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Practice Midterm
I. Short Answer
1.
(+10) You are the Director of the Los Angeles Environmental Agency.
The only source of
emissions in the city is vehicles.
Your Statistics nerds have given you the following
information.
1990
2008
2030
Population
(in Millions)
4
6
8
Probability own
Vehicle
.90
.95
1
Annual Miles
Driven Conditional
that own vehicle in
1000s
10
12
Q
Average Emissions
per Mile
4
X
Z
You have promised the Mayor to reduce vehicle emissions in 2008 and 2030 back to
1990s levels.
Solve for X such that you achieve this goal.
If you expect that Q will
equal 14, what must Z equal to achieve this goal?
Briefly explain the role of scale
and technique effects in determining pollution levels.
2.
Mike owns one tree.
Its height, measured in feet, is a function of the tree’s age, measured in
years, with production function
(
29
age
Feet
50
=
.
Assume that the real price per foot of wood is always equal to $40.
Suppose the cost of
cutting down the tree is $10. (note that this is a fixed cost)
Assume that the interest rate
always equals 4%.
Mike’s goal is to maximize the PDV of his profits.
a.
(+4) Write down the profit function as a function of age, and
describe
how you will
find the optimal tree cutting age.
(you need not actually find the age)
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View Full Documentb.
(+4) Now suppose the interest rate is increase to 8% permanently.
Will the optimal
tree cutting age increase or decrease?
Explain. (You need not solve for the new
optimum)
c.
(+4) Now suppose that each year there is a
8
1
( or 12.5%) chance that Kahn will
sneak into the forest and cut down Mike’s tree.
In which case Mike will receive $0.
Assume the interest rate is 8%.
Write down the new profit function and
describe
how
you will find the optimal tree cutting age.
(Again you need not actually solve for the
optimum, just characterize the solution)
d.
(+5) Will the optimal tree cutting age be sooner or later in question (c) than in
question (b)?
Explain.
3.
Consider two vehicles called the Prius and the Hummer.
Assume the Prius will get 40mpg
and the Hummer will get 10mpg (miles per gallon).
Assume gasoline is $2.00 per gallon:
Roundtrip Distance
to Work
Roundtrip Distance to
the Beach
Chris
1 mile
10 miles
Jeff
11 miles
0 miles
Assume they each drive to work 5 days a week, and go to the beach once a week.
Chris’ green friends convince him to sell his Hummer to Jeff and buy a Prius.
Can you determine if Chris’ decision decreased the total carbon footprint in Los Angeles?
If not, what else would you need to know?
4.
A steel factory produces 3 units of pollution for every unit of steel it produces.
If 400
identical people live near the factor and each suffers 2 sick days per unit of pollution
exposure.
Suppose each person values not being sick at “w” dollars per sick day.
a.
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 Spring '08
 BRESNOCK
 Economics

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