Consider the following utility functions for wealth w: (i) u(w) = 3w, (ii) u(w) = w^1/3, (iii) u(w) = w + sqrt(w), (iv) u(w) = w*sqrt(w). Which of these is most risk-averse (has the highest Arrow-Pratt coefficient of absolute risk aversion) at w = 1? A. (i) B. (ii) C. (iii) D. (iv)
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Consider the following utility functions for wealth w: (i) u(w) = 3w, (ii) u(w) = w^1/3, (iii) u(w) = w + sqrt(w), (iv) u(w) = w*sqrt(w). Which of these is most risk-averse (has the highest Arrow-Pratt coefficient of absolute risk aversion) at w = 1?
A. (i)
B. (ii)
C. (iii)
D. (iv)
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- Consider two individuals whose utility function over wealth I is ?(?) = √?. Both people face a 10 percent chance of getting sick, and foreach the total cost of illness equals $50,000. Suppose person A has a total net worth of $100,000, and person B has a total net worth of $1,000,000. Both people have the option to buy an actuarially fair insurance contract that would fully insure them against the cost of the illness. a. Using expected utility calculations, show that person A would certainly buy full, actuarially fair insurance. b. Suppose an insurance company wants to maximize profits and wants to charge each customer the maximum price they are willing to pay. How much should the insurance company charge each client so that both buy the contract? c. What is surprising about your result in part b? What does this tell you about how insurance companies may be pricing health insurance contracts in the real world?A Risk Lover prefers the expected utility of wealth to the utility of the expected value of wealth. It is because a risk lover has a convex utility function It is because a risk lover has a concave utility functionSuppose that left-handed people are more prone to injury than right-handed people. Lefties have an 80 percent chance of suffering an injury leading to a $1,000 loss (in terms of medical expenses and the monetary equivalent of pain and suffering) but righties have only a 20 percent chance of suffering such an injury. The population contains equal numbers of lefties and righties. Individuals all have logarithmic utility-of-wealth functions and initial wealth of $10,000. Assume perfectly competitive insurance market and find (i) the first best and (ii) the second-best contracts.
- Consider the following claim: “If a decision maker prefers one given lottery that yields $x with probability 1 over another given lottery whose expected return is $x, then we can fully characterize the agent's risk attitude. That is, this information comparing two given lotteries is enough to determine if the decision maker is risk averse, risk loving or risk neutral.” If this claim is TRUE, then provide a proof. If it is FALSE, then prove your argument by providing an explanation.Prospect Z = ($7 , 0.25 ; $19 , 0.50 ; $26 , 0.25) If Anna's utility of wealth function is given by u(x)=x, what is the value of CE(Z) for Anna? (In other words, what is Anna's certainty equivalent for prospect Z?) (Note: The answer may not be a whole number; please round to the nearest hundredth) (Note: The numbers may change between questions, so read carefully)Please answer true or false for each of the following statements. A risk-averse consumer has increasing marginal utility. A risk-neutral consumer is willing to pay a positive risk-premium to avoid risk. A risk-neutral consumer has a linear utility function. A risk-loving consumer has a convex utility function. A risk-averse consumer can increase her expected utility by buying multiple stocks whose outcomes are not closely related, instead of buying only one stock.
- If a risk‐neutral individual owns a home worth $200,000 and there is a three percent chance the home will be destroyed by fire in the next year, then we know that:a) He is willing to pay much more than $6,000 for full cover.b) He is willing to pay much less than $6,000 for full cover.c) He is willing to pay at most $6,000 for full cover.d) None of the above are correct.e) All of the above are correct.Can you explain how Constant Relative Risk Aversion utility function should be understood and how it works mathematicallyLet W0 represents an individual’s current wealth and U(W) is this individual’s von Neumann-Morgenstern utility index (or utility function) that reflects how s/he feels about various levels of wealth. Assume this individual marginal utility of wealth decreases a wealth increases. Which of the following statements is true? a. This individual will prefer to keep his or her current wealth rather than taking a fair gamble. b. For this individual, a 50-50 chance of winning or losing c dollars yields less expected utility than does refusing the bet. c. This individual is said to be risk averse. d. All of the above.
- Jamal has a utility function U = W1/2, where W is his wealth in millions of dollars and U is the utility he obtains from that wealth. In the final stage of a game show, the host offers Jamal a choice between (A) $4 million for sure, or (B) a gamble that pays $1 million with probability 0.6 and $9 million with probability 0.4. (1) Does A or B offer Jamal a higher expected utility? Explain your reasoning with calculations. (2) Should Jamal pick A or B? Why? I would like help with the unanswered last parts of the questions.The von-Neumann Morgenstern utility function is of the form u(e) - In(e). There is a lottery over consumption outcomes: with probability 0.3, the consumption will be 1 and with probability 0.7 the consumption will be 3; Compute the risk premium (round to 2 decimals).Risk aversion is best explained by a. Timidity b. Increasing marginal utility of income c. Constant marginal utility of income Decreasing marginal utility of income A Risk Lover prefers the expected utility of wealth to the utility of the expected value of wealth. a. TRUE. It is because a risk lover has a convex utility function b. FALSE. It is because a risk lover has a concave utility function