Economics 423, Midterm Examination #2, Fall 2005 – Professor Hackett 

Name: Answer Key   [Worth one point :-) ]   Answers in green font

 

PART I: Students enrolled for 4 units only: Please provide the best answer to each of the following three questions, each of which is worth 10 points:

 

Consider the following model of a marine capture fishery. Fishery stock = X, effort = E, stock growth is given by F(X) = aX – bX2. In a steady-state equilibrium where harvest equals stock growth, we have stock X = a/b – E/b, and harvest H = E[a/b – E/b]. For simplicity, assume the sales price per pound of fish = $1, so that total revenue = $1 x H = E[a/b – E/b], and marginal revenue product = a/b – 2E/b. Total effort cost = cE, and marginal effort cost = c.

 

1. (a) Derive the equation for the open-access level of effort in a steady-state equilibrium. (b) If “a” = 1000, “b” = $1, and “c” = $200, derive the numerical values for open-access equilibrium effort (E), stock (X), and harvest (H). Show your work and indicate your answer below:

 

The open access solution is found where profit equals zero è TR = TC. Based on the equations above, that means E[a/b – E/b] = cE. From this equation one can derive the following (reduced-form) solution: EO = a – bc.

 

1.a.       EO = a - bc

 

 

1.b.       EO = 1000 – 200 = 800

           

            XO = 1000 – 800 = 200

 

            HO = 800*200 = 160,000

 

2. Derive the equation for the group-optimal level of effort in a steady-state equilibrium. (b) If “a” = 1000, “b” = $1, and “c” = $200, derive the numerical values for group-optimal equilibrium effort (E), stock (X), and harvest (H). Show your work and indicate your answer below:

 

The group optimum solution is found where profit is maximized è marginal revenue product equals marginal effort cost (MR = MC). Based on the equations above, that means a/b – 2E/b = c. From this equation one can derive the following (reduced-form) solution: E* = (a – bc)/2.

 

2.a.       E* = (a – bc)/2

 

 

2.b.       E* = (1000 – 200)/2 = 400

           

            X* = (1000 – 400) = 600

 

            H* = 400*600 = 240,000

 

 

3. Use the diagram below to carefully indicate the correct numerical equilibrium levels of harvest H (“y” axis) and stock X (“x” axis) associated with questions 1 and 2 above for open-access and group-optimal steady-state equilibria. Hint: By way of comparison, shown below is the stock level and harvest rate consistent with maximum sustainable yield.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



PART II: Students enrolled for 3 units only: Please provide the best answer to each of the three questions below, each of which is worth 10 points.

 

1. (i) What is the purpose of the contingent valuation method? Briefly list the reason(s) for using the contingent valuation method for measuring the value of some aspect of the natural environment, relative to other measurement methods. (ii) Briefly list the shortcomings of the contingent valuation method. (iii) What is the purpose of the travel cost method? List the reason(s) for using the travel cost method for measuring the value of some aspect of the natural environment, relative to other measurement methods. (iv) Briefly list the shortcomings of the travel cost method.

 

CVM:

 

Purpose = Valuation of environmental or natural resource conservation, preservation, or restoration, presented as a policy choice or contingency. Valuation results can become data for benefit/cost analysis

 

Reasons for using = Measure all non-market values, including both active use values and especially non-use values such as existence, option, or bequest value

 

Shortcomings = As a stated preference approach, CVM values do not derive from actual economic choices. People are unused to assigning economic value to the environmental attributes in a CVM study, and problems can arise in the way the attributes are framed in the questionnaire. Some CVM valuation studies suffer from embedding bias.

 

TCM:

 

Purpose = Valuation of environmental or natural resource conservation, preservation, or restoration, particularly sites with recreational value. Valuation results can become data for benefit/cost analysis

 

Reasons for using = Measure non-market use values associated with a site, such as for hiking, river access, hunting or fishing. Revealed preference data are based on actual economic choices and thus are less controversial.

 

Shortcomings = Cannot measure non-use values, and thus omits important aspect of overall site valuation. Subject to difficulties in attributing costs to a particular site when users engaged in multi-site travel.

