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Problem Set 3:
1) Imagine the government of California has proposed a new tax on vehicles based on the amount
of emissions they produce in a year. In 2019, there will be 20 tons of emissions produced. The
governor’s office has run the calculations and found that the socially optimal level is 14 tons and
the marginal damage from each unit of pollution is $150.
a) Imagine there are two types of drivers in California: commuters and non-commuters.
Imagine that the marginal cost of reducing pollution for commuters is MCA_C=150Q and the
marginal cost of reducing pollution for non-commuters is MCA_N=30Q. Each type initially
created ten tons of pollution each. Their total cost of reductions is equal to TCA_C=75Q^2
and TCA_N=15Q^2. How much would each type choose to reduce under the tax?
b) Imagine the governor instead suggested forcing all drivers to reduce their emissions by 30%
from their 2019 levels. How would the costs of reduction here compare to the taxation case
(please provide actual numbers)? Do you think such a shift is a good idea Why or why not?
Are there conditions under which your answer would change?
c) Imagine the governor now wants to do a cap-and-trade program instead of a Pigouvian tax?
Assume we know the true marginal damage level and socially optimal quantity. Do you think
this will affect the overall success of the program (judged as getting as close to the socially
optimal level of pollution as cheaply as possible)?
d) Imagine the California EPA does a new calculation and finds that they initially underestimated the marginal damages produced by vehicle emissions. They now believe it would
be socially optimal to reduce emissions by 12 tons. Under the governor’s new cap-and-trade
proposal how much would you expect each group of drivers to reduce. What would the
equilibrium permit price be?
2) Many farmers in the California Central Valley get their water from a shared aquifer. The more
farmers who use the water, the more expensive it is for everyone because accessing the water
requires significantly more energy.
a) Assume that the marginal benefit each new farmer drilling into the aquifer is equal to 100-10Q,
but that the marginal social surplus from 100-20Q. What number of farmers will drill a well?
What quantity would maximize social surplus? Intuitively, what is driving this difference?
b) Imagine that the farms in the community were run as a collective where everyone split their
profits at the end of the year. What number of farmers do you think would drill a well in this
case? Justify your answer.
c) Imagine that farms are located in an isolated rural community where everyone has known each
other for many years? What number of farmers do you think would drill a well in this case?
Justify your answer.
d) Challenge question: Imagine one farmer owned the rights to the entire aquifer. How many
farmers do you think would drill into aquifer in this case? Justify your answer.
3) The city of Chula Vista is deciding whether or not to build a new municipal tennis court. The
courts will cost $1 million to build. Tennis players in Chula Vista value the new courts at $100
per person and non-players value it at $1 per person. Assume there are 20,000 tennis players
and 180,000 non players in Chula Vista (we are only counting adults). The city wants to make
the courts free to everyone and so wants to finance the construction through taxes.
a) If the city created a tax equal to the average cost of the courts to be paid by each adult
citizen, how much would each individual pay? Do you think the tax would be approved?
Why or why not?
b) If the city instead instituted a tennis player tax where it asked each person if they were a
tennis player and then taxed them at the rate $1,000,000/20,000 players do you think it
would collect enough revenue to pay for the courts? Why or why not?
c) If the city proposed a tennis racquet tax to the voters, where all individuals who owned a
tennis racquet would have to pay $1,000,000/20,000 players to finance the courts, do you
think it would pass? How could this help solve the problem in (b)? Would this raise enough
revenue to finance the courts (assume all tennis players also own tennis racquets and no
non-tennis players own racquets)? Can you think of any unintended consequences that
Challenge: Assume that 20% of the people in Chula Vista live in houses worth $500,000 and
80% live in houses worth $200,000. Further assume that 30% of the people living in the
$500,000 houses play tennis and only 5% of the people living in the $200,000 houses play
tennis. Do you think a tax of $24.84/person on houses worth $500,000 and $.04/person on
houses worth $200,000 would pass? Why or why not? What are the advantages and
disadvantages of a tax like this relative to a tennis racquet tax?
4) The federal government is deciding how to raise money to increase spending on national
defense. The President happens to hate boats and suggests levying a tax on luxury yachts to
help pay for it. Assume that demand for yachts is highly elastic where P=100-Q, MC=9Q and the
tax (assessed on suppliers) equal to 30.
What is the DWL caused by this tax?
b) Do you think this tax is a good idea? Why or why not?
c) Your colleague on the Council of Economic Advisors says that the most efficient taxes are levied
on goods with highly inelastic demand. Thus, he suggests a head tax (a uniform tax per person)
for all residents in the United States to pay for the increase in military spending. Would you
recommend that the President accept this idea? Why or why not?
5) Consider the hotel market in a remote city. The city is not a tourist destination and there is no
information about the hotels online or in a guidebook. Previously, the city was under a
Communist government and all the hotels were state-owned. Half of these hotels were highquality and half were low-quality. Now the country has transitioned to capitalism and all hotels
are under private ownership. People are willing to pay $200/night to stay in a high-quality hotel
and $50/night in a low-quality hotel. Operators of high-quality hotels are willing to sell a room
for $150/night and operators of a low-quality hotel will sell rooms for as low as $25/night.
a) Imagine that customers cannot distinguish between high and low quality hotels based on
appearance or any other source of information. Once these hotels become privately-owned,
what will the equilibrium hotel price be? What will be the distribution of high and low-quality
b) Imagine that Lonely Planet (a travel guide company) came to the city and wrote truthful reviews
of all the hotels (and these reviews were known to be truthful by customers)? Would the
outcome be the same? Why or why not?
c) Imagine that the Lonely Plant writer required bribes for good reviews. However, she required a
$175 bribe from bad hotels and only a $10 bribe from good hotels because she was taking a risk
making a bad hotel sound good. Imagine in this hypothetical world, new customers still believed
Lonely Planet provided truthful reviews (i.e. their reputation didn’t suffer despite their lying).
What would the equilibrium price (or prices) and distribution of high and low quality hotels be?
d) Imagine an established high-quality hotel brand like the Ritz-Carlton entered the city. Do you
think they would need to bribe the review writer to be recognized as high-quality? Why or why
e) Aside from reviews, are there other ways high-quality hotels could signal their quality? Give an
example and explain how this would work?
Do you think consumers of hotels use statistical discrimination in the real world? What types of
things (without seeing the inside of a hotel) would help identify your willingness to pay for a
6a) Your friend tells you that most insurance is a scam because most people are paying the
insurance company more than their average expected costs. Is he right that this is the case? If so,
why do so many people buy insurance?
6b) Imagine you are an insurance regulator for the state of California. The legislature is considering
banning car insurance company’s ability to charge customers different rates based on their past
driving history. Do you think this is a good idea? Why or why not?
6c) What if California also included a mandate that all drivers must have insurance in its new policy
(in fact this is actually the case in real life, but for a different reason than adverse selection.)? Would
that change your opinion?
6d) What if this same proposed law also banned deductibles? Would that make you more or less
likely to support the policy?
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