Draw a utility function over income u( I) that describes a man who is a risk lover when his income is low but risk averse when his income is high. Can you explain why such a utility function might reasonably describe a person’s preferences?
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Draw a utility function over income u( I) that describes a man who is a risk lover when his income is low but risk averse when his income is high. Can you explain why such a utility function might reasonably describe a person’s preferences?
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- Draw a utility function over income u(I) that describes a man who is a risk lover when his income is low but risk averse when his income is high. 1.) Using the 3-point curved line drawing tool, draw the low income portion of his utility function. Label it U₁. 2.) Using the 3-point curved line drawing tool, draw the high income portion of his utility function. Label it UH. Carefully follow the instructions above, and only draw the required objects. C 500- 450- 400- 350- 300- 250- 200- 150- 100- 50- 0 Utility 20,000 40,000 60,000 80,000 100,000 IncomeDraw a utility function (with income on the horizontal axis) for an individual who is risk-loving at low levels of income, risk-neutral at moderate levels of income, and risk-averse at high levels of income (with each of these three regions clearly labeled). How would someone who looked at this graph (and had no other information about the individual) be able to figure out the individual’s attitude toward risk (averse/loving/neutral) in each region?Consider an individual whose utility function over income I is U(I), where U is increasing smoothly in I (U’ > 0) and convex (U’’ > 0). a) Draw a utility function in U - I space that fits this description. b) Explain the connection between U’’ and risk aversion.
- 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 Suppose that insurance companies do not know specific probabilities of adverse events for Tess or Lex, but do know the average probability of an adverse event. If they assumed that both Tess and Lex purchase full insurance, what is the actuarially fair premium charged? Round to two decimal placesUsing the 3-point curved line drawing tool, draw a utility function for income that describes a person who is a risk lover. Label it 'Utility.' Carefully follow the instructions above, and only draw the required object. 500- 400- 300- 200- 100- Utility 20 40 60 Income (thousands) 80 100Scenario 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 Calculate Lex’s and Tess' expected utilities without insurance. (each one separated) Round to two decimal places for both
- Microeconomics Wilfred’s expected utility function is px1^0.5+(1−p)x2^0.5, where p is the probability that he consumes x1 and 1 - p is the probability that he consumes x2. Wilfred is offered a choice between getting a sure payment of $Z or a lottery in which he receives $2500 with probability p = 0.4 and $3700 with probability 1 - p. Wilfred will choose the sure payment if Z > CE and the lottery if Z < CE, where the value of CE is equal to ___ (please round your final answer to two decimal places if necessary)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 placesSuppose a person chooses to play a gamble that is free to play. In this gamble, they have a 10% chance of $100.00, and a 90% chance of nothing. Their utility function is represented in the following equation: U=W 1/2 where W is equal to the amount of "winnings" (or the income). Suppose now Brown Insurance Company offers the person the option of purchasing insurance to insure they will win the $100. What is the minimum amount Brown Insurance would charge you to insure your win? 0.90 O. 99 01 O 10
- Economics Consider two friends Anna and Elsa whose gains and losses are listed as follows: Anna's investment is worth $2.5 million (decreased from $3.5 to $2.5 million) Elsa's investment is worth $2.2 million (increased from $2 to $2.2 million) For each of them write down the reference utility function (First determine the reference point (use a parameter) and derive reference utility function for each).Natasha has utility function u(I) = (10*I)0.5, where I is her annual income (in thousands). (a) Is she a risk loving, risk averse or risk neutral individual? She is [risk loving, risk adverse, risk neutral] , as her utility function is [concave, convex, linear] (b) Suppose that she is currently earning an income of $40,000 (I = 40) and can earn that income next year with certainty. She is offered a chance to take a new job that offers a 0.6 probability of earning $44,000 and a 0.4 probability of earning $33,000. She should [take, not take] the new job because her expected utility of (approximately) [18.27,19.82,20,20.95,21.14] is [greater than, less than, equal to] her current utility of [18.27,19.85,20,20.95,21.14] .Alex has a utility function U = W2, 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 Alex a choice between (A) $9 million for sure, or (B) a gamble that pays $1 million with probability 0.4 and $16 million with probability 0.6. Use the blue curve (circle points) to graph Alex's utility function at wealth levels of $0, $1 million, $4 million, $9 million, and $16 million. Utility (Thousands) 5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0 0 2 4 6 8 10 12 14 Wealth (Millions of dollars) 16 18 20 V Utility Function (?)