**Utility Functions Analysis**Consider the following utility functions:a) \( U = xy \)b) \( U = (xy)^{1/3} \)c) \( U = \min(x, y/2) \)d) \( U = 2x + 3y \)e) \( U = x^2y^2 + xy \)**Task:**1. Check if any of the utility functions (a) to (e) are homogeneous. If so, state the degree of homogeneity of each.

the utility function measures the welfare or satisfaction of a consumer as a function of the consumption of real goods, such as food or clothing here we find the given by following method as;A function is homogeneous of order k, if U(tx, ty) = tkU(x,y) (a) U(x,y) = xy Now, by multiplying t with x and y , we get: = (tx) (ty) U(tx, ty) = t2 (xy) Hence, the function is homogeneous and of degree 2. (b) U = (xy)1/3 U(tx, ty) = (tx)1/3 (ty)1/3 = t1/3 x1/3 t1/3 y1/3 = t2/3 (xy)1/3 Hence, this function is homogeneous and of degree 1/3. (c) U = min(x, y/2) U(tx, ty) = min(tx, ty/2) The function is homogeneous and of degree 1. (d) U = 2x + 3y U(tx, ty) = 2 (tx) + 3(ty) = t(2x + 3y) The function is homogenous and of degree 1. (e) U = x2y2 + xy U(tx ,ty) = (tx)2(ty)2 + (tx)(ty) = t4 (x2y2) + t2 (xy) = t2 (t2 x2y2 + xy) This function is not homogeneous.

Answered: a) U= xy b) U= (xy)3 c) U=min(x,y/2) d)…

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a) U= xy b) U= (xy)3 c) U=min(x,y/2) d) U= 2x + 3y e) U=x?y² + xy 1. Check if any of utility functions a) – e) are homogeneous. If so, state the degree of homogeneity of each.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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