4.11 CES utility The CES utility function we have used in this chapter is given by U(x, y) a. Show that the first-order conditions for a constrained utility maximum with this function require individuals to choose goods in the proportion 1/(8–1) Px \Py ) y b. Show that the result in part (a) implies that individuals will allocate their funds equally between x and y for the Cobb- Douglas case (ô = 0), as we have shown before in several problems.

4.11 CES utility The CES utility function we have used in this chapter is given by U(x, y) a. Show that the first-order conditions for a constrained utility maximum with this function require individuals to choose goods in the proportion 1/(8–1) Px \Py ) y b. Show that the result in part (a) implies that individuals will allocate their funds equally between x and y for the Cobb- Douglas case (ô = 0), as we have shown before in several problems.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter4: Utility Maximization And Choice

Section: Chapter Questions

Problem 4.11P

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Question d)
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Rafe is optimally choosing to consume 6 apples and 3 bananas. The prices of apples and bananas are p. = 7 and pb - 7. Which of the following utility functions over quantities of apples (a) and bananas (b) could represent Rafe's preferences? = u(a, b)-a4/5 61/5 Ou(a, b) = a¹/5 64/5 Ou(a, b)-a2/3 b1/3 Ou(a, b)-a¹/3 2/3
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 graphically
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The price of X is $20 and the price of Y is $40. Y 30 Uz 24 40 Units of good X based on the graph, at point B, Multiple Choiİce < Prev B. 14 Units of good Y
Let the following table represents the total utility of a given consumer, in the cardinal utility approach. Q 1 2 3 4 5 6 7 TUX 8 14 18 20 20 18 16 TUY 6 10 13 15 16 16 14 MUX MUY MUX/PX MUY/PY Calculate the MUX and MUY and fill the table in the 4th and 5th rows. If the two products (X&Y) are free goods how many of X and Y should the consumer take to maximize utility? What is the maximum utility of X and Y if they are free? Let now price of X is 4 birr per unit and price of Y is 2 birr per unit. Calculate MUX/PX and MUY/PY and fill the 6th and 7th row. Assuming the consumer has any amount of money (enough budget) how many of X and Y should the consumer buy, to maximize utility? What is the total utility of X and Y? Let now price of X is 4 birr per unit and price of Y is 2 birr per unit and budget of the consumer for consumption of X and Y is 20 birr. Given budget constraint how many of X and Y should the consumer buy to maximize utility?
1. For each of the following scaling functions for a von Neumann-Morgenstern utility func- tion, determine the Marginal Rate of Substitution between X1 and X2 and the equation for an indifference curve through the consumption bundle (100,100) (solve for X2 on the left hand side of the equation). State 1 is the bad outcome that occurs with probability 0.2 and State 2 the good outcome that occurs with probability 0.8. Graph these indif- ference curves and comment on what you see. Is a consumer with these preferences risk averse, risk neutral, or risk loving? (a) V(X) = InX (b) V(X)= VX (c) V(X)= X (d) V(X)= X²
Sam's extended family spends $3,200 per month on wine and beer. Their utility function is given by U = 200WB, where W represents the number of bottles of wine that they buy, and B represents the number of cases of beer that they buy. Wine costs $25 per bottle and beer costs $32 per case. Sam's family wants to maximize their utility. Calculate how many bottles of wine and how many cases of beer they should buy. Show your calculation(s).
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Consider the classic consumer's choice problem of an individual who is allocating Y dollars of wealth amongst two goods. Let c1 denote the amount of good 1 that the individual would like to consume at a price of Pı per unit and c2 denote the amount of good 2 that the individual would like to consume at a price of P2 per unit. The individual's utility is defined over the consumption of these two goods (only). Suppose we allow the individual's happiness to be measured by a utility function u(c1, c2) which is increasing and strictly concave in both goods while also satisfying the Inada condition, limcı→0 du(c1,c2) = limc1→0 du(c1,c2) dc2 = 0. The Inada conditions simply say that the slope of the utility function becomes vertical in the direction of the good that has its consumption level go to zero. By assuming increasing and strictly concave utility in both directions, we are assuming that the shape of the utility function is such that, holding constant the amount of one good, as the…