Economics 331b
Spring 2011
Here are a bunch of questions that have been used on past exams and problem
sets. We will take some variant of these for one of the 40 minute segments of the
final exam. Some are relatively easy, others are for advanced graduate students,
some are economics, others are statistics.
1. Define a “sustainable equilibrium” as one in which all flows and stocks can be
maintained indefinitely at a given level (e.g., stocks and flows of fish, oil,
atmospheric CO2, and so forth are either constant or non-declining). Defend or
criticize the desirability of such an equilibrium from the point of view of
standard welfare economics.
2. A standard way of estimating impacts of climate change is to examine the impact
of year-to-year variations in temperature and precipitation, or heat waves, on
outcomes such as agricultural production, mortality, and land prices. Explain the
pros and cons of this approach.
3. We hear much about green this and green that. Green architecture, green
economics, green buildings, green universities, green ethics, green engineering,
and the like. Suppose you are asked to write an economic theory of “green X,”
where X is an application. Do so using the analyses you have learned in the
course. [Note: we never discussed this, but it was lurking always in the
background.]
4. You work in a science agency. Your boss, who is an eminent physicist, says that
raising the price of carbon will have no effect on emissions or climate change.
Write a short economic analysis of the role of carbon prices in helping to deal
efficiently with global warming to clarify the issue for your boss.
1
5. According to the Encyclopedia of Meteorology, “A. T. Burrows defined a ‘hot
wave’ as a spell of three or more days on each of which the maximum shade
temperature reaches or exceeds 90 °F (32 °C).” Some public-health officials who
have studied climate change are concerned that the increased frequency of heat
waves will be a major public-health problem, particularly in tropical and subtropical countries. The figure below shows a time series plot of temperature and
mortality in Europe in the 2002-2005 period. One researcher wrote, “In the last
quarter of the 20th century, the average atmospheric temperature rose by about 1
degree Fahrenheit. By 2000, that increase was responsible for the annual loss of
about 160,000 lives and the loss of 5.5 million years of healthy life, according to
estimates by the World Health Organization. The toll is expected to double to
about 300,000 lives and 11 million years of healthy life by 2020.” (The Climate
Institute)
(a) Describe a possible methodology by which the estimates in the quotation from
the Climate Institute were derived.
(b) Evaluate whether such a methodology is likely to be a reliable approach to
estimating the damages from global warming.
2
6. During the 2008 Presidential campaign, Senator McCain proposed a “gas tax
holiday,” that is, a temporary cut of the federal gasoline tax. In light of the theory of a
unified global oil market, analyze the incidence of such a gas tax holiday. I.e., what are
the effects on prices and quantities in different parts of the oil market (i.e., oil products
and different countries).
7. We have studied ice cores and other proxies. This question concerns a typical
statistical error in constructing proxies. It is an application of econometric methods
(required for economists) but was not covered in class per se.
Ice cores, tree rings, and other variables are often converted into temperature
proxies. The technique used is often the following. We assume that P(v) is an imperfect
proxy for T(v), T(v) is actual temperature, and v is either time or a time-like variable.
We have a short period in which we observe both P and T and a longer period in which
we observe only P. We fit a regression of T(v) = a + bP(v) + e(v) over the period in
which the data overlap, where e(v) is a random error. We then predict out of sample
temperature as
ˆ  v  , where aˆ and bˆ are the regression estimates and Tˆ  v 
Tˆ  v   aˆ  bP
is the
proxy for temperature.
Explain why this technique is incorrect. What is the appropriate statistical technique?
3
8. The McKinsey Report has asserted that many houses are underinsulated (see
Figure below). That is, the level of insulation is less than would be appropriate to
balance marginal social cost and marginal social benefit.
a. Describe a calculation that would be appropriate to test this assertion. Be specific
in terms of what must be measured.
b. Assuming that your test in (a) has confirmed empirically the McKinsey assertion,
state three leading reasons for the underinsulation hypothesis.
c. Take one of the three reasons. Design an empirical approach (either one using
randomized experiments or econometric tests with an identified equation) to test the
importance of this reason.
4
9. In the Solow growth model, we assume an exogenous savings rate, implying that
savings are determined outside the model. Suppose we relax this assumption
from the point of view of households and firms who maximize their lifetime
utility and profits (respectively). How would you solve this optimization
problem? You don't need to solve the model mathematically. You can write the
equations, but most importantly you should explain the intuition behind the
model and solution.
