Answer to Question #243792 in Microeconomics for MEHK

Question

Consider the utility function u(x) = ; and a standard budget constraint: p₁x₁+p₂x₂=I.

 

a. Are the preferences convex?

 

b. Are the preferences represented by this function homothetic? 

Answer 1

Solution:

a.). Yes, the preferences are convex.

This is because an individual prefers to consume two goods together and the convex preferences represent an individual’s ordering of various outcomes, normally with regard to the quantities of different products consumed.

 

b.). Yes, the preferences represented by this function are homothetic.

This is because the preferences are represented by the utility function which is homogeneous of degree one. The function is also a monotonic transformation of a homogenous function since there exists a strictly increasing function.