2. (Measures of Risk Aversion in EUT) In class we discussed the Arrow-Pratt coefficientof absolute risk aversion:r(x):Another measure of risk aversion that is often used is the Arrow-Pratt coefficient ofrelative risk aversion:q(x) =u₁(x) = 1- ep• U₂(x) =21-P-11-p• Uz(x) = ln(x)==• u₁(x) = ax• u₁(x) = x-ax²u"(x)u'(x)Both measures capture different aspects of risk aversion. One way to see the differenceis to consider an agent who has a budget to allocate to a portfolio of a safe asset (abond) and a risky asset (a stock). The higher r(x), the more dollars the agent willallocate to the bond. The higher q(z), the bigger the share of the agent's portfolio thatwill be allocated to the bond.1Tu" (x)u'(x)The questions below refer to the following utility functions, which are often used inapplications. Here is the agent's income or wealth, and p and a are parameters:(a) Calculate r(x) and g(x) for each of the above utility functions.(b) Are r(r) and q(z) increasing, decreasing, or constant with respect to z ineach of the above cases?

Absolute Risk Aversion refers to the level of risk an individual can accept.Relative Risk Aversion…

2. (Measures of Risk Aversion in EUT) In class we discussed the Arrow-Pratt coefficient of absolute risk aversion: u"(x) u'(x) r(x) = Another measure of risk aversion that is often used is the Arrow-Pratt coefficient of relative risk aversion: xu" (x) u'(x) q(x) = Both measures capture different aspects of risk aversion. One way to see the difference is to consider an agent who has a budget to allocate to a portfolio of a safe asset (a bond) and a risky asset (a stock). The higher r(r), the more dollars the agent will allocate to the bond. The higher q(z), the bigger the share of the agent's portfolio that will be allocated to the bond.

2. (Measures of Risk Aversion in EUT) In class we discussed the Arrow-Pratt coefficient of absolute risk aversion: u"(x) u'(x) r(x) = Another measure of risk aversion that is often used is the Arrow-Pratt coefficient of relative risk aversion: xu" (x) u'(x) q(x) = Both measures capture different aspects of risk aversion. One way to see the difference is to consider an agent who has a budget to allocate to a portfolio of a safe asset (a bond) and a risky asset (a stock). The higher r(r), the more dollars the agent will allocate to the bond. The higher q(z), the bigger the share of the agent's portfolio that will be allocated to the bond.

