1. Show if the following utility functions represent risk averse, risk neutral or risk loving preferences. u(c) = 10° + 3 u(c) = C² + 3C i. ii. 111. u(c) = e 4C
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- Define risk aversion and give an example of a risk-averse person?Scenario 2 Tess and Lex earn $40,000 per year and all earnings are spent on consumption (c). Tess and Lex both have the utility function (sqrt c) . Both could experience an adverse event that results in earnings of $0 per year. Tess has a 1% chance of experiencing an adverse event and Lex has a 12% chance of experiencing an adverse event. Tess and Lex are both aware of their risk of an adverse event. Refer to Scenario 2 If an insurance company knows the probability of Tess experiencing an adverse event, what is the actuarially fair premium charged to Tess per $1 of benefit? Round to two decimal placesConsider a risk averse individual who has utility function u(a) which is increasing with u(0) = 0. There are two risky assets: A,B. For A, every dollar invested gives return $0 with probability 1/3 and $3 with probability 2/3. For B, every dollar invested gives return is $0 with probability 1/4 and $3 with probability 3/4. The individual has $120 to invest. Consider two investment choices: (1) invest entire $120 in A and (2) invest $60 in A, $60 in B. (a) Drawing diagram of the utility function and showing your work, determine the expected utility of the individual from choice 1. (b)Drawing diagram of the utility function and showing your work, determine the expected utility of the individual from choice 2 when return from A is bad. (c) Drawing diagram of the utility function and showing your work, determine the expected utility of the individual from choice 2 when return from A is good. (d) Drawing diagram of the utility function and showing your work, determine the…
- 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)?Anna is risk averse and has a utility function of the form u(w) pocket she has €9 and a lottery ticket worth €40 with a probability of 50% and nothing otherwise. She can sell this lottery ticket to Ben who is risk neutral and has €30 in his pocket. Find the range of prices that would make such a transaction possibleKhalid has a utility function U = W1/2, where W is his wealth in millions of dollarsand U is the utility he obtains from the wealth. In a game show, the host offershim a choice between (A) $4 million for sure, or (B) a gamble that pays $1million with probability 0.6 and $9 million with probability 0.4.i. Graph Khalid’s utility function with the help of above utility function. Ishe risk lover? Explain. ii. Does A or B choice offer Khalid a higher expected prize? Explain yourreasoning with appropriate calculations. iii. Does A or B offer Khalid a higher expected utility? Again, show yourcalculations. iv. Should Jamal pick A or B choice? Why?
- Explain the relationship between U" >0 and risk aversion.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)Jamal has autility function U=W1/2,where W is his wealth in millions of dollars and U is the utitlity he obtains from that wealth.Inthe final stage of a game show,the host offers offers Jamal a choice(A)$4 million dollar for sure,or (B) a gamble that pays $1 million with probability 0.6 and $9million with probability 0.4. a.Graph Jamal's utitility function.Is he risk averse?Explain. b.Does A or B offers Jamal a higher expected price?Explain your reasoning with appropriate calculations. c.Does A or B offer Jamal a higher expected utility? d.Should Jamal pick A or B? Why?
- A risk-averse manager is considering a project that will cost £100. There is a 10 percent chance the project will generate revenues of £100, an 80 percent chance it will yield revenues of £50, and a 10 percent chance it will yield revenues of £500. Should the manager adopt the project? Explain. What will a risk-neutral and risk-loving manager do in the same situation?Can you explain how Constant Relative Risk Aversion utility function should be understood and how it works mathematicallyJamal 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. a. b. c. d. Graph Jamal’s utility function. Is he risk averse? Explain. (2+2) Does A or B offer Jamal a higher expected prize? Explain your reasoning with appropriate calculations. (1) Does A or B offer Jamal a higher expected utility? Explain your reasoning with calculations. (2) Should Jamal pick A or B? Why?
