Solutions Econ 290 September 2006
Quiz 1
Quiz 2
Quiz 3
Midterm
Quiz 4
1. List the factors that determine the optimal annual harvest of a renewable resource. (2 marks)
The size of the optimal annual harvest depends on the biological
interest rate (i.e. growth rate of the resource), the regular interest rate (or
discount rate), the price of the resource, and the cost of harvesting. ½ mark each point.
Students may write that “ownership” affects the optimal harvest. That’s ok.
It affects the actual harvest rather than the socially optimal harvest.
2. Briefly, what is Hartwick’s rule and what intuition does it support? (2 marks)
Hartwick’s rule states that, to keep consumption sustainable, rents
from resource extraction, specifically “Total Hotelling Rent”, should be
invested in capital.
The intuition is that capital should be left intact. If the capital or wealth base is intact, the
nation can maintain its standard of living.
Another way of putting it is that the nation should “live off the
interest” of its capital. Another way of
putting it is that declining resource stocks must be made up for by increased
stocks of physical or human capital.
3 a. The nation of Smeltdown has non-renewable resource extraction equal to 100,000 tonnes this year. The resource sells for $100 per tonne. Extraction of the last tonne cost $30. What is Total Hotelling Rent for Smeltdown this year? ( 1 mark)
Total Hotelling Rent = (P-MC) R = $70 x 100,000 = $7, 000,000.
½ mark if said “$70”.
3 b. If Smeltdown also has national savings equal to $20,000,000; capital depreciation equivalent to $5,000,000; education spending of $18,000,000; and environmental damage equal to $25,000,000 (all amounts being for this year), what is “Genuine Savings” for Smeltdown this year?
Genuine Savings (millions) = 20 – 5 + 18 – 25 – 7 = 1 million
The 7 million is Total Hotelling Rent needed to make up for declining
resource stocks.
If they left this Total Hotelling Rent out, give them only 1 out of 2 marks.
4 Consider the neoclassical production function Y = A Ka Lb Rc. How would an ecological economist like to improve this model? (2 marks)
An ecological economist would like to add E, ecosystem services, to the
production function.
An ecological economist would also like to see substitutability
declining as R (or E) declines.
An economist would define pollution as any residuals in the environment
in excess of the socially optimal amount.
Quiz 2
1. Consider the following Environmental Kuznets Curve (3 marks)
a) Label the horizontal axis. GNP per person
b) Is this curve consistent with the Kuznets hypothesis? If not, sketch the hypothesized shape. The hypothesized shape is an inverted “U”.
c) What kind of residuals might give rise to this shape of Kuznets curve? Residuals that have obvious downsides for all citizens and for which the costs of cleanup are spread out among citizens are likely to be in this category. One example is smog.
2. List three conditions necessary for the market price of a good to reflect the good’s true value-in-trade to society. (3 marks) For the market price to reflect value-in-trade to society, the market must be competitive, information must be available to all, there should be no price discrimination, and there should be no externalities.
3.Consider the following diagram. (5 marks)
This diagram was a picture of supply intersecting demand. Above the supply curve is a higher curve labeled “social marginal cost.”
a) Label the market price of corn. This is the price where supply intersects demand.
b) Shade in the producer surplus that exists at market equilibrium. This area is inside the triangle whose points are the market price, the point where supply intersects demand, and the vertical intercept of the supply function.
c) What is the socially correct value-in-trade of corn? The socially correct v.i.t. is the price level where social marginal cost intersects demand.
d) Is there a positive or negative externality on the production of corn? There is a negative externality on the production of corn. The marginal cost to society overall is the farmers’ marginal cost plus other costs not borne by the farmers.
e) Is the amount of corn traded too high or too low relative to the socially correct amount? The amount of corn traded exceeds the socially correct amount.
4. Imagine that the Economics Department and the French Department are considering purchasing classroom clocks for use in Kingston Hall. The Economics Department’s marginal willingness to pay is P = 360 – 90 Q. The French Department’s marginal willingness to pay is P = 360 – 30 Q.
a) What is the maximum number of clocks the Economics Department would ever be interested in (assuming the clocks aren’t free)? What is the maximum number the French Department would be interested in? (1 mark). The Economics Department will purchase up to 4 clocks, and the French Department, up to 12 clocks.
b) Graph the aggregate demand function for the departments. (4 marks)
Between a quantity of 0 and 4 clocks, both departments are interested in buying, and the total marginal willingness to pay (i.e. the total inverse demand function) is P = 720 – 120 Q. After 4 clocks, only the French Department is willing to pay, so P = 360 – 30 Q. Thus the aggregate demand function is graphed this way: The vertical intercept is 720. The horizontal intercept is 12. A kink occurs at (4, 240). Connect the dots.
