Question

Problem 5. Consider a risk averse agent with a Bernoulli function $u(x) = -e^{-\lambda x}$ and initial wealth $W = 1000$. She faces the risk of losing 100 dollars, which occur with probability 1/4. An insurance company offers a policy that costs 1/3 dollar per dollar of coverage (per dollar paid back in the event of a loss of the 100 dollars). Denote by $z$ the amount of purchased coverage. a) Find the optimal $z^$ that the DM will choose (it will be a function of $\lambda$). Hint: see Slides 2 of the week of 2/22. b) Suppose for some reason, $\lambda$ of the DM increased but all the other parameters of the problem remained the same. Would her optimal $z^$ go up, down or stay the same?

          Problem 5. Consider a risk averse agent with a Bernoulli function $u(x) = -e^{-\lambda x}$ and initial wealth
$W = 1000$. She faces the risk of losing 100 dollars, which occur with probability 1/4. An insurance
company offers a policy that costs 1/3 dollar per dollar of coverage (per dollar paid back in the
event of a loss of the 100 dollars). Denote by $z$ the amount of purchased coverage.
a) Find the optimal $z^*$ that the DM will choose (it will be a function of $\lambda$). Hint: see Slides 2 of
the week of 2/22.
b) Suppose for some reason, $\lambda$ of the DM increased but all the other parameters of the problem
remained the same. Would her optimal $z^*$ go up, down or stay the same?

Problem 5. Consider a risk averse agent with a Bernoulli function u(x) = -e^-λ x and initial wealth
W = 1000. She faces the risk of losing 100 dollars, which occur with probability 1/4. An insurance
company offers a policy that costs 1/3 dollar per dollar of coverage (per dollar paid back in the
event of a loss of the 100 dollars). Denote by z the amount of purchased coverage.
a) Find the optimal z^* that the DM will choose (it will be a function of λ). Hint: see Slides 2 of
the week of 2/22.
b) Suppose for some reason, λ of the DM increased but all the other parameters of the problem
remained the same. Would her optimal z^* go up, down or stay the same?

Added by John Y.

Question

Please give Ace some feedback