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) = 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.

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) = 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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