3. [In class, we noted that the consumer will spend all their money if they have in-creasing preferences. Here, we give a calculus-based condition for the consumerto spend all their money, that doesn't assume more is always better. The con-dition is a stronger version of what is sometimes called "local non-satiation".]Let E X, and let MU, denote the marginal utility for good i € {1,2} at r.(a) Suppose some good i has MU, #0 (it could be positive or negative), andsuppose the consumer is not spending all her money at bundle x (that ispr 0 if MU; <0. Argue that the consumerwould not optimally choose r.x(b) Suppose MU₁(x) = MU₂(x) = 0, the good is affordable (p ≤ m), and uis concave. Explain why r is optimal.

A utility function is said to have non-satiation properties if more of any good always leads to a…

Let E X, and let MU, denote the marginal utility for good i E {1, 2} at r. (a) Suppose some good i has MU, #0 (it could be positive or negative), and suppose the consumer is not spending all her money at bundle x (that is px 0 if MU; <0. Argue that the consumer would not optimally choose x.

Let E X, and let MU, denote the marginal utility for good i E {1, 2} at r. (a) Suppose some good i has MU, #0 (it could be positive or negative), and suppose the consumer is not spending all her money at bundle x (that is px 0 if MU; <0. Argue that the consumer would not optimally choose x.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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