ECON7030 Microeconomic Analysis

Tutorial Exercise 7 (Week 8)

Question 1

A new virus called the The Pandora Virus is out of its box! Epimetheus has an initial

wealth of $10,000 and a von-Neumann Morgenstern utility function (overwealth) given

by u(w) = lnw. Living a relatively vibrant social life, Epimetheus has aprobability of

30% of contracting the virus. Conditional on contracting the virus, there is a 30% chance

that it becomes severe, which has the effect of reducing his wealth by$6000; and a 70%

chance that he suffers minor illnesses, which has the effect of reducing his wealth by $100.

(a) Calculate Epimetheus’s expected utility.

(b) Suppose the government can enforce a lockdown, which will reduce Epimetheus’s

probability of contracting the virus to 10%. However, a lockdownwill also reduce

Epimetheus’s wealth (whether or not he contracts the virus) by x dollars. Write

down the equation that defines the maximum amount of x that Epimetheus is willing

to suffer for the lockdown. (Note: There is no need to solve for x numerically.)

(c) Hippocrates Pharmaceuticals has developed a vaccine. For simplicity, suppose vac-

cination brings no externality. The vaccine reduces the vaccinated person’s prob-

ability of contracting the virus to 5%. Moreover, upon contracting the virus, a

vaccinated person develops a severe illness with a probability of 10%, and suffers

minor illnesses with probability 90%. Calculate Epimetheus’s expected utility after

receiving the vaccine, assuming that the vaccine is free and causes no reduction in

utility.

(d) Epimetheus reads about the vaccine on social media and suffers a disutility of 0.1

utils (utility unit) from fear if he gets the vaccine. Will Epimetheus take the vaccine

voluntarily?

Question 2

Suppose there is an urn containing 300 balls, of those 100 balls are red, while the remaining

200 balls are either black or white with unknown proportions. The balls are well-mixed

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that any individual ball is as likely to be drawn as any other. Consider the first pair of

gambles:

Gamble 1A: You receive $10 if you draw a red ball, $0 otherwise.

Gamble 1B: You receive $10 if you draw a black ball, $0 otherwise.

Then consider a second pair of gambles:

Gamble 2A: You receive $10 if you draw a red or white ball, $0 otherwise.

Gamble 2B: You receive $10 if you draw a black or white ball, $0 otherwise.

Before starting on this exercise, think about which gamble you would prefer from each

pair. (There is no right or wrong answer. Just choose what you like.)

(a) Normalise the utility from getting $0 to 0, and let u10 be the utility from getting

$10. Let p be the proportion of black balls among the 200 balls of unknown colours

(i.e., there are 200p black balls in the urn). Suppose an expected utility maximiser

strictly prefers Gamble 1A among the first pair of gambles, what must his/her belief

about p be?

(b) Now suppose an expected utility maximiser strictly prefers Gamble 2B among the

second pair of gambles, what must his/her belief about p be?

(c) Given your answer to (a) and (b), can an expected utility maximiser strictly prefers

1A to 1B, while strictly prefers 2B to 2A?

(d) Economic experiments typically find a significant proportion of subjects choosing

1A and 2B simultaneously. (Are you one of them?) What do you think might be

the reason for that?

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