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

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ISBN:9780190931919

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Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Concept explainers

Form Utility

The term utility in general refers to the satisfaction earned from usage of a particular product or service. Utility always plays an important role because it influences various important elements like demand & thereby the price of the good or service as well. Though utility is not easy to measure, various types of economic models can be used indirectly. There can be various types of utilities like economic utility, marginal utility, cardinal utility, form utility.

Question

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

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