10. Define rigorously the difference between a technological and a pecuniary
externality. Provide one example of each from the climate-change area. For your
examples, provide policies to correct the externalities if those are appropriate.
11. Standard economic theory bases the determination of the discount rate on goods
(or the consumption discount rate) on the “Ramsey equation.”
a. State the Ramsey equation and define each of the terms carefully.
b. What are the conditions under which the discount rate on goods
could be negative? Give an example and state whether these are
plausible conditions.
12. Two major approaches to control and global warming are cap-and-trade and a
carbon tax.
a. Use a diagram to show the basic equivalence between cap-andtrade and a carbon tax.
b. Explain one important difference between cap-and-trade and a
carbon tax. Explain why one approach is superior to the other for
this specific difference.
5
13. Agronomists have observed the relationship shown in the following figure between
cereal yields and rainfall in Niger for different years. Climate models suggest that
rainfall in Niger will decline by 20 percent from its mean value of 750 mm per year over
the period to 2075. Explain the estimated economic impact of climate change on the
value of Niger’s agricultural production that you would expect in 2075.
14. Assume that the demand for air conditioning has a price elasticity of -2 with respect
to the total cost of air conditioning. At current prices and technology, the total cost is
$10 per unit of cooling, of which $8 is electricity and $2 is capital costs. The Department
of Energy is proposing a regulation that reduces electricity use per unit of cooling by 10
percent at zero additional capital cost. Environmentalists say that the regulation is
undesirable because of the “rebound effect.”
6
a. Define the rebound effect.
b. Calculate the rebound effect and determine whether the rebound
effect would offset the regulatory effect.
c. Estimate the welfare effect of the regulation (assuming no
externalities). Explain why such a regulation might be welfareimproving even if the rebound effect offsets any effect on energy
use.
15. Dr. Fysysist proposes the following: Carbon emissions are estimated to be 20 billion
tons of carbon per year (GtC/yr) in the first year with a growth rate of zero; the
tolerable amount of total carbon emissions is 280 GtC; there is a perfectly substitutable
backstop technology available at $1000 per tC; half of emissions go into the atmosphere
and stay there forever; and emissions are completely price-inelastic until the backstop
price is reached and then are infinitely price-elastic at that point. Dr F asks you to
calculate the efficient price of carbon along the path. [Hint: remember the rule of 70.]
a. Assuming that the discount rate is zero, which he thinks is the
appropriate rate.
b. Assuming that the discount rate is 7 percent per year, which is
what some economists recommend.
c. Assume that growth of emissions is g and that emissions are 5 at a
carbon price of $100 with a price elasticity of demand of -1.
Calculate the efficiency price. (You need only construct the
appropriate equation as the solution requires a calculator.)
16. Secretary Chu asks you what you think about using energy independence as a goal
of U.S. policy. He particularly wants to understand the pros and cons of reducing oil
imports (holding consumption constant). Help him out.
7
17. This is a horribly difficult question but if you are really into mathematical
economics, you might give it a try.
Consider an optimal growth problem as follows. The objective function is

W   log[C(t )]e   t dt
0
Where C(t) is consumption. The emissions of CO2 [E(t)] are equal to consumption times
one minus the abatement rate [1-μ(t)]:
E(t) = [1 - (t)]Q(t), 0    1
Concentrations [M(t)] are determined by emissions and the diffusion of carbon
from the atmosphere:
dM(t)
  E(t )   M(t )
dt
Temperature change is proportional to concentrations, where T(0) = 0 and M(0) = 0.
T(t) =  M(t -  )
Note that temperature increase is determined by concentrations with a lag of θ>0
periods.
Finally, consumption is determined by gross output [Q(t)], which is exogenous,
damages [D(t)], and emissions costs [Z(t)], where these are given by:
D(t) =  Q(t )T(t )
Z(t )  Q(t )(t )
C(t )  Q(t )  Z(t )  D(t )
 ,  , ,  ,  , , are all positive constants
For simplicity, we will consider only steady-states in which all variables are
constant, including Q(t) = Q*.
(a) Solve for the steady state values of all parameters as a function of the control
rate, μ(t) = μ*.
(b) Determine the optimal control rate, ̂ * .
(c)Explain how the optimal control rate is affects by the utility discount rate, ρ.
8