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

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ISBN:9780190931919

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Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

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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

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 consumer
to 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), and
suppose the consumer is not spending all her money at bundle x (that is
pr<m). Also assume , > 0 if MU; <0. Argue that the consumer
would not optimally choose r.
x
(b) Suppose MU₁(x) = MU₂(x) = 0, the good is affordable (p ≤ m), and u
is concave. Explain why r is optimal.

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