Economics 423, Midterm Examination #2, fall 2007 – Professor Hackett 

Name: Key

PART I. ONLY for students attending the 4^th unit lab: There are two problems given below. Please select ONE problem to answer, and CROSS out the other with a big X. Each of the three questions in the problem you select is worth 10 points:

4^th unit students problem 1: Dynamically efficient allocation of a non-renewable resource:

Suppose that there are 1200 units of a nonrenewable resource available over two periods (0 and 1). Demand in each period is given by P = 2000 - Q. Marginal cost is a constant 400 in both periods. The discount rate is 10 percent.

1. What is the dynamically efficient allocation of the 1200 units of the nonrenewable resource, and what will be the prices in the two periods? Please show your work.

Q₀ = 647.62 P₀ = $1,352.38

Solution: Use Hotelling’s rule. See Chapter 5 and PPT slides.

Q₁ = 552.38 P₁ = $1,447.62

2. Suppose that the basic setup of the problem above were the same, except that now the discount rate rises to 20 percent. Re-compute the dynamically efficient allocation of the 1200 units of the nonrenewable resource. Please show your work.

Q₀ = 690.9 P₀ = $1,309.1

Solution: Use Hotelling’s rule. See Chapter 5 and PPT slides.

Q₁ = 509.1 P₁ = $1,490.9

3. (i) Correctly draw the price paths for questions 1 and 2 above in a single fully-labeled diagram below. (ii) Provide a brief economic explanation for why the two price paths have different slopes.

Price on “y” axis, time period on “x” axis. Plot price data and compare.

PART I, Continued: 4^th unit students problem 2: The bioeconomics 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]. Total revenue = $P * H = PE[a/b – E/b], and marginal revenue product = P[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, and P = $2, derive the numerical values for open-access equilibrium effort (E), stock (X), and harvest (H). Show your work:

1.a. E^O = a – (bc)/p (equation) Set TRP = TEC, solve for E.

1.b. E^O = 900 (numerical value)

X^O = 100 (numerical value)

H^O = 90,000 (numerical value)

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

2.a. E^* = 0.5*(a – (bc)/p) (equation) Set MRP = MEC, solve for E.

2.b. E^* = 450 (numerical value)

X^* = 550 (numerical value)

H^* = 247,500 (numerical value)

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.

PART II. For students NOT participating in the 4^th unit lab: There are 6 questions in PART II. Please answer any 3 of them, and CROSS OUT the 3 you do NOT want me to grade. Each of the 3 questions you answer is worth 10 points:

1. Based on the Gordon model diagram above, the group optimal level of effort = 10.

2. Based on the Gordon model diagram above, maximum sustainable yield occurs when effort = 17.

3. Based on the Gordon model diagram above, full rent dissipation occurs when effort = 19.

4. (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 supply or demand curve, and the equilibrium level of effective support changes for proposed legislation to impose a greenhouse-gas cap and trade system in the US if powerful agricultural interest groups join with environmentalists in supporting proposed this legislation. (iii) Briefly explain in words the different forms that political currency can take.

See figure 8.1, page 210 of textbook. Demand shifts out. Political currency: dollar donations, votes, endorsements, revolving-door job offers, etc.

PART II. (students NOT in the 4^th unit lab), continued:

5. Suppose that an environmental law for chemical plants includes a provision that those who violate the law must pay a penalty equal to three times the economic gains from violating the law. Suppose that these facilities have continuous compliance monitors on their stacks that properly detect violations 90 percent of the time. Suppose it is common knowledge that in recent years such cases have been successfully prosecuted 60 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?

(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

.9 * .6 * 3X = exp penalty; compare to X, the gain from being out of compliance

6. Suppose that there are four firms that are capable of supplying pollution allowances – firms A, B, C, and D. There are other firms that demand these allowances. Suppose that each of these four firms has a linear upward-sloping pollution allowance supply curve equal to their marginal abatement cost curve. Suppose that the “y” intercept for firm A’s supply curve is the lowest, followed by firm B, then firm C, with firm D having the highest “y” intercept value for its allowance supply curve. Suppose that there is a single, uniform equilibrium market price for pollution allowances. In the space below, carefully draw a fully labeled diagram showing each of these firms’ allowance supply curves, and clearly indicate on your diagram the quantity of allowances that each will supply at the equilibrium market price of an allowance. Briefly explain your result.

See figure 10.3 on page 265 of the textbook.

PART III. All students: There are 7 questions in PART III. Please answer any 5 of them, and CROSS OUT the 2 you do NOT want me to grade. Each of the 5 questions you answer is worth 10 points:

MEC = marginal effort cost; AEC = average effort cost; TEC = total effort cost; MRP = marginal revenue product; ARP = average revenue product; TRP = total revenue product

