Department of Economics
U.C. Berkeley
Problem Set #2 Suggested Solutions
Fall 2014
Economics 1
Prof. Olney
PROBLEM SET #2 Suggested Solutions
1. (2 points total)
Manuel owns the only store on an isolated but populated island that sells bottled soda: Manuel’s Island Soda & More.
(A) At the right is a graph that illustrates the market
Manuel faces. Annotate the graph appropriately as
you answer these three questions.
What is his profit-maximizing quantity? 200 bottles per
day
What price will he charge? ~$1.75
What is his daily profit? ($1.75-1.50)*200 = $50 per day
(B) Assume that the market Manuel faces alone is
instead shared by lots of sellers in a perfectly
competitive market, and that the sum of their
individual quantities supplied at each price equals
the quantity that monopolist Manuel would supply
at that price. In that case, would the quantity and
price be the same as the answers you gave in part
(a)? Explain your answer.
If the market were instead perfectly competitive, the equilibrium price and quantity would be at the intersection of the demand and supply
curves. With the assumption that the sum of their individual quantities supplied at each price equals the quantity that monopolist Manuel
would supply at that price, we conclude that the monopolist’s MC curve is the Supply curve for this hypothetical perfectly competitive
industry. Equilibrium quantity would be ~260 bottles per day; equilibrium price would be $1.50 per bottle.
A perfectly competitive industry produces a larger quantity (260 > 200) and sells that product at a lower price ($1.50 < $1.75) than a
monopolized industry, all else constant.
(C) Returning to the part (a) scenario: Monopolist
Manuel must now pay the state a tax equal to 1¢ per
ounce for each bottled soda he sells. Will he be
able to pass the entire tax on to his customers? Or
will he have to bear some burden of the tax?
Explain your answer. At the right, sketch in a graph
that supports your answer.
Manuel cannot pass the entire tax on to his consumers
because demand is not perfectly inelastic; demand is
downward sloping.
To draw the graph, we assumed 20 ounce bottles, so the
tax is 20 cents per bottle. The tax shifts the MC & ATC
curves up by 20 cents. Note that the ATC curve hits its
minimum at the same quantity as it did before the tax
was implemented.
As shown at the right, the price paid by consumers for
one bottle of soda increases from $1.75 to about $1.80 as
a result of the increased costs (the tax). The seller,
Manuel, sends the 20 cent per bottle tax to the government and retains $1.60. They have shared the burden of the tax.
Department of Economics
U.C. Berkeley
Problem Set #2 Suggested Solutions
Fall 2014
Economics 1
Prof. Olney
2. (2 points total)
Now suppose instead that bottled soda is sold in stores that are in an industry characterized by monopolistic competition.
(A) Pre-tax: At the right draw a graph that shows the
profit-maximizing quantity of bottled soda sold in
an individual store in a monopolistically
competitive industry that is in long-run equilibrium
before the tax is implemented. Label all your
curves and points with subscript "1."
Being in long-run equilibrium in monopolistic
competition means the individual firm is earning zero
economic profit. The ATC is just tangent to the demand
curve at the profit-maximizing quantity (and still, of
course, hits its minimum when it crosses MC).
(B) Post-tax: Now each store must pay the state a tax
equal to 1¢ per ounce for each bottled soda sold. In
the short run, what effect will the tax have on the
profit-maximizing quantity and price of bottled
soda? Explain your answer. At the right, illustrate
your answer using subscripts "2" in your graph.
The tax increases both the MC & ATC by 1¢ per ounce
for each bottled soda. You can make whatever
assumption you want about the size of a bottle. If these
are 16 oz bottles of soda, that’s an increase of 16¢ per
bottle. If they are 20 oz bottles, it’s a 20¢ increase per
bottle. In either case, both the MC & ATC curves shift up
by the amount of the tax. Note that the post-tax ATC will
hit its minimum at the same quantity as it did before the
tax was implemented.
The costs rise more than the price because demand is not
perfectly price inelastic; demand slopes down. The
profit-maximizing quantity decreases from Q1 to Q2; the
profit-maximizing price increases from P1 to P2. The
seller retains P2 – T after sending the tax money to the
government.
