EEP1/ECON3 Environmental Economics and Policy
Midterm II Suggested Solutions
Fall 09
By Luosha Du and Koichiro Ito
1.
(5pts) Give a definition:
a. Isoquant
Isoquant is the set of all the efficient techniques that produces a certain output. It
represents different combinations of inputs that produce the same amount of output.
Grading policy: full credit for saying either of two sentences above. 0.5 point for
something else but still has “the same output level”.
b. Cost function, C(Q)
The cost function, C(Q) is the minimum amount of money necessary to buy the inputs that
will produce output Q. That is, it represents the minimum cost to produce output Q.
Grading policy: full credit for saying either of the two sentences above. We prefer the
answer above, but you can get a full credit if you say, C(Q)=FC+VC.
c. Revealed preference methods
Revealed preference methods expose underlying preferences from observable action.
Grading policy: full credit for saying the above statement or similar. 0.5 for mentioning
“observable actions”, “data from actual behavior”, or similar.
d. Fixed cost
Fixed cost is the cost incurred even if there is no production. That is, FC = C(0). In
another words, it is the cost that does not vary with production level.
Grading policy: full credit for saying either of the sentences above or similar.
e. Hedonic method
Hedonic pricing model explains the price of an item as a function of that item’s attributes.
Grading policy: full credit for saying the sentence above. Other acceptable answers
could be “using variation in the price of the purchased good to infer the value of
attached environmental good or the value of its characteristics” or similar.
2. (7pts)Draw a diagram using isocost lines and isoquant curves and use it to explain why a tax on a
polluting input is more expensive to a firm than a requirement to use less of the input. Assume
that requirement and the tax both lead to the same technique and the same output. Follow these
steps:
a. (1pt) Draw a diagram with an isoquant curve, an isocost line and a chosen input bundle
(technique).
b. (1pt) Why is the technique you marked chosen?
c. (1pt) Assume the input on the horizontal axis causes pollution and the government
restricts its use. Use your diagram to show what happens, output held constant. Label
your result.
d. (2pts) Now show how a tax can lead to the same result. Explain.
e. (2pts) Use your diagram to show which method costs the firm more. Explain
The following answer is just an example. You can get full credit as long as your diagram is
consistent with your prices, costs, and explanations.
(a) Suppose that a firm makes one unit of output Q using two inputs X1 and X2, and that P1 = 1
and P2 = 2. If I1 is the isoquant curve for Q = 1, the firm chooses the input bundle (4, 4) to
produce Q =1.
X2
10
6
4
I1
2
0
4
10
12
X1
Grading policy:
Your diagram needs an isoquant curve, an isocost line, chosen input bundle that is on the
tangency point between the isoquant curve and isocost line.
(b) It is because the input bundle (4, 4) allows the firm to produce Q = 1 with the minimum cost
since it is the tangency point between the isoquant curve and the isocost line.
Grading policy:
You need to mention “minimum cost” to get a full credit. If you just say “because it is tangent
on… not mentioning the minimum cost”, you’ll get 0.5.
(c) Suppose that the government introduces a technology based effluent standard (TBES) based
on “A”. Or, the government introduces an effluent standard that limits the use of X1, up to 2.
With either regulation, the firm no more can choose the input bundle (4, 4) and will choose (2,
6). The vertical intercept of the new isocost line is 7, so the cost = 7*P2 = 14.
X2
A
10
7
6
0
2
5
10
12
14
Grading policy:
Either TBES or an effluent standard is fine for this question. The key thing is that the new isocost
line resulted from the regulation must be parallel with the original isocost line (0.5 point will be
taken off if you don’t get this). Furthermore, your new input bundle needs to be on the same
isoquant curve and consistent with the government’s restriction that you provided (0.5 point).
(d) Suppose instead that the government introduces a tax on X1. The tax makes the slope of the
isocost line steeper and the government needs to set a tax rate that makes the isocost line have a
tangency point with the isoquant curve at (2, 6). With this tax, the vertical intercept of the new
isocost line is 10, so the cost = 10*P2 = 20.
X2
10
6
0
2
5
10
12
X1
Grading policy:
A new isocost line with a tax needs: 1) a steeper slope than the original one because you tax on
the good on the horizontal axis; 2) a tangency point with the same isoquant curve exactly at the
same point as with the restriction you described in part c). Each of them counts 1 point.
(e) As I showed in part c) and d), the tax costs $20 and the TBES costs $14, so the tax cots the
firm more than the standard.
Grading policy:
1 point for just saying that the tax costs more than the standard because the firm has to pay a
higher price for the good on the horizontal axis with the tax than the standard. To get a full
credit, you need to calculate the firm’s cost with the tax and standard to show the cost is larger
with the tax OR you need to argue that the cost is larger with the tax using your diagram.
