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

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

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter4: Utility Maximization And Choice

Section: Chapter Questions

Problem 4.14P

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Emma has a utility function U(x1, x2, x3) = log x1 + 0.8 log x2 + 0.72 log x3 over 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 flflexibility; (B) context effffects; (C) time inconsistency; (D) intransitivity.
Emma has a utility functionU(x1, x2, x3) = logx1+ 0.8logx2+ 0.72logx3 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.
If total utility increases as wealth increases, the first derivative of the utility function is negative. TRUE OR FALSE
Existence of representative consumer Suppose households 1 and 2 have one-period utility functions u(c1) and w(c2), respectively, where u and w are both increasing, strictly concave, twice-differentiable functions of a scalar consumption rate. Consider the Pareto problem: Subject to the constraint c1 + c2 = c. Show that the solution of this problem has the form of a concave utility function vθ(c), which depends on the Pareto weight θ. Show that vθ(c) = θu (c1) = (1 − θ)w (c2). The function vθ(c) is the utility function of the representative consumer. Such a representative consumer always lurks within a complete markets competitive equilibrium even with heterogeneous preferences. At a competitive equilibrium, the marginal utilities of the representative agent and each and every agent are proportional.
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Mats, who has reference-dependent preferences over beer and money, goes to the local pub with a friend, but is not planning on drinking any beer or spending any of his 50 Euro in cash. Let his end-of-evening outcomes in pints of beer consumed and cash be c1 and c2, respectively, and let his reference point in pints of beer and cash be r1 and r2, respectively. Then, Mats’ utility is given by v(6c1 − 6r1) + v(c2 − r2), where v(x) = x for x ≥ 0, and v(x) = 1.5x for x < 0. (a) Suppose that the price of beer is pB. Calculate Mats’ utility from drinking one pint of beer at this price. What is Mats’ utility from drinking no beer? And, comparing these two utility values, what is the maximum price pB that Mats would pay for one beer? (b) Suppose that Mats unexpectedly gets a pint of beer as part of a promotion at the pub, and incorporates its consumption into his reference point in beer. [Hint: this means that (r1, r2) = (1, 50).] Suppose that Mats could sell the beer at a price pS.…
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Bob has a utility function U(x, y) = √x1 + 0.8√x2 + 0.64√x3 over his incomes x1, x2, 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. . Which of the following preferences agree with Bob’s utility? (A) (9, 10, 11) ≻ (9, 10, 12); (B) (9, 10, 11) ≻ (11, 10, 9);(C) (9, 10, 11) ≻ (9, 11, 10); (D) none of the above. Bob’s utility function implies (A) time stationarity; (B) transitivity; (C) impatience; (D) all of the above.
***PLEASE NOTE: QUESTION HAS TWO PARTS REQUIRING ANSWER*** Q: Johnny Football has a utility function of the form ? = √?. Johnny is beginning his senior year of college football. If he is not seriously injured, he will receive a $1,000,000 contract for playing professional football. If any injury ends his football career, he will take a job as a refuse removal facilitator in his hometown that pays $10,000. There is a 10% chance that Johnny will be injured badly enough to end his career. a. What is Johnny’s expected utility? b. How much would Johnny be willing to pay to remove the financial riskhe faces? That is, what $p would he pay for a $1,000,000 insurancepolicy so that he would have $1,000,000-$p even if he had a seriousinjury? Assume he wouldn’t work for $10,000 if he had the insuranceand he was injured. Hint: You should set his utility with certainty(U($1,000,000-$p)) equal to his expected utility with risk (found inpart a) and solve for p.
what is the derivative of the utility function UU = log (100-2PPii) + log(PPjj+PPdd) with respect to PPjj. Budget constaint XXii = 100 - 2PPii