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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 UL. 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. 500- 450- 400- 350- 300- 250- 200- 150- 100- 50- 0- Utility 20.000 40.000 60,000 80,000 Income 100,000When the second order derivative of a function is greater than zero than the agent is risk lover. question; Asses the risk attitude of an agent represented by the expected utility function u(x)= 2x2-5. However my course material writes that this agent is risk neutral because it is affine. My question is that whys is this so despite the fact that the second order derivative is '4' which is >0. Kindly explain this to me with complete steps.2. Alice believes that her car would cost £12500 to replace if it was stolen or damaged. Based on crime statistics for the area she lives in, she believes that the probability of her car being stolen or damaged is 0.15. (i) Alice's utility function is given by U(w) = ln(w) for w > 0 and she as £35000 in the bank. Calculate how much Alice would be prepared to pay (in a single payment) to insure her car against theft or damage (ii) Repeat the calculation in the previous part but now assume Alice has £500000 in the bank.
- 1. Consider the following utility functions, u(w) and v(w), which are functions of wealth w and the parameter p, where 06. If intertemporal preferences are consistent and the lifetime utility function is additive, then the discount function 8(t) must be (a) bounded (b) exponential (c) hyperbolic (d) linear (e) logarithmic1. A woman with current wealth X has the opportunity to bet an amount on the occurrence of an event that she knows will occur with probability P. If she wagers W, she will received 2W, if the event occur and o if it does not. Assume that the Bernoulli utility function takes the form u(x) = -e-rx with r>0. How much should she wager? Does her utility function exhibit CARA, DARA, IARA?a) Compute the (absolute) risk aversion measure dependent r(W) of utility function -e -aW Is r(W) on W?2) Explain how utility could be used in a decision where performance is not measuredby monetary value.A person's utility function is given by U(x, y, z) = 7xyz, where x, y, z denote then number of units of three commodities X,Y, and Z that the person consumes. The pricesr per unit of X,Y, and Z are 5 euro, 1 euro, and 3 euro respectively. If ther person has a budget of 270 euro, the person's utility is maximised when they consume units of X, units of Y, and units of Z. The person's maximum utility is If the person's budget is increased to 271 euro, then using the method of lagrange multipliers we find that the maximum utility is approximatelyYour utility function is given by M1/2. You have $100 and are planning to invest in a venture where you can win or lose 50 with equal probability. Will you accept the venture? What is the minimum gain you need to make in the good scenario such that you will invest in the venture?6. An analyst is assessing a DM's utility function for profit Y, in dollars, ranging from -400,000 to 2,000,000, and wishes to use a function: U(Y) : = Y+400,000 B 2,400,000 9 -400,000 ≤ y ≤ 2,000,000 She determined that the DM is indifferent between Alternative A and Alternative B: Alternative A: Probability 0.5 of making profit $2,000,000 Probability 0.5 of making profit -$400,000 Alternative B: Probability 1.0 of making profit of $800,000 (a) What would you use for the DM's utility function? Show your work. 6 (b) Why could you use Expected Value when analyzing problems involving profit for this DM?ayesha derives utility from travelling and outdoor dinning o weekends as given utility function U(t,d)=TD.the price of a day spent travelling is $160{Pt=160} and price of dining outdoor $200{Pd=200}.ayesha annual budget for this is $8000. find ayesha's utility maximizing choice of days travelling and dining outside. and alsoo find uutility level from consuming that bundles .show findings graphicallySEE MORE QUESTIONS