Fall 2023: Problem set 6
Micro 1
Due date: November 17, 2022
Total: 30 points
1. Consider the following vNM utility function u : [0, 200] → R where
√
u(z) = z.
Consider the lottery L that gives z = 64 with probability 0.25 and z = 36 with
probability 0.75.
(a) (3 points) Calculate the EU of the lottery L.
(b) (4 points) Find the certainty equivalent for the lottery L.
(c) (5 points) Using answers from parts (a) and (b), show that the agent has a
risk-averse preference.
2. (5 points) Johny rejects the following lottery : (($5, 0.5), −$5, 0.5) . What can we
say about Johny’s risk preference? Clearly articulate your logic. [Rejection means
if the lottery is offered for free he will not accept it. ]
3. (8 points) Suppose a DM has the following endowment of contingent consumption:
($50,$100), where the probability of state 1 is 0.1. Suppose insurance is offered at
a premium of 20 cents per dollar. Write down the dollar value of his contingent
consumption, if he hypothetically sells his entire endowment at the market price.
Assume state 1 consumption is priced at p1 = 1. How would your answer change
if we assume state 2 consumption is priced at p2 = 1?
4. (5 points) Consider the following consumer deciding whether to buy fire insurance
for her new house. The probability of a fire incident is .1. In case of a fire, her
total wealth is $1000 whereas if there is no fire incident her wealth would be $4000.
Suppose each unit of insurance is sold at 30 cents per dollar. If her vNM utility
function is given by
u(x) = ln x,
find the optimal level of fire insurance for her.
