Economics 131
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经济学期末代考 Suppose the market for mineral water in a small isolated country is perfectly competitive.The marginal cost for mineral water production
FINAL EXAM 经济学期末代考
1.Suppose the market for mineral water in a small isolated country is perfectly competitive. 经济学期末代考
The marginal cost for mineral water production is MC = 22+3Q, and the demand for mineral water is P = 85-6Q, where P is the price (in cents per gallon), and Q is the quantity of mineral water produced (in million gallons per month). Suppose the processing procedure in mineral water production generates pollution, which incurs an external damage to the environment. The total external cost is given by MEC = 1.5Q.
a) Calculate the marginal social cost function, and show it in a graph together with the supply (MC) and demand curves. Label each curve clearly.
b) Compute the competitive equilibrium price and quantity in this market. Is this
competitive equilibrium efficient? Why or why not? Show the equilibrium price and
quantity in the graph from part a. 经济学期末代考
c) What is the efficient quantity in this market? Compute it and show it in the graph from part a.
d) Does the competitive equilibrium generate a deadweight loss? If so, compute it and show it in the graph from part a.
e) If the government intends to impose a production tax to reach the socially optimal level of production, how much should the per unit tax be? How much is the government revenue after the tax is imposed?
Answer: 经济学期末代考
a.MSC = 22+3Q+1.5Q = 22+4.5Q
b.Competitive equilibrium: Pc =43 cents, Qc =7 million gallons/month. This quantity is not efficient because of the negative externality (see next part).
c.Efficiency: Qe = 6 million gallons/month. (Q at which demand intersects MSC).
d.DWL = 5.25 million cents/month, or $52,500/month. 经济学期末代考
e.The Pigouvian tax should be equal to the MEC at the efficient quantity of 6 million
gallons: t=MEC(6)=1.5*6=9 cents/gallon.
With this tax the new equilibrium output will be the efficient one, which is 6 million gallons/month. Total revenue will be 6*9=54 million cents/month, or $540,000/month.
2. The Diaguitas, an ancient tribe located in the Calchaqui Valley, have decided that they will stay for two more years (the current year and the next) in their current location, after which they will migrate to another place.
Their archeologists have determined that the valley’s aquifer has a total of 250 gallons of water left. The aquifer is not recharging, and therefore water can be considered a depletable resource (similar to oil). There is no other water source in the region. The Diaguitas are impatient people, with a discount rate of 15%.
The tribe’s demand for water is constant in time, and it is equal to P = 100 – 0.23Q. The marginal cost of extracting water is $0 per gallon the current year, and it is expected to rise to $8 per gallon next year. 经济学期末代考
a) Compute the efficient extraction of water in each year. Show the efficient quantities in a graph.
b) Find the price of water in each period that the tribe’s administration should charge to achieve the efficient allocation.
c) How does your answer to part a) changes if the total stock of water in the aquifer was 1000 gallons? Give a precise numerical answer and show it in a separate graph. 经济学期末代考
d) After you came up with the solution to part a), the tribal council met and decided to change the discount rate to 25%, arguing that 15% was way too low. How would your answer to part a) change knowing the new discount rate? You don’t need to give a numerical answer, just give a reasoning of how the quantities in each year would change.
Explain your reasoning.
Answer:
a.The conditions for efficiency are Q0+ Q1 = 250 and MNB0 = PV(MNB1). Solving, we get Q*0 = 162.79, Q*1 = 87.21.
b.To achieve efficiency in period one, we need that total consumption equals 162.79. Plugging this into the demand curve, we obtain that the price that will lead consumers to consume this amount is P*0=62.56. Similarly, P*1 = 79.94.
c.In this case we can reach the point at which MB=MC in each period separately:
In year 0: 100-0.23Q0=0 à Q0 =434.78. 经济学期末代考
In year 1: 100-0.23Q1=8 à Q1 =400.
Total consumption is 434.78+400=834.78. The remaining quantity is left unused at the end of period 1.
d.When you use a higher discount rate, you value net benefits in the future less. Hence, the efficient allocation will call for using more of the resource in the first year and less in the second.