 

2. (i) Carefully draw a single fully labeled diagram below correctly showing Keohane's equilibrium political economy market model of effective support for legislation or administrative rules. (ii) Show how the equilibrium is changed when those groups that demand effective support are joined by several new and powerful interest groups.

 

(i) See the diagram in the political economy chapter of your textbook, and/or the PowerPoint slides for this topic on the course website. (ii) This will increase the demand for effective support for the regulation in question. An outward shift in demand will result in an increase in the equilibrium quantity of effective support, and an increase in the equilibrium price in political currency.

 

3. Suppose that proposed environmental legislation includes a provision that those who violate the law must pay a penalty equal to triple the economic gains from being out of compliance with environmental law. It is common knowledge that 50 percent of all facilities are inspected for compliance each year, and that in recent years judges have imposed the full statutory penalty 90 percent of the time that a violation is detected. Based on this information, will the proposed legislation create deterrence (i) for risk-neutral violators, (ii) for risk-loving violators, and/or for (iii) risk-averse violators?

 

Let “X” stand for the economic gains from being out of compliance. Then the expected penalty is given by the following expression: 0.90 * 0.50 * 3X, which simplifies to the expected penalty being 1.35X. Note that the expected penalty exceeds the economic gains from being out of compliance (1.35X > X).

 


(i) Is the risk-neutral violator deterred? Circle one:           YES     NO       CANNOT BE

DETERMINED

 


(ii) Is the risk-loving violator deterred? Circle one:           YES     NO       CANNOT BE

DETERMINED

 


(iii) Is the risk-averse violator deterred? Circle one:         YES     NO       CANNOT BE

DETERMINED

 

Part III. ALL STUDENTS: There are five questions below. Please answer any three of them, and cross out the two that you do not wish to answer with a BIG X. Each question is worth 10 points.

 

 

1. Suppose that the marginal benefit from reducing emissions is given by the equation MB = 100 - Z, and marginal cost from reducing emissions is given by the equation MC = Z. Note that "Z" is the percentage of total emissions to be reduced. Solve for the percentage of total emissions reduced that maximizes total net benefits. Show your work.

 

Total net benefit is maximized at a level of emissions reduction where MB = MC. If we substitute the right-hand-side values for MB and MC from the question, we get: 100 – Z = Z. Solving for Z results in Z* = 50.

 

2. Suppose that a risk-neutral chemical factory can save $20 million per year in compliance costs by not complying with environmental regulations. Suppose that the probability of the infraction being detected by field monitors is 70 percent, and that the probability of a judge imposing the statutory penalty given detection is 80 percent. If the statutory penalty calls for a fine equal to double the annual cost savings gained by the offender, then will this system create deterrence? Show your work.

 

Expected penalty = 0.70 * 0.80 * 2 * $20 million = $22.4 million.

Cost savings from being out of compliance = $20 million.

Therefore the system creates deterrence given the firm is risk-neutral.

 

3. Given the information in question 2 above, what is the minimum statutory penalty that would be just sufficient to create deterrence for this risk-neutral firm? Show your work.

 

Let “Y” stand for the minimum statutory penalty. Then the numerical value for Y must satisfy the following:

 

0.70 * 0.80 * Y = $20,000,001  (the extra $1 is to provide minimal deterrence). Solving for Y yields the following value:

 

Y = $35,714,287.

 

4. Suppose that a job is identical to many others in a competitive labor market except that there is an additional 8 per 100,000 annual chance of accidental death, and that the job pays a risk premium of $1,000 per year. Use the "value of a statistical life" approach to determine the implied economic value of a statistical life. Show your work.

