC = 2000 10E where E measure emissions (? of pollutants)

ow

into the river. The M D curve (damages in?

icted upon the food processor) is measured

as:

0

E 40

MD =

1

E 20 E 40

2

(a) If the Chemical plant believes they have the right to pollute, at what level will the

factory set emissions, E0 ?

(b) What are the Total Damages in?

icted upon the Food processor as a result of this?

(c) If the Food processor has the right to determine the level of emissions in the river,

and the ?rm can sell the right to emit to the Chemical plant, what is the outcome

predicted by the Coase Theorem?

(d) What conditions must be satis?ed in order for the Coase theorem to hold?

(e) Suppose there is another user of the river, Recreational users. Recreational users

are also hurt by the emissions of the Chemical plant. The M D curve for recre1

ational users is M DR = 4 E. What is the Social marginal damages function?

(f) What is the socially optimal level of emissions by the Chemical plant, E ? Can

assigning the right to pollute to the Chemical plant still bring about the socially

optimal level of emissions, E ?

5. The emissions from a particular industrial activity impose costs on the rest of society.

The costs are measured by a Marginal Damages function M D = 1 E: The industry

3

has 3 ?rms that operate in a competitive fashion. The costs of reducing emissions for

an individual ?rm is measured by the Marginal Abatement Cost function, M AC =

150 2E. All three ?rms use the same technology for reducing emissions (the same

M AC function).

(a) If there is no regulation of emissions at what level will each ?rm set emissions, E0 ?

(b) What are the Total costs (Damages and Abatement Costs) in (a)?

(c) What is the socially optimal level of Total Emissions (from all three ?rms)?

(d) What Emission tax, tE will bring about the socially optimal level of Total Emissions?

6. The emissions from a particular industrial activity impose costs on the rest of society.

The costs are measured by a Marginal Damages function M D = 1 E: The industry

3

has 3 ?rms (?rm 1; 2; 3) that operate in a competitive fashion. The costs of reducing

emissions for an individual ?rm is measured by the Marginal Abatement Cost function.

The ?rms have di?erent M AC functions: M AC1 = 150 2E1 ; M AC2 = 100 E2 ;

M AC3 = 200 E3 .

(a) Determine the socially optimal level of Total Emissions, E .

(b) The regulator imposes a uniform Emission Standard on each of the three ?rms:

^

^

^

E1 = E2 = E3 = E . What are the Total Abatement Costs that each ?rm must

3

incur to comply with the standard?

3

(c) Explain whether the uniform Emission Standard set by the regulator achieves the

optimal level of Total Emissions at the minimum Abatement Cost.

^ ^

^

(d) Determine the ?rm-speci?c standards, E1 ; E2 and E3 that achieves the optimal

level of Total Emissions in the most cost-e?ective manner.

4

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