3. The total catch of crab in a given year depends on the number of hours spent crabbing and the current stock of crab.
In particular, the crabbers have estimated that the catch is given by the function
h =1.8 * E * S
where h is the total catch per year (in million crabs), E is the number of hours spent fishing (in thousands) and S is the current stock of crab (in millions). The benefit from the crab caught is given by
B(E) = 9 − (E − 3)2
The cost of effort is given by
C(E) = 4E
[MB(E) = -2E + 6, MC(E) = 4.]It was also estimated that the population of Alaskan king crab grows according to the
function
g =10S − 2S2
Currently the stock is 3.5 million crab. 经济学期末代考
a) Compute the socially efficient level of fishing effort and sketch it in a graph.
b) What is the catch at the efficient effort level? Is it sustainable? Explain.
c) Assume that the crab fishery is a common pool resource, open to any fisher that wants to fish there. Compute the level of effort that will be devoted to fishing in competitive conditions and the harvest that will be obtained. Is it sustainable? Show it in the graph from part a.
d) Assume that now crabbers have to pay $1 per hour of fishing. Write the new cost function including the tax. Compute the new competitive market allocation with the tax. Do we reach the efficient harvest? Explain. 经济学期末代考
e) Give an example of other method (besides the fishing tax) that can be used to reduce the harvest.
Answer: 经济学期末代考
a) Efficiency requires MB(Ee) = MC(Ee) à Ee = 1 thousand hours.
b) The harvest at the current stock level and with effort equal to 1 is h = 1.8 * 1 * 3.5 = 6.3 million crabs. The growth for this year at the current stock level is g = 10 * 3.5 – 2 * (3.5)2 =10.5 million crabs. Since the harvest at E=1 is lower than the growth, that harvest is sustainable. 经济学期末代考
c) Equilibrium condition: B(Ec) = C(Ec) à Ec = 2 thousand hours. The harvest at the current stock level and with effort equal to 2 is h = 1.8 * 2 * 3.5 = 12.6 million crabs. The growth at the current stock level is g = 10 * 3.5 – 2 * (3.5)2 = 10.5. Since the harvest at E=2 is higher than the growth, it is unsustainable.
Parts d and e not required in Winter 2020:
d) With a tax of $1 per hour, the cost function is C(E) = 5E. The new equilibrium with the tax happens at E’= 1. This is the efficient amount of effort and harvest.
e) We can assign private ownership on the fishery.
4.According to the article titled “Climate Economics” by Geoffrey Heal (discussed in class), there are two potential components (or two rates) that could enter the discount of future values in environmental policy evaluation. 经济学期末代考
a.Explain what these two components are. [You don’t need to remember the names of each, just to give an intuitive explanation of what each component means.]
b.What does Heal argue about the legitimacy of each of these components being taken as positive for environmental policy evaluation? Explain.
Answer: 经济学期末代考
a.i) Current generations may consider themselves as more important than people who will live in the future. Hence, they may want to discount the benefits and costs of future generations.
ii) If we expect future generations to be richer than we are, we can expect their marginal utility for one more dollar of consumption to be lower than ours. This would justify discounting their benefits and costs.
b.Heal argues that the first potential reason is morally indefensible: it is ethically wrong to consider ourselves as more important than future generations. 经济学期末代考
Regarding the second reason, Heal argues that while it is true that the quantity and quality of industrially produced goods is expected to increase over time (because of economic growth), in view of climate change it is also the case that the quality of goods that depend on the environment may go down in the future. So it is unclear that in the balance future generations will be better off.
Because of these arguments, Heal claims that the discount rate that we should use to evaluate climate change policy should be very low, if not zero.
MULTIPLE CHOICE PROBLEMS: 经济学期末代考
1.A cost imposed on someone who is neither the consumer nor the producer is called a
a) pigouvian tax.
b) command and control policy.
c) positive externality.
d) negative externality.
