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- Gina is at a toy store and is buying toy T-Rex's (x), which cost px, 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.Suppose a household has the following lifetime utility function: U=c1/2 + ẞc¹/2 12tt+1 A) Find expressions for the partial derivatives of lifetime utility, U, with respect to period t and period t + 1 consumption. Is marginal utility of consumption in both periods always positive? B) Find expressions for the second derivatives of lifetime utility with respect to period t and t+1 consumption, i.e., 2U and a 20_Are these second derivatives always negative for ac²²+1 any positive values of period t and t+1 consumption? C) Derive an expression for the indifference curve associated with lifetime utility level Uo (i.e., derive an expression for C++₁ as a function of U₁ and c). What is the slope of the indifference curve? How does the magnitude of the slope vary with the value of c?Gina 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.
- 6. 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) logarithmicBetty is looking for a job. She considers job opportunities intwo cities. Bettyís utility is given by y- x, where y is the lifetime income andx is the amount spent on buying a house. The income from City 1 fluctuatesalthough the house price is stable. On the contrary, the income from City2 is stable while the house price fluctuates. If she moves to City 1, Bettycan earn a lifetime income y1 with probability alpha and 1 + y1 with probability1-alpha . The house price in City 1 is x1. Moving to City 2 means that Bettycan earn an income of y2. However, the house price is x2 with probabilitygamma and 1 + x2 with probability 1-gamma . Do the following: (a) Write down theexpected utilities associated with living in the two respective cities, i.e., V1and V2. (b) Derive the condition under which Betty chooses City 1.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 approximately
- 1. Bob has a utility function U (x, y) Vai +0.8 /T2 + 0,64/x3 over his incomes *1, E2, X3 in the next three years. This function is an example of (A) expected utility; (B) quasi-hyperbolic utility function; (C) discounted utility; (D) none of the above.An individual’s utility function is given by where is the amount of leisure measured in hours per week and is income earned measured in cedis per week. Determine the value of the marginal utilities, when = 138 and = 500. Hence estimate the change in utility if the individual works for an extra hour, which increases earned income by GH¢15 per week. Does the law of diminishing utility hold for this function?2. Ann has started working and is saving to buy a house, which requires a down-payment of d. She has a monthly income of y and faces goods prices pa and p3. Ann's utility function is given by u = 3 In a. + (1- 3) In a. %3D Her minimum standard of living renders a utility of uo. Solve for the minimum number of months it takes for Ann to save up to the down-payment, as a function of (d, y, uo, Pa, Ps).
- Emma has a utility functionU(x1, x2, x3) = logx1+ 0.8 logx2+ 0.72 logx3over her incomes x1, x2, x3 in the next three years. This is an example of(A) expected value;(B) quasi-hyperbolic utility function;(C) standard discounted utility;(D) none of the above. Emma’s preferences can exhibit which of the following behavioral patterns?(A) preference for flexibility;(B) context effects;(C) time inconsistency;(D) intransitivity.Rodrigo is taking a year between high school and college to work and save up. His utility from consumption each year is U(c) = discounts future utility by B. Rodrigo is going to make $I his year of working, and whatever he doesn't consume from that income will a savings account which will earn return r before he consumes next year. He has to pay for school expenses E in year two, before he consumes (but after return has been realized). 1-o and he go intoAnne has a job that requires her to travel three out of every four weeks. She has an annual travel budget and can travel either by train or by plane. The airline on which she typically flies das a frequent-travel program that reduces the cose of her tickets according to the number of miles she has flown in a given year. When she reaches 25,000 miles, the airline will reduce the price of her tickects by 25 percent for the remainder of the year. when she reaches 50,000 miles, the airline will reduce the price by 50 percent for the remainder of ther year. Graph Anne's budget line with train miles on the vertical axis and plan miles on the horizontal axis Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.