We know that n differentiable functions x₁(p, m), ..., xn(p,m) of prices and income are generated by some utility maximizing consumer if and only if each of them is homogeneous of degree zero in prices and income, i.e. Σ¿pi xi(p, m)=m, and whose matrix of substitution terms (the Slutsky matrix) is negative semi-definite. This makes Afriat's Theorem and GARP unnecessary Comment.

We know that n differentiable functions x₁(p, m), ..., xn(p,m) of prices and income are generated by some utility maximizing consumer if and only if each of them is homogeneous of degree zero in prices and income, i.e. Σ¿pi xi(p, m)=m, and whose matrix of substitution terms (the Slutsky matrix) is negative semi-definite. This makes Afriat's Theorem and GARP unnecessary Comment.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter4: Utility Maximization And Choice

Section: Chapter Questions

Problem 4.13P

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