Economics 423, Midterm Examination #2, Fall 2008 –
Professor Hackett
Name: ANSWER KEY
[Worth one point :-) ]
Section 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 = 2200 - 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? (show your work)
Q0 = 571.43 P0 = $1,628.57
Q1 = 428.57 P1
= $1,771.43
Solve for Q’s using
Hotelling’s rule, and use substitution into inverse demand equation to solve
for P’s.
2. Suppose that the basic
setup of the problem above were the same, except that now the discount rate
rises to 25 percent. Re-compute the dynamically efficient allocation of the 1000
units of the nonrenewable resource (show your work).
Q0 = 666.67 P0 = $1,533.33
Q1 = 333.33 P1 = $1,866.67
Solve for Q’s using
Hotelling’s rule, and use substitution into inverse demand equation to solve
for P’s.
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.
Create a diagram
with price on “y” axis and time on “x” axis. Plot period 0 and period 1 prices
for 1 and 2 above. You should find that the price path is steeper for the
higher discount rate, which is consistent with the idea that higher discount
rates result in a stronger emphasis on current consumption over future
consumption.
Section 2: The bio-economics 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” = $500, and P = $3, 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
= 833.33 (numerical value) (solution
method: solve for effort Eo where TRP = TEC; use this value to then
solve for X and then H)
XO = 166.67 (numerical value)
HO = 138,889 (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” = $500, and P = $3, derive the numerical values for open-access 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*
= 416.67 (numerical value) (solution
method: solve for effort Eo where MRP = MEC; use this value to then
solve for X and then H)
X* = 583.33 (numerical value)
H* = 243,056 (numerical value)
3: Use the diagram below to carefully indicate the correct numerical equilibrium levels of stock growth F(X) or harvest H (“y” axis) and stock X (“x” axis) associated with questions 1 and 2 above.
PART II. ONLY for students NOT participating in 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. (a) Carefully draw a single fully labeled diagram below correctly showing the level of environmental and natural resource law enforcement that maximizes total net benefits. Your diagram should include both a marginal benefit curve and a marginal cost curve. (b) On the same diagram, show how the answer to part “a” above changes if scientific evidence emerges that the damages to the environment from those who violate environmental law are much larger than originally thought.
Diagram should have $/unit on “y”
axis and units of law enforcement on “x” axis. Typical MB curve is
downward-sloping and MC curve is upward-sloping. Intersection is where total
net benefits are maximized.
For part (b), the MB curve shifts
outwards to the right, resulting in a higher level of enforcement that
maximizes total net benefits.
2. (a) In the context of local self-governance of a common-pool resource, briefly describe the advantage of an inclusive voting rule. (b) Likewise, briefly describe the disadvantage of an inclusive voting rule. (c) When appropriators who are heterogeneous in historical harvest levels come together to set harvest limits, does the field research suggest they will agree to an equal division of the resource, or to harvest shares proportionate to historical harvest levels?
a. Advantage of inclusive voting rule: Leads to more stability; lower monitoring and enforcement costs. Less likely to result in costly fighting and disagreement over time.
b. Disadvantage of inclusive voting rule: Delay costs are likely, which may manifest in the form of
more deterioration of the common-pool resource.
c. Harvest rule (circle one): Equal division Proportionate to historical harvest levels
3. Suppose that proposed environmental legislation includes a provision that major point-source emitters that violate the law must pay a penalty equal to two times the economic gains from violating the law. Continuous compliance technology assures that all violations will be detected. Data indicate that regulators will impose the penalty one-third of the time, and provide warnings two-thirds of the time. Based on this information (show your work):
(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
1 * 0.333 * 2X =
0.67X < X è risk neutral entity not deterred….
PART II. ONLY for students NOT enrolled in the 4th unit lab,
continued
4. (a) 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. Carefully
indicate on the diagram the open access and the group optimal levels of effort.
(b) In the same diagram, show how open
access and group-optimal levels of effort change if diesel fuel prices drop
substantially.
