# this is the macroeconomic intermediate question

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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*) = 2*w*^{3 }+*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.

Copyright2018 by Brendan M. Price. All rights reserved.1

## 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*) = 2*w*^{3 }+*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*) = 2*w*^{3 }+*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*) = 2*w*^{3 }+*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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