Question 15 w (1-x) -, where x=0.3. Calculate Selwyn's coefficient of relative 1-x Selwyn has a utility function of the formu (W) = - risk aversion when his wealth is equal to £12. Round your answer to 1 decimal place. Add your answer
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- Upon graduating from UT this May, you take on a management position working at UtMax theater. You will consider the utility of seeing performance over 1 month, and suppose that at a regular price of $$$ per ticket (my assigned ticket price is 145), customers will see no performance, however with the price reduced by $5, customers will see one performance per month and when reduced by $10, customers will see two performances. As long as the number performances, x, is small, your demand function for performance can be modeled by p=D(x). Write down your demand function.T Suppose your classmate Gilberto offers you a wager: He will choose a playing card at random from a deck and pay you $1,000 if it is red, but you have to pay him $1,000 if it is black. Assume your wealth is currently $3,000. The graph shown below plots your utility as a function of wealth. Use the graph to answer the questions that follow. 100 ips ips 88888 UTILITY (Units of utility) + + 2 3 WEALTH (Thousands of dollars) + (? The shape of your utility function implies that you are a the difference in utility between C and A is individual, and, therefore, you rence between A and B. risk-friendly accept the wager because Which of the following sentences most appropriately des risk-averse pain of losing $1,000 is greater than the joy of winning $1,000 for individuals who are risk averse? Check all that apply. The more wealth that risk-averse people have, the more satisfaction they receive from an additional dollar. The more wealth that risk-averse people have, the less satisfaction they…x-100 Consider lottery L as (0.8,6500; 0.2,100), by using u(x)=- as the DM's utility function 80 a) Compute E(u for L). b) Find CE(L). C) Find RP(L).
- Problem 1 Jane has the following utility function: u(w) w^.5 or the square root. function Which of the following prospects would she prefer? P1(.4, 3,000, 600) P2(.7, 1,200, 1,000) P3(.6, 2,000, 100)5.3 (0) Ambrose, the nut and berry consumer, has a utility function U(21,x2) = 4/T +x2, where ¤; is his consumption of nuts and r2 is his consumption of berries. %3D (a) The commodity bundle (25,0) gives Ambrose a utility of 20. Other points that give him the same utility are (16, 4), (9, ), (4, - ), (1, –), and (0, ). Plot these points on the axes below and draw a red indifference curve through them. (b) Suppose that the price of a unit of nuts is 1, the price of a unit of berries is 2, and Ambrose's income is 24. Draw Ambrose's budget line with blue ink. How many units of nuts does he choose to buy? (c) How many units of berries? (d) Find some points on the indifference curve that gives him a utility of 25 and sketch this indifference curve (in red). (e) Now suppose that the prices are as before, but Ambrose's income is 34. Draw his new budget line (with pencil). How many units of nuts will he choose? How many units of berries?why is this Utility from reporting full tax = (1-t)π
- 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.3. Consider a home energy storage (battery) system that can store up to 2 units of energy. At every time step, there is a demand for energy in the home which is drawn from 0,1,2 units with equal probability independent of the demands in the previous time steps. At every point in time, you have to satisfy the demand either by discharging the needed energy from the battery or purchasing power from the grid (or a combination of the two). You could also choose to purchase power from the grid to charge your battery. The grid energy price is either H(igh) or L(ow) according to a Markov chain (Price moves from H to L with probability p, and from L to H with probability q). (a) Model the decision making as an infinite horizon MDP where the objective is to minimize the discounted cost of energy purchased over an infinite horizon. (b) Write down a policy a of your choosing. Perform two steps of the operator T, for your policy, followed by one step of T..18. Choose the correct answer from the given below.
- Every week I spend a total of £400 buying two goods, luxuries (L) and necessities (N). I obtain utility (U) from these goods according to the rule U(L, N) = 10 + L + 20N−2N2. Suppose that I pay £10 for each unit of L and £20 for each unit of N and that I am a utility-maximiser. MUL=1 and MUN=20-4N. Define the Marginal Rate of Substitution (MRS) as MRS ≡ MUL/MUN). Calculate its value at the bundle (L = 0 and N = 4) and at (L = 1 and N = 4). By referring to a graphic illustration of the above calculations or otherwise, argue that an increase in my budget will have no effect on my consumption of N if I am already consuming 2.5 units of N. Calculate my optimum choice of L and N if instead I have £40 to spend. Fully explain your answer.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 approximatelyGina is at a toy store and is buying toy T-Rex's (x), which cost på, and toy yaks (y), which cost py. Her income is I. She likes 3 T-Rex's as much as she likes 4 yaks. These toys are perfect substitutes for her.