# Test 2 (Spring 2008)

```Your name and Perm # ________________________________________________________________
Econ 130
Test 2
John Hartman
May 19, 2008
Instructions:
You have 60 minutes to complete this test, unless you arrive late. Late arrival will lower the time
available to you, and you must finish at the same time as all other students.
Each question shows how many points it is worth. Show all work in order to receive partial credit for
correct work in some cases. Clearly circle your answer(s) or else you may not receive full credit for a
complete and correct solution.
Cheating will not be tolerated during any test. Any suspected cheating will be reported to the relevant
authorities on this issue.
You are allowed to use a nonprogrammable four-function or scientific calculator that is NOT a
communication device. If you use a calculator that does not meet these requirements, you will be
assumed to be cheating.
Unless otherwise specified, you can assume the following:
 Supply curves have positive slope and demand curves have negative slope.
 Negative quantities cannot be supplied or demanded.
 Negative prices are not possible.
You are allowed to turn in your test early if there are at least 10 minutes remaining. As a courtesy to
your classmates, you will not be allowed to leave during the final 10 minutes of the test.
Your test should have 6 questions, worth a total of 40 points. If your test is incomplete, it is your
responsibility to notify a proctor to get a new test.
For your reference, an example of a well-labeled graph is below:
1. Fifty people have individual demand curves for a good given by P = 100 – 4Q, where P is price and
Q is number of units. The marginal cost of the good is 200.
(a) (3 points) How many units of the good are purchased in total (i.e. the total quantity purchased by all
50 people) if this is a private good? Assume a competitive market.
(b) (3 points) How many units of the good are provided in an efficient outcome if this is a public good?
2. Edna has a job that pays her \$6,400 per month. However, in any month, there is a 5 percent chance
that she will get sick, leading to a \$6,000 cost.
(a) (2 points) If Edna’s monthly utility is the square root of her income after medical costs (if any)
are deducted, what is her expected monthly utility?
(b) (2 points) What is the certainty equivalent of this gamble if insurance is impossible to obtain?
(c) (3 points) What is the actuarially fair insurance premium in this case?
(d) (3 points) What is Edna’s willingness to pay for full insurance?
3. (4 points) In 2006, the Social Security primary insurance amount was calculated as follows:
 90 percent of the first \$656 of average indexed monthly earnings (AIME), plus
 32 percent of AIME between \$656 and \$3,955, plus
 15 percent of AIME above \$3,955.
What is the primary insurance amount that Abraham would have received in 2006 if he had AIME of
\$4,000?
4. Lenny and Carl have \$3,000 to split between the two of them. Lenny’s money received is IL and
Carl’s is IC. Lenny’s marginal utility of money is MUL = 5000 – IL. Carl’s marginal utility of money
is MUC = 7500 – IC. If Lenny receives none of the money, his utility is 0. If Carl receives none of the
money, his utility is 1,000,000.
(a) (4 points) If Lenny and Carl are maximizing an additive social welfare function, how will they split
the money?
(b) (4 points; this part is meant to be difficult) If social welfare is equal to the utility of the person who
has the lowest utility, how will the money be distributed to maximize the social welfare function?
5. (6 points) Assume that there are two periods of consumption: Working years (time period 1) and
retirement (time period 2). Because of the Social Security system, Monty receives an endowment of
100 units during his working years and 10 units for his retirement. If Monty’s consumption in periods 1
and 2 are c1 and c2, respectively, and his utility is c13c2, how much does he consume in each period if he
can save or borrow between periods 1 and 2 at a rate of 100%?
6. (6 points) Agnes is about to head to the hospital after sitting on an exploding toilet. The total cost of
being in the hospital is 5,000Q, with Q denoting the number of days in the hospital. Agnes’ total
benefit of being in the hospital is 6,000Q – 250Q2. How long will Agnes want to stay in the hospital if
she must pay 30% of the costs of staying in the hospital?
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