# this is the macroeconomic intermediate question

Risk attitudes

For each of these utility functions, determine whether the agent is risk-averse, risk-neutral, or risk-loving. (Assume that wealth is always positive: w > 0).

• u(w) = 2w3 + w.
• u(w) = 5ln(w) − 4. (ln is the natural logarithm function.)

## 2Now you see it, now you don’t

A student has \$900 in total wealth, consisting of a \$500 laptop as well as \$400 in cash, but

√ there is a 5% chance that her laptop gets stolen during the quarter. Her utility is u(w) = w, where w is her wealth at the end of the quarter.

• Compute the expected value and variance of the student’s end-of-quarter wealth.
• Compute the student’s expected utility, given the risk of having her laptop stolen. Then compute her certainty equivalent.
• A startup called Swipe provides full insurance against the risk of laptop theft. What is the actuarially fair price of this insurance policy? Would the student buy such a policy at the actuarially fair price?
• Explain how Swipe’s insurance contract might create an adverse selection problem. Explain how the contract might create a moral hazard problem.

## 3Portfolios

Explain why each of the following investment strategies reduces, but doesn’t eliminate, the investor’s exposure to risk.

• Investing in several different clean-energy technologies (wind, solar, and hydrogen) instead of just investing in solar.

## 1 Risk attitudes

For each of these utility functions, determine whether the agent is risk-averse, risk-neutral, or risk-loving. (Assume that wealth is always positive: w > 0).
a. u(w) = 2w3 + w.
b. u(w) = 5ln(w) − 4. (ln is the natural logarithm function.)

## 2 Now you see it, now you don’t

A student has \$900 in total wealth, consisting of a \$500 laptop as well as \$400 in cash, but there is a 5% chance that her laptop gets stolen during the quarter. Her utility is u(w) = w, where w is her wealth at the end of the quarter.
a. Compute the expected value and variance of the student’s end-of-quarter wealth.
b. Compute the student’s expected utility, given the risk of having her laptop stolen. Then compute her certainty equivalent.
c. A startup called Swipe provides full insurance against the risk of laptop theft. What is the actuarially fair price of this insurance policy? Would the student buy such a policy at the actuarially fair price?
d. Explain how Swipe’s insurance contract might create an adverse selection problem. Explain how the contract might create a moral hazard problem.
Copyright 2018 by Brendan M. Price. All rights reserved. 1

## 3 Portfolios

Explain why each of the following investment strategies reduces, but doesn’t eliminate, the investor’s exposure to risk.
a. Investing in several different clean-energy technologies (wind, solar, and hydrogen) instead of just investing in solar.

## 1 Risk attitudes

For each of these utility functions, determine whether the agent is risk-averse, risk-neutral, or risk-loving. (Assume that wealth is always positive: w > 0).
a. u(w) = 2w3 + w.
b. u(w) = 5ln(w) − 4. (ln is the natural logarithm function.)

## 2 Now you see it, now you don’t

A student has \$900 in total wealth, consisting of a \$500 laptop as well as \$400 in cash, but there is a 5% chance that her laptop gets stolen during the quarter. Her utility is u(w) = w, where w is her wealth at the end of the quarter.
a. Compute the expected value and variance of the student’s end-of-quarter wealth.
b. Compute the student’s expected utility, given the risk of having her laptop stolen. Then compute her certainty equivalent.
c. A startup called Swipe provides full insurance against the risk of laptop theft. What is the actuarially fair price of this insurance policy? Would the student buy such a policy at the actuarially fair price?
d. Explain how Swipe’s insurance contract might create an adverse selection problem. Explain how the contract might create a moral hazard problem.
Copyright 2018 by Brendan M. Price. All rights reserved. 1

## 3 Portfolios

Explain why each of the following investment strategies reduces, but doesn’t eliminate, the investor’s exposure to risk.
a. Investing in several different clean-energy technologies (wind, solar, and hydrogen) instead of just investing in solar.

## 1 Risk attitudes

For each of these utility functions, determine whether the agent is risk-averse, risk-neutral, or risk-loving. (Assume that wealth is always positive: w > 0).
a. u(w) = 2w3 + w.
b. u(w) = 5ln(w) − 4. (ln is the natural logarithm function.)

## 2 Now you see it, now you don’t

A student has \$900 in total wealth, consisting of a \$500 laptop as well as \$400 in cash, but there is a 5% chance that her laptop gets stolen during the quarter. Her utility is u(w) = w, where w is her wealth at the end of the quarter.
a. Compute the expected value and variance of the student’s end-of-quarter wealth.
b. Compute the student’s expected utility, given the risk of having her laptop stolen. Then compute her certainty equivalent.
c. A startup called Swipe provides full insurance against the risk of laptop theft. What is the actuarially fair price of this insurance policy? Would the student buy such a policy at the actuarially fair price?
d. Explain how Swipe’s insurance contract might create an adverse selection problem. Explain how the contract might create a moral hazard problem.
Copyright 2018 by Brendan M. Price. All rights reserved. 1

## 3 Portfolios

Explain why each of the following investment strategies reduces, but doesn’t eliminate, the investor’s exposure to risk.
a. Investing in several different clean-energy technologies (wind, solar, and hydrogen) instead of just investing in solar.

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