Question: Risk Smoothing Through the Family vs. The Market
You consume only pizza and you live for at most T years.
If your consumption of pizza each year ever falls below 4, then you die because of starvation.
You have no access to financial markets or savings. You receive an endowment of pizza each
year that is iid distributed N(6,1). If your pizza endowment is ever less than
4 you die and you collect no utility from that point until date T.
If your consumption of pizza each year ever falls below 4, then you die because of starvation.
You have no access to financial markets or savings. You receive an endowment of pizza each
year that is iid distributed N(6,1). If your pizza endowment is ever less than
4 you die and you collect no utility from that point until date T.
Your annual utility function = pizza
Assume that your annual discount factor = .95
- Calculate your lifetime expected utility. Show your algebra.
- Now you can marry another person. Each year, this person draws from a pizza endowment with independent draws over time distributed N(6,1). The correlation of your endowment and this person’s endowment = -.3. You have agreed to the following risk sharing contract, each year your consumption = (person a’s endowment + person b’s endowment)/2 .
- Measured in slices of pizza at time 0, how much would you be willing to pay to marry this person?
- Repeat #2 under the assumption that the correlation of your endowments = 0.
- How does your answer to #2 change if at age 0 you are given for free a bond that pays you 1 slice of pizza each year until you die? Explain why this reduces your willingness to pay to marry.