See diagram
in textbook. (b) Marginal effort cost curve shifts downwards, resulting in both
open access and group optimal levels of effort to increase.
5. Suppose there are four
firms that are capable of supplying pollution allowances – firms A, B, C, and D.
Suppose that each 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 C, with 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 the quantity
of allowances that each will supply at the equilibrium market price of an
allowance. Briefly explain your result.
See diagram
in textbook.
Part III. ALL STUDENTS:
There are 5 questions below. Please answer any 3 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 the marginal
benefit from reducing emissions is given by the equation MB = 200 - Z, and
marginal cost from reducing emissions is given by the equation MC = 100 + 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.
200 – Z = 100 + Z è Z = 50
Z = 50
%
2. Suppose that a
risk-neutral petroleum refinery can save $5 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 90 percent,
and that the probability of a sanction being imposed, 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.
0.9 * 0.8 * 10
million = 7.2 million > 5 million è yes, risk-neutral entity is deterred
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.
0.9 * 0.8 * X = 5
million è X = 6,944,444.44 plus a bit extra
Minimum statutory penalty = $6,944,444.44 plus a bit extra
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 $700 per year. Use the "value of a statistical life"
approach to determine the implied economic value of a statistical life. Show
your work.
= 700/(8/100,000)
= 8,750,000
VSL = $8,750,000
Part III. ALL STUDENTS, continued
5. The data in the table
below refers to pollution emissions and marginal pollution abatement cost per
ton in an industry. Total industry-wide emissions are to be reduced by 50
percent (2400 tons/year):
|
Firms |
Historical Emissions (Tons/Yr) |
Marginal Abatement Cost
($/Ton) |
Allowances Bought |
Allowances Sold |
Total Abatement Cost (No
Tradable Allowances) |
Total Abatement Cost
(Tradable Allowances) |
|
A |
800 |
100 |
400 |
40,000 |
80,000 |
|
|
B |
800 |
100 |
400 |
40,000 |
80,000 |
|
|
C |
800 |
100 |
400 |
40,000 |
80,000 |
|
|
D |
600 |
500 |
300 |
150,000 |
||
|
E |
600 |
500 |
300 |
150,000 |
||
|
F |
600 |
800 |
300 |
240,000 |
||
|
G |
600 |
800 |
300 |
240,000 |
||
|
TOTAL |
4,800 |
--- |
1200 |
1200 |
900,000 |
240,000 |
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 (3 points each). Match 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_ This treaty addresses anthropogenic greenhouse-gas emissions. |
|
b. Marginal benefit equals marginal cost |
2. _J_ Environmental valuation technique that estimates non-use values associated with, say, improved wildlife habitat in a remote wilderness area. |
|
c. Total benefit equals total cost |
3. _S_ If the expected penalty is equal to the benefit from violating environmental or resource law, an individual with this attitude toward risk will definitely NOT be deterred from violating the law. |
|
d. Renewable energy credits |
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. _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. Slower economic growth due to stringent environmental regulations |
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 natural aquifers and watersheds. |
|
h. Individual quota system |
8. _R_ This is a tax placed directly on pollution emissions. |
|
i. Hedonic regression method |
9. _O_ This type of regulation is subdivided into technology-based standards and uniform performance-based standards. |
|
j. Contingent valuation method |
10. _P_ Example of a direct compliance cost. |
|
k. Reduce the industry-wide cost of regulatory compliance |
11. _A_ In order for this to generate successful self-regulation, consumers must be well-informed, have viable alternatives, and be capable of impacting a firm’s profits through their purchase decisions. |
|
l. Ecosystem services not traded in markets |
12 _H_ A withdrawal right to a share of total allowable catch that can slow the race for fish (derby) |
|
m. |
13. _D_ Utilities can either meet renewable portfolio standard requirements by generating their own renewable energy, or by buying these from independent renewable energy generators. |
|
n. |
|
|
o. Command-and-control regulation |
|
|
p. The cost of pollution abatement equipment like scrubbers. |
|
|
q. Benefits transfer |
|
|
r. Effluent tax |
|
|
s. Risk loving |
|