At the profit-maximizing quantity Q2, ATC>P2.
Therefore the typical firm is now incurring economic
losses, indicated by the shaded area in the graph to the
left.
(C) In the long run, how will the soda tax affect the stores in this industry? Distinguish between stores that leave the industry (why do
they leave?) and stores that remain. In the long run, who will bear the burden of the tax? Sketch a new graph at the right that
illustrates the pre-tax and post-tax long-run equilibria for a store in this industry.
Department of Economics
U.C. Berkeley
Problem Set #2 Suggested Solutions
Fall 2014
Economics 1
Prof. Olney
The typical firm is now incurring losses, so firms will
begin to exit the industry. Customers of the closed stores
will start shopping at other stores, increasing demand
for the remaining firms. This process of stores exiting
and customers shifting to remaining stores will continue
until the typical remaining store is earning zero
economic profit.
In the long run the customer will bear the entire burden
of the tax, and will have fewer stores to choose from
when buying a soda. The remaining stores will once
again sell their initial profit-maximizing quantity Q1 but
at a price that includes the entirety of the tax.
3. (3 points total)
One argument in support of a bottled soda tax refers to
negative externalities: drinking bottled soda contributes
to obesity, obesity triggers Type 2 diabetes, obesity &
diabetes generate health care costs, and health care costs are not borne completely by the individual. Assume that argument is correct.
Assume bottled soda is sold in a perfectly competitive market that is initially in long-run competitive equilibrium.
(A) In Community E, demand for bottled soda is relatively price-elastic. In Community I, demand for bottled soda is relatively priceinelastic. In the short run, in which community will the consumer bear a larger burden of the soda tax? ___________In the long run,
in which community will the consumer bear a larger burden of the soda tax? __________ Draw two graphs (one on the left for E, one
on the right for I) that support your answers, and below your graphs provide a brief explanation of your answers.
In the short run, the consumer will bear a larger burden of the soda tax in Community I, in which demand is relatively price-inelastic. In
the long run, the consumer will bear the entire burden of the tax in both communities. The drop in quantity sold will be much greater in
Community E than in Community I because of E’s greater price-elasticity of demand.
(B) Now compare two communities: one in which the median annual income is relatively high (say, $80,000 per household) and one in
which the median annual income is relatively low (say, $25,000 per household). Where will consumers bear the greater burden of the tax
in the short run: the high-income or the low-income community? Refer to what you wrote in part (a) to defend your answer.
Demand for soda is probably less price-elastic in the relatively high income community because $2 for a soda is a smaller share of daily
spending when annual income is $80,000 than when income is $25,000. In part (A), we concluded that those in community I – where
demand was more price-inelastic – would bear the greater burden of the tax in the short run. Therefore, in the short run, the consumers in
the high-income community would bear the greater burden of the tax.
Department of Economics
U.C. Berkeley
Problem Set #2 Suggested Solutions
Fall 2014
Economics 1
Prof. Olney
(C) Suppose the proposed tax is the optimal tax in all communities, even though the tax is not the same in all communities. For example,
the proposed tax is 1¢ per ounce in Berkeley and 2¢ per ounce in San Francisco. Offer an explanation for why the optimal tax may
differ from one community to the next. It should be clear from your explanation that you understand the definition of “optimal tax.”
If the proposed 2¢ tax is optimal in San Francisco and the proposed 1¢ tax is optimal in Berkeley, then the marginal damage costs must be
greater in SF than in Berkeley. The “optimal tax” is one that forces the market to fully internalize the externality, which occurs when the
tax is equal to MDC.
Explanations for why MDC is greater in SF than in Berkeley will vary. We’ve got the same chain of events in both communities:
soda → obesity → diabetes → health care → publicly-funded health care.
Your explanation needs to focus on the aspects of the chain that could vary between two communities. For example, your explanation might
reference greater initial levels of soda consumption in SF and a non-linearity in the eventual health care costs. Or you could appeal to
greater publicly-funded health care costs in SF than in Berkeley. Or perhaps all else isn’t constant. For example, perhaps outdoor activity,
which could offset the effects of soda on obesity, is greater in Berkeley than in SF.
