ECON 301 Problem Set Three
Assigned problems due by Thursday, April 27
Assignments must be clearly written, stapled (if submitting hard copy), and without frayed edges, and
the like – messy or difficult to read assignments will not be graded. Write your name on the assignment.
1. (2 points) Girls Scouts are selling cookies in front of a grocery store. Every other shopper who
exits buys a box of cookies (at random). Half of the buyers spend $8 on cookies (two boxes),
and the other half spends $4. The store has 1000 shoppers leaving per day,
a. Find the expected revenue for per day?
b. Find the variance and standard deviation of revenue (among people who bought cookies)?
2. (3 points) Find the fair insurance price (per year) for a $20,000 boat assuming a 2% chance that
it will be destroyed in an accident, leaving a $3,000 salvage value (which the owner keeps)
and no chance of any partial loss.
3. (10 points) Jay pays $400 a year for auto insurance that covers her against liability if sued for
damages in the event of an accident where she is at fault. She expects (correctly) that there is
a 1/1000 chance that in any given year that she will be sued for $100,000.
a. Explain/calculate whether it is rational to buy the insurance (first, find the expected loss.)
b.Draw a graph illustrating Jay’s utility as a function of income, assuming that her marginal
utility of income is declining. Jay is, in fact, willing to pay up to $800 to avoid incurring the
loss. Show on your graph (and explain) that this amount ($800 payment) yields the same
level of utility as with Jay’s expected income without insurance.
c. Show graphically the level of utility if Jay insures at the $400 premium.
d.Suppose there are a thousand Jay’s in the market. There is one insurance company that, for
simplicity, incurs zero administrative costs to supply insurance policies. Calculate the annual
profit the insurance company expects.
e. Suppose the company expects to attract these same annual profits into perpetuity (assume a
discount rate is 5%). What is the company’s worth in present value terms?
f. Suppose the insurance market is competitive. What would you expect the competitive
equilibrium premium to be? Explain.
1/2 4. (5 points) Connie’s utility depends on income, I, where utility is U = I . She wins a prize that
depends on the roll of dice. She receives $400 if she rolls a 3, 4, 6, or 8; otherwise she receives $100.
a. What is the expected payoff from this prize?
(Hint: The probabilities of rolling a 3 is 1/18, of rolling a 4 is 3/36, of rolling a 6 is 5/36, and of
rolling an 8 is 5/36)
b. What is the expected utility from this prize?
c. Connie is offered an alternative of $169 (no dice roll required). Explain whether she accepts
the alternative prize or rolls the dice?
d. What is the minimum payment that Connie will accept to forgo the roll of the dice?

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