ECON MICRO

5th Edition

ISBN:9781337000536

Author:William A. McEachern

Publisher:William A. McEachern

Chapter14: Transaction Costs, Asymmetric Information, And Behavioral Economics

Section: Chapter Questions

Problem 3.8P

See similar textbooks

Similar questions

1. Individual Problems 18-1 You hold an oral, or English, auction among three bidders. You estimate that each bidder has a value of either $88 or $110 for the item, and you attach probabilities to each value of 50%. The winning bidder must pay a price equal to the second highest bid. The following table lists the eight possible combinations for bidder values. Each combination is equally likely to occur. On the following table, indicate the price paid by the winning bidder. Combination Number Bidder 1 Value Bidder 2 Value Bidder 3 Value Probability Price ($) ($) ($) 1 $88 $88 $88 0.125 2 $88 $88 $110 0.125 3 $88 $110 $88 0.125 4 $88 $110 $110 0.125 5 $110 $88 $88 0.125 6 $110 $88 $110 0.125 7 $110 $110 $88 0.125 8 $110 $110 $110 0.125 The expected price paid is . Suppose that bidders 1 and 2 collude and would be willing to bid up to a maximum of their values, but the two bidders…
2 Scenario Your client, InsureCorp, is an insurance company considering launching an 'income insur- ance' product in the nation of Motherland. Income insurance is a product that fully insures a household against changes in income caused by a major injury or illness. At present, no businesses are selling income insurance products in Motherland. Initial market research suggests that there are 15,000 households in Motherland interested in purchasing income insurance. Your client expects that the fixed cost of launching the income insurance product will be $25,000,000 per year, and that each policy issued to a customer will cost the company an additional $2,000 in sales commissions. 2.1 Your task Your client wants you to analyse the potential market for income insurance and report on the following: What is the maximum price the company can charge a household for an income insurance policy? What is the expected profit (or loss) for the company if it becomes a monopoly provider of income…
7. Principal-Agent II A risk-neutral principal can hire a risk-averse agent to undertake a project. There are two possible outcomes for the gross profit of the principal, TL There are also two possible effort levels that the agent can exert, e = 0 or 1; if e = 0, the probability of TH is only 1/3, but if e = 1, the probability of TH increases to 2/3. 20 and TH = 50. The agent's utility from receiving a wage wand exerting effort e is Vw – e, and the agent has a reservation utility of ū = 2. (a) Assume that effort is observable. What wage will the principal offer if she wants to induce low effort? What wage will she offer if she wants to induce high effort? What contract is optimal for the principal?
D3) What is the misconception of the risk-reward relationship? What is the role and the ultimate goal of the decision maker? Examples, implications.
2- Who is risk aversion?
6 What do the average expected value, standard deviation, and coefficient of variation tell you about loss exposures?
3. Suppose Chelsea has the following utility function over wealth: v (y) = ln y (a) Show that Chelsea is risk averse. (b) Consider the lottery that yields the outcome $2 with probability ; and the outcome $8 with probability . How much money would you need to offer Chelsea to buy the lottery from her if the lottery is all she owns? (c) What is the Chelsea's risk premium for this lottery? (d) Suppose Antonio has utility function over wealth given by Va (y) = Vy and suppose Dillon has the following utility function over wealth: Va (y) = In Vy Who is more risk averse, Antonio or Dillon? Show this using two approaches. (e) Who is more risk averse, Chelsea or Dillon? Explain.
7. Individual Problems 16-6 Pharmaceutical Benefits Managers (PBMs) are intermediaries between upstream drug manufacturers and downstream insurance companies. They design formularies (lists of drugs that insurance will cover) and negotiate prices with drug companies. PBMs want a wider variety of drugs available to their insured populations, but at low prices. Suppose that a PBM is negotiating with the makers of two nondrowsy allergy drugs, Claritin and Allegra, for inclusion on the formulary. The "value" or "surplus" created by including one nondrowsy allergy drug on the formulary is $228 million, but the value of adding a second drug is only $68 million. Assume the PBM bargains by telling each drug company that it's going to reach an agreement with the other drug company. Under the non-strategic view of bargaining, the PBM would earn a surplus of of $ million. million, while each drug company would earn a surplus Now suppose the two drug companies merge. What is the likely postmerger…
17. Suppose a risk-neutral power plant needs 10,000 tons of coal for its operations next month. It is uncertain about the future price of coal. Today it sells for $60 a ton but next month it could be $50 or $70 (with equal probability). How much would the power plant be willing to pay today for an option to buy a ton of coal next month at today's price? (Ignore discounting over the short period of a month.) а. 5 b. 4 с. 3 d. NOTE: I KNOW THAT THE ANSWER IS (A), BUT PLEASE INCLUDE ALL THE STEPS HOW TO SOLVE THE PROBLEM BECAUSE I NEED TO PRACTICE. THANK YOU.
2 Consider the two investments listed below with possible outcomes and probabilities: INVESTMENT (in $1000) SAFE RISKY INVESTMENT AMOUNTⓇ 40+ 40+ GOOD SCENARIO OUTCOME 45+ 80+ AVERAGE+ SCENARIO PROB OUTCOME 0.40* 0.40€ 42+ 45+ BAD+ SCENARIO PROB OUTCOME PROB 0.20 35+ 0.20 10+ 0.40€ 0.40+ b) a) Suppose I have utility function U(*) = (x)2. What is the expected utility from each investment? Which investment will I choose, if any? Show and explain your work and provide the intuition. c) What is the value of the risk premium for the SAFE investment? Show and explain your work and provide the intuition. d) What is the value of the risk premium for the RISKY investment? Show and explain your work and provide the intuition.< +
1.) You have determined that if Generics Manufacturer A prevails against the government in court, its shares are worth $160. If it loses, it must pay a large settlement, meaning shares are only worth $34. The decision is expected later today and shares currently trade at $55. What probability is the market suggesting GMA has of winning? (Adapted from a Citi S&T Interview question).
5. Shift-in-charge Nazar Al Rushdy: Nazar is pessimistic about the market price. What is your guidance for Nazar? The decision to employ decision trees in crucial situations has been taken by Salem Al Harthi, the plant manager. The table below presents data on demand for a duration of 6 hours along with their respective probabilities. The first row of the table provides the probability of demand for the initial three hours when a leak occurs, denoted in parentheses. Subsequently, the following three rows indicate the probabilities of high, medium, and low demand for the succeeding three hours. To illustrate, if the initial 3-hour market price was low, the probabilities of high demand, medium demand, and low demand in the next three hours are 0.2, 0.3, and 0.5, respectively. Market price High Market price Medium Initial 3-hrs (0.2) Initial 3-hrs (0.5) Market price Low Initial 3-hrs (0.3) High demand (next (0.5) (0.4) (0.2) 3 hrs) Medium demand (0.3) (0.2) (0.3) (next 3 hours) Low demand…