Consider the following 6 utility functions: U1 = /x + 2y U2 = v2x + Jy U3 = 2x2 + y? + Jy U5 = min(x,y) +2 U6 = 2 In(x) + In(y) U4 %3D a) For each, find the expressions for marginal utilities and the marginal rate of substitution, and determine whether monotonicity and convexity are met.

Consider the following 6 utility functions: U1 = /x + 2y U2 = v2x + Jy U3 = 2x2 + y? + Jy U5 = min(x,y) +2 U6 = 2 In(x) + In(y) U4 %3D a) For each, find the expressions for marginal utilities and the marginal rate of substitution, and determine whether monotonicity and convexity are met.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter3: Preferences And Utility

Section: Chapter Questions

Problem 3.11P

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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

Consider the following 6 utility functions:
U1 = Vx + 2y
U2 = v2x + Vy
Uz = 2x2 + y?
+ Vy
U4
2
Ug = min(x,y)+;
2
Us = 2 In(x) + In(y)
%3D
a) For each, find the expressions for marginal utilities and the marginal rate of substitution, and
determine whether monotonicity and convexity are met.

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