4. (1 point total)
The state of California provides public financial support for public colleges and universities: community colleges, the CSU campuses, and
the UC campuses. But the state does not provide financial support for private colleges and universities such as USF, Stanford, USC,
University of Phoenix, and the Claremont Colleges. Use economic concepts to explain why the state might support some colleges &
universities and not others.
There are positive externalities associated with education; that is, the individuals who receive an education are not the only ones who
benefit. Individuals who receive a higher education receive better jobs and higher wages – a private benefit – but society also benefits from
having a more educated population. More educated individuals are healthier, less likely to commit crimes, more likely to be employed, and
more likely to vote. The government also benefits. If educated people are more likely to be employed and have higher salaries, the
government can collect more tax revenue. Since higher education likely reduces rates of criminal activity, the government spends less on
prisons and police for the state. (Crime is likely reduced more by finishing high school than by attending college, but it seems that higher
education does help to reduce crime. For more info, you can read “The Effect of Education on Crime,” American Economic Review 94
(March 2004): 155-189 by Lance Lochner and Berkeley Economics Professor Enrico Moretti. http://www.jstor.org/stable/3592774)
Higher education also leads to innovation: lots of great computer developments happened at Berkeley, and a few elements on the periodic
table were discovered here as well. (Note that there is no such element as Stanfordium.) While not all of these innovations directly led to
cost reductions or benefit increases to the state government, many of them likely have. For example, research on energy use, public
transit, and city and regional planning is often directly related to projects built by the state government.
Or, did you take a look at the article Prof. Olney tweeted on October 8: http://bit.ly/1BOhNKt showed the University research that goes
into your smartphone. Notice how many of those institutions are public universities, and how much of the research conducted at private
universities was funded by the government.
All of which says: because education produces positive externalities, there is an economic justification for public subsidies. Those
subsidies can be paid to the university in the form of state funding, or they can be paid to individuals in the form of CalGrants and so on.
But why does the state support some colleges and not others? If some colleges and universities produce more positive externalities than
others, there is a justification for supporting some and not others. So the question here is really this: what are the positive externalities
generated by UC, CSU, and community colleges that are not generated by Stanford, USC, and the Claremont Colleges?
If you grew up in California, how many of your K-12 teachers graduated from CSU or UC schools rather than private colleges? How
many had attended community college on their way to getting a 4-year degree? Probably most. Public colleges and universities generate
more teachers than do the private colleges and universities – a positive externality that justifies public subsidies.
What about helping the world? The world’s poorest citizens have benefited from Berkeley graduates. Berkeley has produced the most total
Peace Corps volunteers in the organization’s almost 50-year history (well over 3,000) which makes us the number 1 all-time producer of
Peace Corps volunteers. Berkeley is also consistently in the top 5 of colleges and universities nationwide in producing Teach for America
teachers. The benefits from Berkeley graduates’ giving back escape easy economic quantification, but they are vast in both economic and
social terms. Simply put, Berkeley graduates have a tradition of public service that is unsurpassed. More so than any other university,
Berkeley graduates take their education and use it to generate positive externalities around the globe.
For more information, you can read Bob Herbert’s October 2009 NY Times article about UC Berkeley.
http://www.nytimes.com/2009/10/03/opinion/03herbert.html?_r=1
Department of Economics
U.C. Berkeley
Problem Set #2 Suggested Solutions
5.
Fall 2014
Economics 1
Prof. Olney
(2 points total)
Asymmetric information problems beset many important markets. Some markets are plagued by problems of adverse selection; others by
moral hazard. In the absence of a remedy, markets characterized by asymmetric information will fail. The classic reference is “The
Market for Lemons,” by Berkeley Professor and Nobel Laureate George Akerlof, Quarterly Journal of Economics (August 1970),
http://www.jstor.org/stable/1879431.
Write a one-page essay in which you address these points:
$
Give an example of a market in which there are asymmetric information problems. Your example can be historical or contemporary,
but cannot be fictional. Describe the nature of the asymmetry and explain why it leads to market failure.
$
How is the asymmetry in information addressed in that market (if it is)? Do you think that is the best approach to solving the
asymmetric information problem? Why or why not?
