Econ 423 Exam #1, Fall 2005 – Prof Hackett Your Name: Answer Key (answers in blue)

PART I -- 1. (12 pts) Suppose that in addition to the status quo (current management system), four policy options are being considered in the context of a natural resource management decision. Five members of society are affected by the management decision. The table below shows how these five people feel about the proposed management options relative to the status quo. The numbers represent the amount (in units of utility) by which the different options make them better off or worse off relative to the status quo.

Policy Options	Affected Members of Society					Net Social Utility
	Ari	Nick	Ivy	Felicia	Miranda
Option 1	60	20	30	40	120	270
Option 2	30	0	20	-20	170	200
Option 3	0	-15	15	30	30	60
Option 4	-30	30	0	-30	200	170

1.a. Compute the net social utility for each option and report it in the table above.

1.b. Which of the above options, if any, is Pareto efficient relative to the status quo? ____1____

1.c. Which of the above options, if any, is Kaldor-Hicks efficient relative to the status quo? _____1____

1.d. Which of the above options, if any, is utilitarian-ethical relative to the status quo? ____1_____

Next 3 questions (4 unit students only): Assume an otherwise well-functioning competitive market with the following:

Demand: P = 1050 – 0.2Q; Private-cost supply: P = 50 + 0.3Q. Production of each unit of output Q above leads to a marginal external cost of $200, which implies social-cost supply: P = 250 + 0.3Q.

2. (8 points) Assuming firms can freely pollute in the absence of regulation, compute the "free market" equilibrium P, Q, and total gross gains from trade (CS + PS) using the private-cost supply equation. Show your work.

1050 – 0.2q = 50 + 0.3q è q = 2000 p = 1050 – 0.2(2000) = 650

Total gross gains = [(1050 – 50)*2000]/2 = 1,000,000

Equilibrium P = $650, Q = 2000 units, and total gross gains from trade = $1,000,000

3. (8 points) Compute the dollar amount of total external cost generated when firms can freely pollute in the market equilibrium above, and derive the true net gains from trade. Show your work.

TEC = q*MEC = 2000*200 = 400,000

Tot. net gains = Total gross gains – TEC = 1,000,000 – 400,000 = 600,000

Total external cost = $400,000 and total net gains from trade = $600,000

4. (8 points) Assuming firms pay a Pigouvian tax and thus operate along the social cost supply curve, compute the "socially optimal" equilibrium P, Q, and true net gains from trade. Assume the Pigouvian tax revenue fully offsets any remaining negative externalities. Show your work.

1050 – 0.2q = 250 + 0.3q è q = 1600 p = 1050 – 0.2*1600 = 730

True net gains = [(1050 – 250)*1600]/2 = 640,000

Equilibrium P = $730, Q = 1600 units, and total gains from trade = $640,000

Next 2 questions (3 unit students only)

2. (12 pts) Carefully draw and fully label a supply-demand diagram with negative externalities that illustrates (i) the free-market equilibrium when firms only pay marginal private costs, and (ii) the socially optimal equilibrium based on a Pigouvian tax. (iii) Show the difference in equilibrium prices and equilibrium quantities, and (iv) show the inefficiency caused by negative externalities.

See Figure 4.4 in 2^nd edition of textbook

3. (12 pts) Carefully draw and fully label a supply-demand diagram with positive externalities that illustrates (i) the free-market equilibrium when demand only reflects private benefits to the buyers, and (ii) the socially optimal equilibrium with demand based on social benefits. (iii) Show the difference in equilibrium prices and equilibrium quantities. (iv) In one sentence, describe an example of a market with positive externalities, and in one sentence describe an efficiency-enhancing government intervention applicable to your example.

See Figure 4.1 and accompanying narrative in 2^nd edition of textbook.

Remainder of exam: (all students)

Question 4 or 5. (10 points) 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 100 in both periods. The discount rate is 20 percent. What is the dynamically efficient allocation of the 1000 units of the nonrenewable resource? Get within $5 of the PV of marginal profit being equal – show your work using Hotelling’s rule.

See Powerpoint slides and 2^nd edition textbook content in chapter 5 for details on how to do this.

Exact solution: Q₀ = 627.3, Q₁ = 372.7.

Check on work – Does the division of the 1000 units as outlined above satisfy Hotelling’s rule?

P₀ = 2000 – 627.3 = 1372.7; Period zero marginal profit (P₀ – MC) = 1272.7

P₁ = 2000 – 372.7 = 1627.3; PV of period one marginal profit = (P₁ – MC)/1.2 = 1272.7

Therefore Hotelling’s rule holds – the PV of marginal profit is equal over the two periods….

Q₀ = 627.3

Q₁ = 372.7

Question 5 or 6 (9 points) (i) Carefully draw and fully label a diagram that shows the price trend line for the question above. (ii) Draw a second price trend line in the same diagram for the same situation, except that the discount rate is substantially higher and label it as such. (iii) Draw a third price trend line in the same diagram for the same situation, except that the discount rate is zero and label it as such. (iii) Briefly but succinctly explain in words how discount rates affect the price trend line for non-renewable resources.

Time

PART II: Matching (3 points each). Clearly write the letter for the word or phrase (on the left) beside the description (on the right) that matches it. Each word or phrase has at most one uniquely correct match.

Word or Phrase	Description
A. High discount rates	1. B The property rights regime that describes the ownership of the Humboldt Bay National Wildlife Refuge.
B. State (government) property	2. Q The concept underlying deontological ethics.
C. Usufructuary rights	3. S These often have secondary markets where previously used resource competes with "virgin" resource sold in primary markets.
D. Kaldor-Hicks efficient	4. K The property rights regime in which the rights of access, withdrawal, management, and exclusion are held in common by a group of proprietors.
E. Tragedy of the commons	5. R The gap between price and marginal cost that occurs in competitive commodity markets due to resource scarcity.
F. Positive externality	6. N Occurs when price is above equilibrium in a well-functioning competitive market.
G. Buy too much	7. F An external benefit generated from production and exchange and enjoyed without payment by members of society.
H. Pigouvian tax	8. A These will cause current nonrenewable resource prices to be relatively low, but future prices to be relatively high. [Note: also accepted L, but not as good]
I. Opportunity cost	9. G Consumers do this in markets suffering from unresolved negative externalities because price reflects marginal private cost rather than marginal social cost.
J. Pareto efficient	10. H Name of a policy intervention that internalizes negative externalities.
K. Common property	11. J This efficiency criterion can only be satisfied when a policy option makes some better off and nobody worse off relative to the status quo.
L. Appropriation externality	12. I When a choice is made in the context of scarcity, this is the value of the best option that had to be given up.
M. Open access	13. C Certain use and withdrawal rights to property that is owned by others.
N. Excess supply	14. O Measure of market inefficiency that represents lost gains from trade.
O. Deadweight (social) loss	15. E Occurs in a common-pool resource under open access conditions (or other failed property rights systems) due to self-interested appropriators. [Note: also accepted L, but not as good]
P. Consequentialism
Q. Categorical imperative
R. Marginal profit
S. Recyclable natural resources