Consider a strictly concave and continuously differentiable utility function U(T1, T2) describing well-behaved preferences. Derive the necessary and sufficient condi- tions on the second order derivatives of U(1, 2) so that ₁ and 2 are normal goods [Hint: There is a relationship between the Hessian of U(₁, 2) and the sign of the denominator of an expression relevant to this analysis]. Use these conditions to verify what is the relationship, if any, between the normality of ²U (11,12). the goods and the sign of Əx₁₂

Consider a strictly concave and continuously differentiable utility function U(T1, T2) describing well-behaved preferences. Derive the necessary and sufficient condi- tions on the second order derivatives of U(1, 2) so that ₁ and 2 are normal goods [Hint: There is a relationship between the Hessian of U(₁, 2) and the sign of the denominator of an expression relevant to this analysis]. Use these conditions to verify what is the relationship, if any, between the normality of ²U (11,12). the goods and the sign of Əx₁₂

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter3: Preferences And Utility

Section: Chapter Questions

Problem 3.13P

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