Effort	MEC or AEC	TEC	MRP	ARP	TRP	Group Profit
5	3500	17,500	6,000	7,000	35,000	17,500
6	3500	21,000	5,500	6,750	40,500	19,500
7	3500	24,500	5,000	6,500	45,500	21,000
8	3500	28,000	4,500	6,250	50,000	22,000
9	3500	31,500	4,000	6,000	54,000	22,500
10	3500	35,000	3,500	5,750	57,500	22,500
11	3500	38,500	3,000	5,500	60,500	22,000
12	3500	42,000	2,500	5,250	63,000	21,000
13	3500	45,500	2,000	5,000	65,000	19,500
14	3500	49,000	1,500	4,750	66,500	17,500
15	3500	52,500	1,000	4,500	67,500	15,000
16	3500	56,000	500	4,250	68,000	12,000
17	3500	59,500	0	4,000	68,000	8,500
18	3500	63,000	-500	3,750	67,500	4,500
19	3500	66,500	-1,000	3,500	66,500	0
20	3500	70,000	-1,500	3,250	65,000	-5,000

Suppose that there are 5 fishers participating in the fishery described in the table above. They get together and agree to set their total group effort at the group optimal level (identified using marginal analysis), with total effort divided equally among the 5 fishers. Group profits are divided in proportion to each fisher’s share of total group effort.

1. Each individual fisher’s effort will equal 2, and each fisher will get profit of $ 4,500.

2. Now suppose that one of the fishers decides to provide 3 times the effort that he agreed to provide in question 1 above. Each of the other 4 continues to abide by the agreement. Group profits are divided in proportion to each fisher’s share of total group effort.

Total group effort = 14, the cheater gets profit of $7,500, and each of the non-cheaters get profit of $2,500.

3. Now suppose that the agreement breaks down. One fisher sets her effort at 3, while each of the other 4 fishers sets their effort at 4. In this case:

Each fisher gets a profit of $0.

4. Suppose that a job is identical to many others in a competitive labor market except that there is an additional 7 per 100,000 annual chance of accidental death, and that the job pays a risk premium of $600 per year. Use the "value of a statistical life" approach to determine the implied economic value of a statistical life. Show your work.

VSL = $ 8,571,428.5

$600/0.00007

For the following two questions, select one of the following economic policy tools for your answer:

A. Carbon (greenhouse gas) tax;

B. Cap and trade;

C. Subsidies for particular targeted low-greenhouse-gas technologies.

5. This economic tool for reducing greenhouse-gas emissions provides certainty regarding the quantity of emissions reduced (assuming emissions can be adequately measured, there are no questionable offsets, and the policy is enforced). But if we don’t know how many firms will decide to invest in low greenhouse-gas production methods, then this tool does not provide certainty regarding the cost of greenhouse-gas emissions. The tool is letter B.

6. This economic tool for reducing greenhouse-gas emissions strengthens the incentive for consumers and firms to make “climate-friendly” investments. But if at the time the policy is created we don’t know which technology will end up being the most effective, then this tool can actually retard the development of the best and most effective low greenhouse-gas technologies. This tool is letter C.

7. The data 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 (300 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	100	50	0	50	2,500	5,000
B	100	250	0	50	12,500	25,000
C	100	450	0	50	22,500	45,000
D	100	650	50	0	32,500
E	100	850	50	0	42,500
F	100	1,050	50	0	52,500
TOTAL	600	---	150	150	165,000	75,000

a. Suppose that each firm must cut its emissions by 50 percent under a performance-based standard without trading. Correctly fill in the "total abatement cost" column for "no tradable allowances" in the table above.

b. Now suppose that each firm is given a 50 ton/year allowance, and these allowances are fully tradable. Correctly fill in the "allowances bought", "allowances sold", and "total abatement cost, tradable allowances" columns in the table above.

PART IV. All students: There are 10 questions below, each worth 2 points. Please match the word or phrase that uniquely matches the description on the right side of the table.

Word or Phrase	Description
a. A firm’s reputation with environmentally conscious consumers	1. _M__ This program reduces greenhouse-gas emissions by requiring a minimum percentage of generation from renewable energy sources.
b. Marginal benefit equals marginal cost	2. _H__ The European Union’s Emissions Trading Scheme utilizes this economic policy tool to reduce greenhouse-gas emissions.
c. Average revenue product equals average effort cost	3. _N__ This non-market valuation technique estimates use value from the costs of recreational site visitation.
d. Renewable Energy Credits	4. _J__ Environmental valuation technique that was used to estimate existence value for the damage to Prince William Sound due to the Exxon Valdez oil spill.
e. Local hot spots adjacent to polluting facilities	5. _E__ If a pollutant is uniformly mixed, like certain greenhouse gases, then unrestricted trading of allowances will not create this problem.
f. Risk aversion	6. _B__ Occurs at the level of pollution control where total net benefit is maximized.
g. Risk loving	7. _L__ In order for a polluter to be convicted of a felony violation of environmental law, the case must be referred to this entity.
h. Cap and trade system	8. _A_ Can create an incentive for firms to self-regulate emissions.
i. Hedonic regression method	9. _O__ A type of command-and-control regulation.
j. Contingent valuation method	10 _K__ The California Energy Commission found that this option offered the lowest cost alternative for resolving fish passage and water quality problems on the Klamath River.
k. Dam removal and restoration
l. US Department of Justice
m. Renewable portfolio standard
n. Travel cost method
o. Technology-based standard
p. Present value of marginal profits
q. Subtractability
r. Keeping the dams, but adding fish ladders and other mitigation measures
s. Total benefit equals total cost