Problem Set 3: Public goods (continued), inter-temporal choice and

adverse selection

1. Suppose people’s preferences are as given in the table below:

Voter Option A Option B Option C

1 70 40 20 2 10 80 30 3 40 20 80

Total 120 140 130

a) Under the VCG mechanism, which option will be chosen?

b) Which voter(s) are pivotal?

c) What fees would each agent have to pay under the VCG mechanism?

2. When Hollywood stars Burt Reynolds and Loni Anderson were getting divorced Ms. Anderson

reportedly asked Mr Reynolds for a settlement of either $15 million or $75,000 a month for the rest

of her life. Explain how Mr. Reynolds’ financial advisor should go about advising him, showing some

example calculations.

3. Molly has an income of £400 in period 1 and an income of £500 in period 2. Suppose her utility

function is 𝑐10.4𝑐2

0.6 and the interest rate is 10%.

a) How much would she choose to consume in each period?

b) How would her choices change if her income in period 1 halved and her income in period 2 stayed

the same?

c) What happens to her choices if interest rates increase?

4. Suppose that it is common knowledge that 12% of the second hand cars people would like to sell

are “lemons” and the rest are “plums”. These sellers would sell a lemon for £1500 and a plum for

£2000. People shopping for a second hand car value lemons at £1600 and plums at £2200, but before

they buy a car they do not know if it is a lemon or a plum. Assume that there are many more sellers

than buyers, so the market for second hand cars is competitive. What cars are sold, and at what

price(s)?

How would this change if buyers valued lemons at £1800?

Finally, how would this change if buyers valued lemons at £1600 as in the original problem, but 36%

of all cars were known to be lemons?

5. High productivity workers produce £2,000,000 worth of goods over their lifetime (in present value

terms), whereas low productivity workers only produce £500,000 worth in their lifetime. 20% of all

workers are high productivity, but an employer is unable to tell to which group a given worker belongs

(even after they have worked for them for a lifetime). It costs high productivity workers £100,000 in

disutility to successfully complete a year in higher education, while it costs low productivity workers

£300,000 to do the same thing (as it takes them longer to do the problem sets). Assume that people

can stay in higher education for as long as they wish, and that people who leave education later both

retire later and die later, so the number of years they spend in education has no impact on how many

years they work in total (or how many years of retirement they get).

a) Will there be a separating and/or pooling equilibrium in this market? How many years of higher

education will high and low types complete in the equilibria that you find?

b) A possible implication of this model is that education is a socially wasteful activity. Explain why. Do

you agree?

6. There are two types of people wishing to buy flowers: business people and young couples. Suppose

there are equal numbers of people in both groups. Business people value flowers at £5 + 𝑡£4 where

𝑡 = 1 if they are able to pick up the flowers in the train station on the way home from work and 𝑡 = 0

if they have to buy them online. Young couples value flowers at £4 + 𝑡£2. Suppose that there is an

infinite supply of flowers both at the train station and online, and that they can be produced at zero

cost to the flower seller (a monopolist). Given the flower seller cannot tell whether someone is a

business person when they buy their flowers, what price should they set for flowers at the train station

and flowers on the internet?