Economics 423, Midterm Examination #2, Spring 2007 –
Professor Hackett
Name: Answer Key
[Worth one point :-) ]
4th
unit students problem 1:
Dynamically efficient allocation of a non-renewable resource:
Suppose that there are 1000 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 200 in both
periods. The discount rate is 10 percent.
1. What is the dynamically
efficient allocation of the 1000 units of the nonrenewable resource, and what
will be the prices in the two periods? (within $50 of satisfying Hotelling's
rule; show your work)
Q0 = 561.90 P0
= $1,438.1
Q1 = 438.1 P1
= $1,561.9
How? See PPT
slides for 4th unit lab
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
1000 units of the nonrenewable resource (within $50 of satisfying Hotelling's
rule; show your work).
Q0 = 618.18 P0
= $1,381.82
Q1 = 381.82 P1
= $1,618.18
How? See PPT
slides for 4th unit lab
3. (a) Use the space below to
carefully draw a single fully labeled diagram correctly showing the two price
paths (for P0 and P1) over time for questions 1 and 2
immediately above. (b) Explain why one price path is steeper than the other.
Draw diagram with price
on ‘y’ axis, time on ‘x’ axis. Plot P0 and P1 in the two answers above. Note that
price path is steeper when discount rate ‘r’ increases. This is due to a
stronger time preference for today’s benefits over those of the future.
4th 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” = $300, and P = $2, derive the numerical values for open-access equilibrium effort (E), stock (X), and harvest (H). Show your work:
1.a. EO = a – (bc)/p (equation)
1.b. EO = 850 (numerical value)
XO = 150 (numerical value)
HO = 127,500 (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” = $300, 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)
2.b. E* = 425 (numerical value)
X* = 575 (numerical value)
H* = 244,375 (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. ONLY for students NOT attending the 4th unit lab: There are 5 questions below. Please select any 3 of them to answer. CROSS OUT the 2 questions you do NOT want to answer. Each question is worth 10 points.
1. Carefully draw a single fully labeled diagram below correctly showing decreasing marginal benefits (MB) and increasing marginal costs (MC) associated with environmental and natural resource law enforcement. (i) Identify on your diagram a level of enforcement where MB > MC. Explain why this is (or is not) the level of enforcement that maximizes total net benefit. (ii) Suppose that the MC curve shifted outwards to the right, due to new surveillance technology. Show how this would affect the level of enforcement that maximizes total net benefit. Briefly explain in one sentence.
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 supply or demand curve, and the equilibrium level of effective support, changes if policy makers are forced to watch a video showing the environmental harms the legislation is designed to stop, and as a result the personal values of many policy makers formerly hostile to the legislation change and become aligned with the proposed legislation. (iii) Briefly explain in words how the opportunity for legislators to leave office and work as lobbyists for regulated industry serves as a form of political currency, and how it affects the supply of effective support for legislation proposing to increase regulation of the industry.
(i) See figure 8.1 in 3rd
edition of your textbook for the course.
(ii) Supply curve shifts out,
resulting in an increase in the equilibrium level of support.
(iii) This is a form of political
currency, as it is a type of shady promise of future compensation in return for
voting in a manner favorable to the potential future employers (the regulated
industry). This will result in a decrease in the supply of effective support
for legislation proposing to increase regulation of the industry.
3. Suppose that proposed environmental legislation includes a provision that those who violate the law must pay a penalty equal to two times the economic gains from violating the law. It is common knowledge that 60 percent of all facilities are inspected for compliance each year, and that in recent years judges have imposed the full statutory penalty 50 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
4. (i) In the space provided below, carefully
draw a fully labeled diagram showing the Gordon model of a marine capture
fishery. Be sure to label all of your lines and curves. (ii) Carefully indicate
on the diagram the open access and the group optimal levels of effort. (iii)
Show how the open access and group-optimal level of effort would change if
marginal effort cost declined due to large government fishing subsidies.
(i) and (ii)
See figure 5.6 on page 109 of the 3rd edition of your textbook.
(iii) A
parallel downward shift in MEC curve, which will result in an increase in both
the group optimal and the open access levels of effort.
5. (i) Re-draw the
Gordon diagram, and (using arrows or different colored lines) correctly show
how the curve(s) in the diagram will shift, and how the open access and group
optimal level of effort will change, if the price per pound of fish were to
substantially decrease. (ii) In words, briefly provide an intuitive and correct
explanation for this change.
(i). See
above. For the impact of a reduction in the price of fish, this will cause a
leftward shift in the ARP and MRP curves, which will result in a decrease in
both the group optimal and the open access levels of effort.
(ii) While
the natural resource’s abundance level has not changed, its value has declined,
which will reduce both ARP and MRP. Since MRP is lower for any given level of
effort, the level of effort where MRP = MEC will be lower, as will be the level
of effort where ARP = AEC.
