Which of the following utility functions represent preferences that are NOT homothetic?(a) U(X, Y) = 10X ² + y²(b) U(X, Y) = ln(X) + 42 ln(Y) + ²(c) U(X,Y) = 4X¾ +7Y(d) U(X,Y)= XY(e) All of the above utility functions represent homothetic preferences

A utility function is homothetic if it can be represented as a monotonic transformation of a homogeneous function. In other words, if the marginal rate of substitution is the same along any ray from the origin, then the utility function is homothetic.Option (a) U = 10x^0.5 + y^0.5MRS = MU(x) /MU(y) MU(x) = 5 /x0.5 MU(y ) = 1/y0.5 MRS = 5y0.5/x0.5This utility function is homothetic. The marginal rate of substitution depends only on the ratio of x and y, but not on their levels. Therefore, the utility function is not homothetic.Option (b) U = ln(x) + 42ln(y) + KMRS = y/42x This utility function is homothetic. The marginal rate of substitution is ( y/42x), which depends only on the ratio of x and y, not on their levels. Therefore, the utility function is homothetic.Option (c) U = 4(x^0.33) + 7YThis utility function is not homothetic. The marginal rate of substitution depends not only on the ratio of x and y, but also on their levels. Therefore, the utility function is not homothetic.Option (d) U = (x^0.7 ) (y^0.3 )This utility function is homothetic. The marginal rate of substitution is (0.7/0.3)(y/x), which depends only on the ratio of x and y, not on their levels. Therefore, the utility function is homothetic.So, the first and third utility functions are not homothetic while the second and fourth ones are homothetic.Therefore , Option (C) is correct.

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Which of the following utility functions represent preferences that are NOT homothetic? (a) U(X, Y) = 10X ³² +Y/² (b) U(X, Y) = ln(X) + 42 ln(Y) + π² (c) U(X,Y) = 4X} +7Y (d) U(X,Y)= Xiyi (a) All of the above utility function rosent homothotic proforoncos

Which of the following utility functions represent preferences that are NOT homothetic? (a) U(X, Y) = 10X ³² +Y/² (b) U(X, Y) = ln(X) + 42 ln(Y) + π² (c) U(X,Y) = 4X} +7Y (d) U(X,Y)= Xiyi (a) All of the above utility function rosent homothotic proforoncos

Economics (MindTap Course List)

13th Edition

ISBN:9781337617383

Author:Roger A. Arnold

Publisher:Roger A. Arnold

ChapterE: Budget Constraint And Indifference Curve Analysis

Section: Chapter Questions

Problem 3QP

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