Specifications: 400 words maximum, one page maximum. (“Works Cited” list can be on a second page and does not count against
the 400 word maximum.) Double space. 10-11-12 pt font. 1" margins on all sides. Your name, date, and the word count in the top right
corner. Attach your paper directly behind the problem set sheets..
Grading: 0 - 1 - 2 points, taking into account content, following specifications, and writing quality.
Of course, there are lots of specific examples, so we can’t provide you with “this is what you should have written.”
Guidelines:
a. Did you follow the specifications? Maximum 400 words? Maximum one page? 1” margins? Double-spaced? 10 or 11 or 12 pt
font? Your name, date, and word count in the top right corner? Your essay stapled at the back of your problem set? Attached your
“works cited” list (either at the end of page 1 or on a separate page)?
If so, you remained eligible for full credit. If not, you lost a point right off the top.
b. Did you choose an example of a market that is affected by asymmetric information problems? Did you describe the nature of the
asymmetry and explain why it leads to market failure? Did you discuss how the asymmetry in information addressed in that market? If so,
good!
c. When you answered the questions about whether or not you think that is the best approach to solving the asymmetric information
problem, did you recognize that this is a normative question? Did you remember that in order to answer any normative question, you must
first explicitly state what goal we are trying to achieve? Did you explicitly state a goal, and then write up your analysis in light of that
goal? If so, good!
Here are two examples of asymmetric info from Fall 2013 problem set:
b.
The Affordable Care Act (aka, “Obamacare”) requires that everyone purchase health insurance. Use the concept of
asymmetric information to explain why a health insurance market will work better if everyone is required to buy insurance.
One type of asymmetric information is adverse selection: before a transaction begins (or, before a contract is entered into), one
party to the transaction knows more about their present & future behavior than does the other party. In the case of health insurance,
the person buying insurance knows more about their health and their risky behaviors than does the insurance company.
If the health insurance companies could perfectly predict who was likely to get sick or injured and who was not, they would simply
charge different prices based on risk. Those likely to get sick would pay a lot for health insurance. Those unlikely to get sick
wouldn’t pay much at all. Everyone would pay something because getting hit by a bus is, by and large, a random event.
Department of Economics
U.C. Berkeley
Problem Set #2 Suggested Solutions
Fall 2014
Economics 1
Prof. Olney
But because of asymmetric information, you know more about your health and your behaviors than does the insurance company. In
the extreme, the insurance company doesn’t know if any given applicant is a high-risk or low-risk applicant. So the profit
maximizing thing for the insurance company to do is to charge everyone a high price.
But in that case the pool of applicants will be affected by adverse selection: the people buying health insurance will be
disproportionately the sick people. Here’s why.
If buying health insurance is an option, then it is likely that those people who know they are likely to get sick will buy insurance.
They smoke and didn’t say so on their health insurance application. They never wash their hands. They drink to excess and didn’t
reveal this in their application. There is a family history of heart disease or diabetes or cancer. Those are the folks who are likely to
buy health insurance because the insurance premium is less than their expected spending on health care.
At the same time, if buying health insurance is an option, then healthy people will not buy insurance. They don’t anticipate getting
sick or having accidents. They live a healthy life style. Their family history is peppered with people who live to be 102 and then die
in their sleep. These folks are unlikely to buy health insurance because the insurance premium is higher than their expected spending
on health care.
When the insurance company charges everyone a high price, then the low-risk healthy people decline to buy insurance. The insurance
company will realize the pool of applicants is now an on-average higher-risk pool, and will increase premiums. More healthy people
will drop out of the market because of the higher premium. This process – higher premium, healthy people drop out of market, onaverage less-healthy applicants in the pool, higher premium – has the potential to spiral out of control to the point where health
insurance is priced so high that no one purchases it.
On the other hand, if everyone is required to obtain health insurance, then insurance companies know the pool of applicants is a truly
random sample of the population – healthy and non-healthy people alike – and can lower premiums for everyone. That’s the theory.
For the background on these ideas, see the article by Berkeley economist Prof. George Akerlof, “The Market for ‘Lemons.’”
http://www.jstor.org/stable/1879431 This article is based on the work for which Prof. Akerlof received the Nobel Prize in Economics.
c.
