3The following utility function is known as CES (constant elasticity of substitution) function:U (x, y) = (ax° + By')'/º, where a > 0, B > 0%3Da) Is this function homothetic?b) How does the MRSY depend on the ratio x/y? Specifically, show that the MRSxy is strictlydecreasing in the ratio x/y for all values d < 1, increasing in the ratio x/y for all values &> 1 andconstant for 8 = 1. (Hint: take the derivative of the MRS with respect to the ratio x/y as z =and take the derivative with respect to z)x,yx/yc) Show that if x = y, the MRS of this function depends only on the ratio /B.

The utility function of an individual shows the level of satisfaction which can be derived from the…

The following utility function is known as CES (constant elasticity of substitution) function: U (x, y) = (ax° + By')'/º, where a > 0, B > 0 a) Is this function homothetic? b) How does the M RSy depend on the ratio x/y? Specifically, show that the MRSy is strictly decreasing in the ratio x/y for all values S < 1, increasing in the ratio x/y for all values &>1 and constant for 8 = 1. (Hint: take the derivative of the MRS with respect to the ratio x/y as z = x/y and take the derivative with respect to z) c) Show that if x = y, the MRS of this function depends only on the ratio a/6.

The following utility function is known as CES (constant elasticity of substitution) function: U (x, y) = (ax° + By')'/º, where a > 0, B > 0 a) Is this function homothetic? b) How does the M RSy depend on the ratio x/y? Specifically, show that the MRSy is strictly decreasing in the ratio x/y for all values S < 1, increasing in the ratio x/y for all values &>1 and constant for 8 = 1. (Hint: take the derivative of the MRS with respect to the ratio x/y as z = x/y and take the derivative with respect to z) c) Show that if x = y, the MRS of this function depends only on the ratio a/6.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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