Quiz 3
1. Queen's is considering offering its students who live in residence a meal plan consisting exclusively of locally-grown ingredients. Queen's is hiring you to produce a survey of students in residence to determine how much more (if anything) they would be willing to pay for a locally-grown menu.
If you had just six questions to ask in your questionnaire, what would they be?
We need some identifying questions:
What is your gender?
Which of the following applies to you:
"I a) have plenty of money to pay my expenses; b) have enough money to pay
my expenses with a safety cushion; c) have just enough money to pay my
expenses; d) am finding it difficult to pay my expenses."
We need some questions about habits:
How many times a week do you take advantage
of your meal plan and eat in the cafeteria?
Do you ever shop at the farmers' market?
We need to uncover WTP (and WTA would be
nice too).
Do you feel it is important to eat
locally-grown food?
Would you be willing to pay $20 a month more
for a meal plan consisting solely of locally-grown food? If yes, would you be
willing to pay $30 a month more? If no, would you be willing to pay $10 a month
more?
Other good questions:
If a local non-profit group were to
subsidize $50 per month of a locally-grown menu, would you be willing to pay
the remaining $50 per month for such a menu?
What types of food do you currently consume
the most?
What do you consider
"locally-grown" food?
If Queen's is unable to provide you with a
locally grown menu, how much should Queen's compensate you for this?
2. Consider this graph of a competitive market for motorcycles in Kingston each summer.
Let Pstar be the price of motorcycles before the tax.
a) Draw in the new quantity of motorcyles sold. This is Qn
b) Draw in the new price that motorcycle suppliers earn. This is Ps, found on the supply curve at Qn.
c) Draw in the new price that buyers pay. This is Pd
d) Who is hurt most by the tax? Consumers are hurt most by the tax, because the demand curve is less elastic than the supply curve.
e) If a police project requires motorcycles, at what price to Kingstonians should motorcycles be costed? Motorcycles should be costed at the true cost of an additional motorcycle to Kingston society, given current output levels. The answer is Ps.
f) If a police project replaces motorcycles with other vehicels, and the motorcycles are released to Kingston society for other uses, what is the value of the suddenly available motorcycles? Because of the tax, motorcycles are artificially scarce in Kingston. The MWTP exceeds MC. Kingstonians would be willing to pay Pd for an extra motorcycle (assuming it's in brand new condition). That is the marginal benefit to society.
1. What is involved in making GDP "green"? (3 marks) To make GDP green, include the value of ecosystem services. Subtract off environmental damage suffered, and subtract off economic depreciation i.e. the amount by which Total Hotelling Rent exceeds investment. (GDP already includes education spending. Physical capital depreciation is already subtraced off of GDP to form "NDP".)
2. A community orchard provides apples to anyone who cares to harvest them. When there is one harvester in the orchard, 300 apples are harvested per hour. When there are two harvesters, 300 apples are harvested per harvester per hour. When there are 3 workers, the # apples per worker per hour is 300 also. When there are 4 workers, it's 275; when there are 5, 250; when there are 6, 225; and when there are 7 workers, 200 apples per worker per hour are harvested. a) Discuss and explain the externality problem that exists here. Do not be too brief. (3 marks)
Since anyone can enter the orchard to harvest (non-excludability), and since each person's apples are therefore unavailable to others (rivalry), the orchard is an open-access resource. In this extreme case of a negative externality, harvesters consider their own private benefits rather than the social benefits of their harvesting activity. When crowding becomes an issue and the low-hanging fruit becomes scarce, private benefits are higher than social benefits, leading to more workers in the orchard than is socially optimal.
b)What is the marginal benefit to society (per hour) of having a 6th worker in the orchard? (2 marks) With 5 workers, there are 250 x 5 = 1250 apples harvested for society. With 6 workers, there are 225 x 6 = 1350 apples harvested. The net social gain from the 6th worker is 1350 - 1250 = 100 apples.
3. Consider a community experiencing wastewater discharge into a nearby lake. Two groups experience damages due to the pollution. The first group's marginal damages can be described by MD1 = 15 E, where E is thousands of gallons of discharge per year. The second group's marginal damages are MD2 = 5 E. As for clean-up, the community-wide MAC function is 3000 - 10 E. What is the socially correct level of discharge, from an economic point of view? Show your work. (3 marks)
The marginal damages must be added vertically. Fortunately, both groups have damages over the entire range of possible emission levels, so simply add MD total = MD1 + MD2 = 20 E. Set MD = 20 E equal to MAC = 3000 - 10 E and you will find that E-star is 100 (thousand gallons per year).
