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For the utility function U = Wa, what values of “a” correspond to being risk averse, risk neutral, and risk preferring?
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- For constants a and b, 0 < b, b 1, and expected profit E(p), the expected utility function of a person who is risk-neutral can be written as E(U) = Which one: a+b^p a + (E(p))^b. a - bE(p). a + bE(p). a + (E(p))^(-b).Can you explain how Constant Relative Risk Aversion utility function should be understood and how it works mathematicallyIf the utility function is U (W) = ((W0.75) / (0.75)), what is the absolute risk aversion coefficient?
- Show that an agent with utility function u(x) = log x is more risk aversethan an agent with utility function ˜u(x) = √x.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)Please draw a utility function that exhibits risk-loving behavior for small gambles (low values)and risk-averse behavior for larger gambles (high value).
- What is the mostly commonly used utility functions for the following and why: Risk Aversion Risk Seeking Risk NeutralCalculate the risk premium of John when he faces the risky prospect X = {1, 4, 9, 16; 0.2, 0.4, 0.4, 0.0} . His utility function is u ( x ) = x , where x is wealth. (Use two decimals)An agent makes decisions using U(ct) = (ct−χct−1)1−γ 1−γ . Answer the following: (a) Suppose χ = 0. Derive an expression for the coefficient of relative risk aversion RR(ct)? (b) Suppose 0 < χ ≤ 1. Derive an expression for the coefficient of relative risk aversion RR(ct)?
- In the field of financial management, it has been observed that there is a trade-off between the rate of return that one earns on investments and the amount of risk that one must bear to earn that return. a) Draw a set of indifference curves between risk and return for a person that is risk-averse (a person that does not like risk).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 functionDefine the term risk aversion?