Risky Prospect K is defined as: K = ($5, 0.30 ; $11,0.70) If my utility of wealth function is given by u (x) = x" and a=0.5, what is my certainty equivalent for prospect K? (Wha
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- 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)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 $x, then we can fully characterize the agent's risk attitude. That is, this information comparing two given lotteries is enough to determine if the decision maker is risk averse, risk loving or risk neutral.” If this claim is TRUE, then provide a proof. If it is FALSE, then prove your argument by providing an explanation.Please answer true or false for each of the following statements. A risk-averse consumer has increasing marginal utility. A risk-neutral consumer is willing to pay a positive risk-premium to avoid risk. A risk-neutral consumer has a linear utility function. A risk-loving consumer has a convex utility function. A risk-averse consumer can increase her expected utility by buying multiple stocks whose outcomes are not closely related, instead of buying only one stock.
- A Risk Lover prefers the expected utility of wealth to the utility of the expected value of wealth. It is because a risk lover has a convex utility function It is because a risk lover has a concave utility functionSuppose Alex’s utility function is u ($x) = √x. Assume her initial wealth is 0. Is it possible that Alex’s expected utility from the prospect equals $5, why? What is the possible range of Alex’s expected utility?How do their perceptions of probability (in their 'weighting function') in prospect theory cause biases in their decision making?
- Calculate the expected utility of John when he faces the risky prospect X = {1, 2, 3, 4; 0.2, 0.4, 0.4, 0.2} . His utility function is u(x) = 4 ln x, where x is wealth and ln represents the natural log. (Use two decimals)Leo owns one share of Anteras, a semiconductor chip company which may have to recall millions of chips. The stock currently trades at $100/share. Leo believes the probability that they have to recall the chips is 50%. If the chips have to be recalled, the stock price will be cut in half, but otherwise it will remain $100. The expected value of Leo's share is ______ Assume Leo has the utility function, U(X)=√X. The minimum price Leo would accept to sell his share is _______ Leo's risk premium is ________Loss aversion refers to the idea that people ________. generally tend to avoid risky activities are more prone to making losses than gains in day-to-day transactions psychologically weight a loss more heavily than they psychologically weight a gain are unwilling to undertake expenditures that reduce the probability of future losses
- 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).Suppose 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 two investors A and B.If the Certainty-Equivalent end-of-period wealth of A is less than the Certainty-Equivalent end-of-period wealth of B for the same portfolio choice,then A. Risk aversion of A > Risk aversion of B B. Risk aversion of A = Risk aversion of B C. Risk aversion of A< Risk aversion of B D. Not enough Information Justify your choice in a sentence or two：