Part III. ALL STUDENTS: There are 5 questions below. Everyone
must answer question 1 below. Of the remaining 4, please answer any 2 of
them, and cross out the 2 questions you do not wish to answer with a BIG
X. Each question is worth 10 points.
1. Suppose that there are six independent renewable energy power producers that are capable of supplying renewable energy credits (REC’s) – firms L, M, N, O, P, and Q, listed in order from lowest to highest marginal costs of renewable energy generation. Suppose that each has a horizontal REC supply curve. The length of each firms’ REC supply curve line segment is equal to the quantity of renewable energy each has available to sell. Thus the REC market supply curve looks like a step function. For simplicity, suppose that there is a regular linear downward-sloping allowance demand curve from public utilities that do not produce their own renewable energy, and that intersects the market supply curve through firm M’s line segment. (i) Draw and fully label this diagram, and show the equilibrium price and quantity of REC’s on your diagram. (ii) Show how the diagram and equilibrium price and quantity would change if the state were to increase the 20% renewable portfolio standard requirement to 40% of total power sold by utilities. (iii) Suppose that instead of the state increasing the renewable portfolio standard, the utilities were to increase the quantity of renewable energy that they produce for themselves to meet their renewable portfolio standard. Show how the original equilibrium would change.
`
2. Suppose that a risk-neutral petroleum refinery can save $30 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 50 percent, and that the probability of a judge imposing the statutory penalty given detection is 60 percent. If the statutory penalty calls for a fine equal to 2.5 times the annual cost savings gained by the offender, then will this system create deterrence? Show your work.
Deterrence: YES NO
(circle one)
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.
Minimum statutory penalty = $ 100
million plus a few extra bucks
4. Suppose that a job in
(i) VSL = $ 400,000
(ii) How will the value of a statistical life change if workers are able to demand a risk premium of $400 instead of $200?
INCREASE STAY THE SAME DECREASE (circle one)
5. The data below refers to pollution emissions and marginal pollution abatement cost per ton in an industry. Total industry-wide emissions are to be reduced by 50 percent (3,000 tons/year):
|
Firms |
Historical Emissions (Tons/Yr) |
Marginal Abatement Cost ($/Ton) |
Allowances Bought |
Allowances Sold |
Total Abatement Cost (No Tradable Allowances) |
Total Abatement Cost (Tradable Allowances) |
|
A |
1,000 |
50 |
0 |
500 |
25,000 |
50,000 |
|
B |
1,000 |
250 |
0 |
500 |
125,000 |
250,000 |
|
C |
1,000 |
450 |
0 |
500 |
225,000 |
450,000 |
|
D |
1,000 |
650 |
500 |
0 |
325,000 |
0 |
|
E |
1,000 |
850 |
500 |
0 |
425,000 |
0 |
|
F |
1,000 |
1,050 |
500 |
0 |
525,000 |
0 |
|
TOTAL |
6,000 |
--- |
1,500 |
1,500 |
1,650,000 |
750,000 |
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.
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. A firm’s reputation |
1. _M_ In a deposit-refund system for bottles and cans, you get your deposit back when you do this. |
|
b. Marginal benefit equals marginal cost |
2. _H_ The European Union’s Emissions Trading Scheme gave polluters too many of these, which resulted in low allowance prices and few real cuts in 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 |
|
e. Firms have heterogeneous marginal abatement costs |
5. _E_ In order for cap-and-trade systems to reduce industry-wide costs of compliance, this must be true about the firms in the industry. |
|
f. Risk aversion |
6. _B_ Occurs at the level of pollution control where total net benefit is maximized. |
|
g. Risk loving |
7. _L_ Example of ecosystem service. |
|
h. Greenhouse gas emissions allowances |
8. _K_ In a cap-and-trade system, the sum of all allowances equals this. |
|
i. Hedonic regression method |
9. _O_ A type of command-and-control regulation. |
|
j. Contingent valuation method |
10 _P_ Hotelling’s rule states that the intertemporal allocation of a nonrenewable resource is dynamically efficient if these are equal across all time periods. |
|
k. The cap |
11. _G_ If the expected penalty is equal to the benefit from violating environmental or resource law, an individual with this attitude toward risk will not be deterred from violating the law. |
|
l. Carbon sequestration by natural forests, corals, and plankton |
12. _Q_ This characteristic distinguishes common pool resources from pure public goods. |
|
m. Recycle |
13. _R_ Due to this, when one individual over-appropriates from a common-pool resource, s/he imposes harms on all the other appropriators. |
|
n. Travel cost method |
|
|
o. Technology-based standard |
|
|
p. Present value of marginal profits |
|
|
q. Subtractability |
|
|
r. Appropriation externality |
|
|
s. Total benefit equals total cost |
|