4. Consider a hypothetical community called Ashville. Two firms spew particulate matter into the air while providing electricity for Ashville. The marginal abatement cost function for the first firm is MAC1 = 100 - 10 E1 where E1 is the first firm's emissions of ash, measured in tons per year. The MAC for the second firm is MAC2 = 80 - 4 E2.
a) What is the total amount emitted by each firm? (1 mark) Plug MAC = 0 into each firm's equation to get the horizontal intercept i.e. initial emissions. Initial emissions for the first firm is 10, and for the second firm, 20.
b) Graph the total MAC function for Ashville (4 marks). To make a long story short, this graph has vertical intercept = 100, horizontal intercept = 30, and a kink at (2,80).
5. The town of Ashville is considering a project to clean the air and is hiring you to perform a cost-benefit analysis of the project. The question is whether the net present value of this project to Ashvillians is greater than zero. Which of the following are not legitimate costs and benefits to be counted in your analysis? Select and explain (4 marks).
· damages avoided because of the cleaner air. Appropriate
· abatement costs incurred to bring about the cleaner air. Appropriate
· cost of monitoring the firms to ensure compliance with the project. Appropriate
· losses of walking tour business because of improved bus tour business. The question implies that the bus tour business is no longer suffering damages from the air pollution (somehow). Its business is better. However, its competitor, the walking tour, consequently suffers. This is a ripple effect and is ignored.
· reduced costs of cleaning the exterior of public buildings.Whoops, I shouldn't have added this one because it's already counted in the first point, damages avoided.
· loss of municipal revenue from fines collected under the previous (different) pollution abatement project. These are taxes that Ashville's firms paid to Ashville's government. These taxes are simply redistributions within Ashville society and do not count.
6. Ashville is comparing various projects to improve air quality. Project A costs $100,000 in year 1. It provides benefits of $30,000 in years 1,2,3, and 4. After the fourth year, Project A is over.
a) If the discount rate is 5%, what is the net present value of Project A? (2 marks) You could do this two ways. One is by counting the costs and benefits of each year at the end of the year: NPV = -70,000/(1.05) + 30,000/(1.05)^2 + 30,000/(1.05)^3 + 30,000/(1.05)^4. Or you could have counted things at the beginning of the relevant period: NPV = -70,000 + 30,000/(1.05) + 30,000/(1.05)^2 + 30,000/(1.05)^3
b) Find the net present value of Project A
using a hyperbolic discount rate of your choice (2 marks). Here you go
through the same exercise, but instead of using 1/(1.05)^t ("^" means
exponent) you use a different denominator.
Examples of hyperbolic discount factors are
1/(1.05)^(sqrt(t)) and 1/(1+.05*t).
The denominator 1/(1+.05a))^t is not really a hyperbolic form if "a" is just a constant. If "a" is a constant greater than 1, this will just make discounting worse. If "a" is a fraction, then you are basically just using a smaller discount rate: 0.5a instead of 0.5. Instead, use some a(t), a function of t which gets smaller as t gets bigger. Similarly, using 1/(1.05)^(a(t)) will only work hyperbolically if a(t) increases over time but at a diminishing rate.
1. Let us consider a biofuel based on soap remnants, i.e. the soap leftovers that households throw away. Each litre of "Soapfuel" requires 200 oz. of soap and 3000 BTUs of fossil fuel energy (I'm just making these numbes up). Let's say that the soap itself was made using 200 BTUs of fossil fuel energy per oz. Meanwhile, 1 litre of soapfuel provides 80% the energy of 1 litre of fossil fuel. 1 litre of fossil fuel provides 30,000 BTUs.
a) When doing a cost-benefit analysis of replacing fossil fuel with soapfuel, should the emissions generated in the productionof soapfuel be counted as costs to society? Why/Why not (1 mark) Yes, emissions should be counted, since these are real costs, real negative technical externalities, to society. (Extra: Emissions saved from the fossil fuel replaced by the soapfuel should be counted, too)
b) Whe doing a cost-benefit analysis of replacing fossil fuel with soapfuel, should the emissions generated in the production of soap (not soapfuel) be counted as costs to society? Why/Why not? (1 mark)
No, if soapfuel is made entirely from household castoffs, and the number and size of soap remnants generated does not increase because households can sell them to soapfuel firms, then soapfuel manufacture does not result in extra soap and the residuals associated with soap production.
c)What is the net energy balance of Soapfuel production? Show your work (2 marks)Net energy balance is equal to the ratio of energy produced over fossil fuel energy used. This is worth one mark. The denominator is fossil fuel energy used i.e. 3000 BTUs (1/2 mark). The numerator is energy gained i.e. 0.8X 30,000 (1/2 mark).Hence the NEB is 8. (not worth any marks in and of itself)
2. Imagine that the City of Kingston would like to reduce the amount of trash that residents generate. One policy being considered is legislating that each house is only permitted to put out two bags of garbage per week. Any additional bags will not be picked up by the City. Can you think of two negative aspects of this policy? Recall a criterion we discussed in class for at least one of these aspects. (2 marks)
In class we discussed fairness and cost-effectiveness. Either of these is a legitimate criticism of the policy. It is not fair that a house of 6 students be allotted the same level of trash generation as a house of 2 people. Neither is it cost-effective. This policy has no way to distinguish between those households that can easily abate and those households for whom abatement would be extremely inconvenient. Another point that might be made is that if the City does not pick up the trash, consumers may leave the trash out for the rats, dump it in wetlands, or incinerate it somewhere, increasing damages to the environment.