3. (4pts) Consider a price taking firm and explain:
a. Why p = mc(q) if q is positive
b. Why q =0 if p < minimum point of AVC
(a) The firm produces Q* where P = MC(Q*) because producing this quantity maximizes the
profit. An alternative explanation would be “the firm produces Q* where P = MC(Q*) because
producing more would be profitable when P>MC(Q) and producing more would not be
profitable when P<MC(Q)”.
Grading policy: full credit (2 points) for saying either of the two sentences above or similar.
(b) When P < minimum point of AVC, the firm shuts down because the loss from continuing the
production is larger than the fixed cost, which the firm has to pay if it shuts down.
Grading policy: full credit (2 points) for saying the sentence above or similar (the key here is to
be aware “a continued operation makes the firm loss more money, not just the fixed cost
incurred by the shut-down”). If you argue that the firm shuts down because it experience
“negative profit”, you got point off.
4. (4pts)The Jellybear problem from the homework. See the other side of this exam for some of the
relevant information. These questions pertain to that example.
a. You were provided with the population and distance for the towns that have residents
visiting Jellybear (shown in the following table).
City of Origin Population
Distance
Alabaster
1000
1
Beautiful
3000
3
Cornucopia
5000
5
Delight
7000
7
Let’s assume the travel cost is $1/mile and admission price is $2. What other information
did you need to construct a demand curve for visits? Now consider finding just one point
on the demand curve (for instance, the point where the admission fee is 2). How did you
use the information in the problem to find that point on the demand curve? Explain ALL
the steps.
We need the information on the fraction of population visiting Jellybear from each town
(or you could say “visits/capita for each town”) as a function of total cost (travel cost +
admission fee).
Grading policy: This part counts 1 point. In general, we need a fraction of population of
visiting for each city “as a function of cost” to derive a demand curve. However, because
this question assumes that the admission fee is $2, you can get full credit if you just say
“we need a fraction of population of visiting”.
First, calculate the total cost of visiting for each town using information on distance,
travel cost per mile and admission price. Second, once we have relationship between
fraction of population visiting the Jellybear from each town and total cost, we can
calculate visit/capita for each town. Third, multiplying visit/capita by population to get
the total visits of Jellybear from each town. Fourth, sum up the visits for each town to get
the total visits of Jelllybear. If we graph admission price on the vertical axis and total
number of visits on the horizontal axis, the number we got from the fourth step along with
admission price of $2 allow us to identify the point on the demand curve.
Grading policy: this part counts 1 point. As long as you are talking about how to identify
one point in the demand curve, you get 0.5 point. If you get all steps, additional 0.5 point.
b. Instead assume that you were a researcher and you did not know the relation between
visits per capita and costs. How would you find that relationship using a revealed
preference method? (Your answer does not need to include the details of methods to fit
lines to data points.)
There are at least two ways to find the relation between visits per capita and costs. The
following method uses a variation in costs between places that have different distances
from Jellybear.
1. Find two or more places that have different distances from Jellybear.
2. Calculate the travel cost from these places to Jellybear.
3. Collect the data on visit/capita for Jellybear from each place. One way is to find total
population and total number of people who visit Jellybear for each place. An
alternative way is to (randomly) pick subpopulation of each place and see how many
of them visit Jellybear.
4. Then, you can see the relation between visits per capita and travel costs. (Economists
use regression techniques to the statistical relation of these two variables, but you
don’t have to mention regression techniques here.)
Alternatively, if the admission price changes over time, the data from only one place
would also work under some assumptions.
1. Suppose that the admission fee used to be $1 and increased to $2, for example.
2. Calculate the travel cost plus admission fees.
3. Collect the data on visit/capita for Jellybear from this place both before and after the
price change. One way is to find total population and total number of people who
visit Jellybear for each place. An alternative way is to (randomly) pick subpopulation
of each place and see how many of them visit Jellybear.
4. Then, you can see the relation between visits per capita and travel costs. (Economists
use regression techniques to find this relation statistically, but you don’t have to
mentione regression techniques here)
Grading policy: this part counts 2 points. There are a few key points: 1) You need a
variation in prices. That is, you need more than two places that have different distances
or you need to have more than two different admission prices if you use the data only
from one place (0.5 point); 2) Because the question asks you to use “revealed preference
methods”, you need to observe the data on people’s decision on visiting or not visiting
Jellybear not just by asking (0.5 point); 3) You need to calculate visits per capital not
only the total visits (0.5 point). Additional 0.5 point will be given for a well-organized
explanation (along with those key points). If you mention regression method, we will not
take your points off nor give you extra points.
If you use other revealed preference methods, such as hedonic price method, which is
useful when we ask you to find the use-value of Jellybear park. However, the question
asks to design an experiment to figure out the relationship between visits per capita and
cost rather than the value of the park. So, hedonic price method is not a good alternative.