Economics 423, Midterm
Examination #2, fall 2007 – Professor Hackett
Name:
Key
4th 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:
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” = $200, 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) Set TRP = TEC,
solve for E.
1.b. EO = 900 (numerical value)
XO = 100 (numerical value)
HO = 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 4th 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 4th 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 |