3a). Draw a MAC "curve" for a single household's emissions of trash, where the initial emissions level is 3 bags per week. Let 1 bag per week be the targeted amount. Label that point on your graph (1 mark). With $ or P or MAC on the vertical axis, and Emissions on the horizontal axis, the MAC curve is a line sloping down to a horizontal intercept equal to 3. At E=1 the corresponding point on the MAC is noted. It corresponds to some level of MAC, which I will henceforth call "m". Some students may have drawn in a MD curve which intersects the MAC curve at E=1. That is fine but not necessary. It assumes that the targeted amount is indeed the socially correct amount.
b) Draw in a constant per-bag tax that will result in your household emitting the targeted amount. (1 mark) This is simply a horizontal line at "m".
c)Draw in a tax scheme that will result in the
targeted amount being emitted, but which minimizes the tax burden on the
household. (2 marks) This is a horizontal line at "m" which exists
only for E greater than or equal to 1. For emissions below 1 bag per week, no
tax is charged. (I don't know how to divide this into two marks. Use your
instincts, I guess.)
1. Imagine that the residents of Sydenham Ward
apply a total of 200 gallons of pesticide on lawns each year. The City of
a)
How many permits should the City of
b)
Given that there are, say, 500 homes in Sydenham Ward, what is a sensible way
of allocating the permits among households initially? (1 mark) Giving
each household one permit should be relatively uncontroversial. If there were fewer permits than households,
the City would probably have to sell or auction the permits directly to
households.
c)
How might this program be enforced? (1 mark). Enforcement might be a problem because a resident might sneak
pesticide onto his/her lawn without having the required # of permits. Monitoring will have to take place at the
point where the pesticide is sold.
Perhaps the permit will have to be shown at the point of sale, and its
serial number recorded.
d)
If this program works, which residents will end up using the permits? (1
mark) As with any tradable permit system, the high cost abaters, or those who
care most for the convenience of pesticides, will be the ones who end up with
the permits.
e)
If this program works, what does the permit price tell us? (1 mark) The price of a yearly permit, or the rental
price of a multi-year permit, tells us what the marginal abatement cost is for
Sydenham Ward. It gives us MAC at E=50
gallons.
2. Here is a diagram showing the marginal cost
of abatement of pesticide use for Ms. Sandra Wylie, a resident of Sydenham
Ward.
(Shown
is a downward sloping line with a vertical intercept of 10 and a horizontal
intercept of 0.2 gallons. The rental
price of a permit is shown as a horizontal line equal to $5. The confusion arose because the emissions are
measured in gallons, and so the permit price implies $5 per gallon. However, a permit only covers 1/10 gallon.)
a) At the permit price of $5, how much pesticide
does Ms. Wylie apply this year? If permits cost $5 a gallon, or 50 cents per
1/10 gallon, then Ms. Wylie consumes only 0,1 gallons. This is where her MAC = $5.
b)
What will be her total spending on abatement this year (1 mark)? Well,
she would normally apply 0.2 gallons, but is now applying 0.1 gallons, so she
abates 0.1 gallons. The graph shows that
that will cost her 0.1 * $5 /2 = 25 cents.
c)
What will be her net spending on permits, given the allocation scheme you proposed
in 1b)? (1 mark).
In 1b) we proposed that each household
be given one permit. So Ms. Wylie
already has 1 permit. She decides to
abate 1/10 gallon so all she needs is her one permit. Her net spending on permits is zero.
d)
If Ms. Wylie decides to replace her lawn with a decorative gravel bed, her
permit use will drop to zero. What will
happen to the price of permits in Sydenham Ward (1 mark) ? Being part of a market of 500 participants, Ms. Wylie has no power to
raise the price of permits above market levels.
However, since she does not need the permit at all now, she has the
power to offer it for sale at any price beween zero and the market price. This should lead to a slight decrease in the
price of permits. What will happen
to the overall level of pesticide use in Sydenham Ward? Since there are no market
failures such as lack of information, or a tax on permit sales, the market for
permits should clear at the new, lower price.
Someone will buy Ms. Wylie’s permit, and the same total amount (50
gallons) will be applied to lawns.
