up the utility maximizing Lagrangian and derive the Marshallian demand functions. Explain the difference in what we is being tested when we check the first orden conditions and the second order conditions for a maximum (intuitively, not just the math). Derive the indirect utility function and the expenditure function.

up the utility maximizing Lagrangian and derive the Marshallian demand functions. Explain the difference in what we is being tested when we check the first orden conditions and the second order conditions for a maximum (intuitively, not just the math). Derive the indirect utility function and the expenditure function.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

Consider a utility maximizing consumer who generates utility according to the following
1
utility function: U=Vx +y where x is the quantity of x consumed and y is the quantity
2
of y consumed. Let the price of x, price of y and income be noted as p, Py, and M,
respectively.
Set up the utility maximizing Lagrangian and derive the Marshallian demand
functions.
a
Explain the difference in what we is being tested when we check the first order
conditions and the second order conditions for a maximum (intuitively, not just
the math).
Derive the indirect utility function and the expenditure function.
Derive the Hicksian demand equations without going through the expenditure
minimization process.
b.
C.
d.
Let income = $8, p,=$.25 and p,=$1. What are the quantity demanded of x, and
у?
Draw the consumer choice graph and illustrate the situation in part e. Use the
E.
х,
%3D
f.
graph to illustrate the income and substitution effect stemming from a change in
the price of x to $.50. Use the actual numbers whenever possible.

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