 

VSL = $1,000/(8/100,000) = $1000/0.00008 = $12,500,000
5. The data in the table below refers to pollution emissions and marginal pollution abatement cost per ton in an industry. Total industry-wide emissions are to be reduced by 50 percent (2400 tons/year):

 

Firms

Historical Emissions

(Tons/Yr)

Marginal Abatement Cost ($/Ton)

Allowances Bought

Allowances Sold

Total Abatement Cost (No Tradable Allowances)

Total Abatement Cost (Tradable Allowances)

A

400

200

 

200

40,000

80,000

B

400

400

 

200

80,000

160,000

C

400

600

 

200

120,000

240,000

D

400

800

 

200

160,000

320,000

E

800

1,000

***

***

400,000

400,000

F

800

1,200

400

 

480,000

0

G

800

1,400

400

 

560,000

0

TOTAL

4000

---

800

800

1,840,000

1,200,000

 

a. Suppose that the regulatory target of cutting total emissions by 50 percent is accomplished with a command-and-control regulatory system that requires each firm to cut its emissions by 50 percent. Correctly fill in the "total abatement cost" column for "no tradable allowances" in the table above.

 

b. Now suppose that the regulatory target of cutting total emissions by 50 percent is accomplished by allowing each firm to emit only 50 percent of its historical emissions. These allowances are fully tradable. Correctly fill in the "allowances bought", "allowances sold", and "total abatement cost, tradable allowances" columns in the table above.

 

*** Note: This problem is more challenging than the ones I have used on previous exams. Firms A – D cannot supply enough allowances to meet the quantity demanded by firms E-G. Firms A – D can supply enough for firms F and G. Firm E may try to supply allowances, but can only do so at a price above $1,000 per allowance. Under competitive conditions, however, firms A – D can meet all of firms F and G’s allowance demand at an allowance price less than $1,000 (and above $800), which will drive firm E out as an allowance supplier. At any price below $1,000, however, firm E will want to buy allowances. Therefore we would expect an equilibrium allowance price of $1,000 at which firms A – D sell 800 allowances and firms F and G buy 800 allowances. Firm E is shut out of the allowance market completely, and must cut ½ of its emissions based on its original endowment of only 400 allowances.

PART IV: ALL STUDENTS. Matching (13 matches, 3 points each, 39 points total). There is one uniquely correct match that connects a word or phrase on the left with a description on the right. Only clear and unambiguous answers can be marked as correct.

 

Word or Phrase

Description

a. Risk-averse

1. __P__ Example of the direct cost of environmental regulation.

b. Marginal benefit equals marginal cost

2. __ A__ If the expected penalty is equal to the benefit from violating environmental or resource law, this sort of individual will be deterred from violating the law.

c. Total benefit equals total cost

3. __ G__ People with this attitude towards risk will not be deterred from environmental crime if the expected penalty equals the gain from being out of compliance.

d. Market reputation

4. __ I__ Environmental valuation technique that estimates the value of non-market aspects of the environment (such as a park) that are bundled together with things (such as houses adjacent to the park) that are traded in markets.

e. Firms have heterogeneous marginal abatement costs

5. __ C__ Occurs at the level of pollution control where total net benefits equal zero.

f. Command-and-control regulation

6. __ E__ In order for cap-and-trade systems to reduce industry-wide costs of compliance, this must be true for the firms in the industry.

g. Risk-loving

7. __ L__ Examples of these include nutrient cycling provided by wetlands, carbon absorption by trees and plankton, fruit pollination by wild insects, and water filtering provided by aquifers and watersheds.

h. Environmental taxes

8. __ K__ This can occur when a polluter buys lots of allowances in a cap-and-trade system, and can result in environmental injustice for nearby residents.

i. Hedonic regression method

9. __ F__ This type of regulation is subdivided into technology-based standards and uniform performance-based standards.

j. Travel cost method

10 __ H__ Examples include effluent taxes on pollution emissions and excise taxes on goods made using polluting production methods.

k. A localized pollution “hot spot”

11. __ O__ Law that requires a minimum percentage of a state's total electricity production must come from renewable sources.

l. Ecosystem services not traded in markets

12. __ D__ When effective, this can give firms an incentive to voluntarily over-comply with environmental or resource regulations due to the actions of vigilant, selective, and environmentally conscious consumers.

m. Kyoto Protocol

13. __ M__ Treaty to control greenhouse gases that the US has refused to ratify.

n. Montreal Protocol

 

o. Renewable Portfolio Standard

 

p. The cost of pollution abatement equipment like scrubbers.