2.Two firms, A and B, each currently emit 100 tons of chemicals into the air. The government has decided to reduce the pollution and from now on will require a pollution permit for each ton of pollution emitted into the air. The government gives each firm 40 pollution permits, which it can either use or sell to the other firm. It costs Firm A $200 (constant) for each ton of pollution that it abates, and it costs Firm B $100 (constant) for each ton of pollution that it abates. After the two firms buy or sell pollution permitsfrom each other, we would expect that Firm A will emit
a) 20 fewer tons of pollution into the air, and Firm B will emit 100 fewer tons of pollution. 经济学期末代考
b) 80 fewer tons of pollution into the air, and Firm B will emit 100 tons.
c) 40 fewer tons of pollution into the air, and Firm B will emit 40 fewer tons of pollution.
d) 20 fewer tons of pollution into the air, and Firm B will emit 100 tons.
3.Betty’s cat causes Suzy to sneeze. Betty values her cat’s companionship at $300 per year. 经济学期末代考
The cost to Suzy of tissues and her allergy medication is $350 per year. Based on the Coase theorem, if Betty owns the apartment and they bargain
a) Betty would pay Suzy $400 so that she may keep her cat.
b) Betty would pay Suzy $350 to purchase her tissues and allergy medication.
c) Suzy would pay Betty $325 to give away her cat.
d) Suzy whould move
4.Why do elephants face the threat of extinction while cows do not?
a) Cattle are a valuable source of income for many people, while elephants have no market value. 经济学期末代考
b) There is a high demand for products that come from cows, whereas there is no demand for products that come from elephants.
c) There are still lots of cattle that roam free, while all elephants live in zoos.
d) Cattle are owned by ranchers, while elephants are owned by no one.
5.Suppose that there are two polluters in San Diego, currently producing 20 tons of
pollution per month each, for a total of 40 tons. The local govt. decides to reduce pollution by 25 tons per month (to a total of 15 tons/month). The marginal costs of abating pollution for each polluter are given by MAC1 = 4 + (A1/2) (TAC1 = 4A1 + (A1)2 /4) and MAC2 = A2
(TAC2 = (A2)2 /2). How much will each polluter have to abate in an efficient allocation?
a) A1 = 11, A2 = 14
b) A1 = 12.5, A2 = 12.5 经济学期末代考
c) A1 = 14, A2 = 11
d) A1 = 0, A2 = 25
Suppose that there are two polluters in San Diego, currently producing 20 tons of pollution per month each, for a total of 40 tons. The local govt. decides to reduce pollution by 25 tons per month (to a total of 15 tons/month). The marginal costs of abating pollution for each polluter are given by MAC1 = 4 + (A1/2) (TAC1 = 4A1 + (A1)2 /4) and MAC2 = A2
(TAC2 = (A2)2 /2). What is the emissions charge that if imposed will achieve the efficient allocation?
a) t = 10.
b) t = 11
c) t = 14
d) t = 25
7.Suppose that there are two polluters in San Diego, currently producing 20 tons of pollution per month each, for a total of 40 tons. The local govt. 经济学期末代考
decides to reduce pollution by 25 tons per month (to a total of 15 tons/month). The marginal costs of abating pollution for each polluter are given by MAC1 = 4 + (A1/2) (TAC1 = 4A1 + (A1)2 /4) and MAC2 = A2 (TAC2 = (A2)2 /2). Compared to a uniform standard, how much are the savings for society of achieving an efficient allocation?
a) 1.685
b) 167.185
c) 165
d) none of the above
8.Net social benefits associated with consumption of some amount of the services of an environmental resource are given by which familiar concept from microeconomics?
a) consumer surplus
b) profits
c) producer surplus or economic rent
d) the sum of producer and consumer surplus
9.A problem with using Pigouvian taxes to address externalities is…
a) the effect of transactions costs 经济学期末代考
b) the possibility that polluters will act strategically
c) the amount of information needed to set the tax appropriately
d) the problem of exhaustible resources
10Assume that we are trying to assess the value of the population of salmon in Alaska.
Which of the following represents existence value:
a) The value we expect in the future from potential drugs manufactured from salmon oil 经济学期末代考
b) The value of salmon meat that we can buy at the grocery store.
c) The value of just having more species around, even if we will not interact with them
d) All of the above.
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