Rather than borrowing from banks, informal lending through kin, social, or community networks provides financing
for small businesses and entrepreneurs in many countries. Use the concept of asymmetric information to explain why an
informal lending network might work better than lending through banks.
Both the concepts of adverse selection and moral hazard apply in this case. Again, adverse selection refers to something that
happens before a transaction begins (equivalently, before a contract is signed): a non-random pool of applicants applies. Moral
hazard refers to something that happens during the life of a transaction (equivalently, after the contract is signed but before the
contractual obligation is complete): a change in behavior that affects the likelihood of completing the contract.
In lending markets, the key idea is that the interest rate someone is charged to borrow should be a reflection of the perceived risk the
borrower will default and not pay back all of the borrowed funds. With full information, borrowers who have riskier projects or who
are themselves less likely to repay would pay higher interest rates than would borrowers with safe projects and who are very likely to
repay. But borrowers and lenders don’t share full information with each other.
In the context of lending, adverse selection means that the pool of applicants for loans will be disproportionately bad borrowers. The
logic is similar to that laid out in part (b). Because lenders don’t know with certainty who is a good and who is a bad borrower, they
charge a higher interest rate to everyone. Good borrowers drop out of the market because they are asked to pay an interest rate that is
too high given the risk of their project and likelihood of repayment. Lenders recognize that good borrowers have dropped out of the
market, that the remaining pool contains an even greater share of bad borrowers, and therefore interest rates are increased again. The
better borrowers again drop out of the market. The spiral continues. At its extreme, interest rates rise so high that no borrower is
left in the market.
Department of Economics
U.C. Berkeley
Problem Set #2 Suggested Solutions
Fall 2014
Economics 1
Prof. Olney
Moral hazard in the context of lending means that there is a risk a borrower will change behavior once the contract has been signed,
increasing the risk of default. For example, instead of using the borrowed funds for the safe project outlined in the loan papers, the
borrower will use the money for a much riskier project. Or, instead of repaying the funds on a regular basis as the borrower had done
with past loans (and therefore was expected to do with this loan), the borrower doesn’t make payments regularly. Knowing that
moral hazard is a risk, if lenders cannot distinguish between borrowers who would and would not change behavior, lenders would
increase interest rates. We get into the same spiral as outlined in the previous paragraph.
In lending, solving the problems of asymmetric information typically involve developing ways of screening applicants (decreasing
adverse selection risk) and monitoring borrowers (decreasing moral hazard risk).
Screening applicants means discovering as much information about borrowers as possible before the contract is signed. Credit
reports are one way that banks screen. If lending takes place within kin, social, or community networks, lenders are more likely to
know borrowers than is the case with lending through banks. The more knowledge lenders have of borrowers, the less asymmetric
information problems interfere with the market for loans. Knowing the borrowers well allows lenders to charge higher rates to the
riskier borrowers, lower rates to the safer borrowers, and to be confident they have properly sorted borrowers into those “risky” and
‘safe” categories.
Monitoring applicants means keeping tabs on the borrowers during the life of the loan. With banks, this is accomplished primarily
by checking to be sure payments are made on time and, in some cases, to periodically pull a new credit report to see if the borrower’s
behavior has changed in any other related area. If lending takes place within kin, social, or community networks, lenders are likely to
know the borrowers. Monitoring is as simple as having Sunday dinner with your kin, chatting during a meeting of your social
group, or dropping by your neighbor’s place of business. Being able to monitor borrowers allows lenders to be confident that
borrowers will not adversely change their behavior during the life of the contract.
Because networks can solve or at least reduce asymmetric information problems, lending increases.
In a historical setting, economic historian Naomi Lamoreaux’s book Insider Lending: Banks, Personal Connections, and
Economic Development in Industrial New England provides an analysis of the role of kin and social networks in facilitating
lending in the early 1800s. In a contemporary development setting, see the article by Abhijit Banerjee and Esther Duflo, “Giving
Credit Where It is Due,” Journal of Economic Perspectives 24 (Summer 2010): 61-79. http://www.jstor.org/stable/20799155