There are two commodities: z and y. Let the consumer's consumption set be Rị and his preferencerelation on his consumption set be represented by u(z, y) = VE + 3y. When his income is equal to1 and the prices of good z, Pz = 1 and of good y, Py = 1,1. Solve the utility maximization problem.2. Does the solution calculated here obey the "equal bang for bnek' condition? Explain.Now assume that the preference relation on his consumption set be represented by u(z, y) = 3V7+y.When his income is equal to 1 and the prices of good z, Pz = 1 and of good y, Py = 1,1. Solve the utility maximization problem.2. Does the solution calculated here obey the "equal bang for buck' condition? Explain.

Answered: There are two commodities z and y. Let…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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There are two commodities: z and y. Let the consumer's consumption set be Rị and his preference
relation on his consumption set be represented by u(z, y) = VE + 3y. When his income is equal to
1 and the prices of good z, Pz = 1 and of good y, Py = 1,
1. Solve the utility maximization problem.
2. Does the solution calculated here obey the "equal bang for bnek' condition? Explain.
Now assume that the preference relation on his consumption set be represented by u(z, y) = 3V7+y.
When his income is equal to 1 and the prices of good z, Pz = 1 and of good y, Py = 1,
1. Solve the utility maximization problem.
2. Does the solution calculated here obey the "equal bang for buck' condition? Explain.

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“Since you have asked multiple questions, we will solve the first question for you. If you want any specific question to be solved then please specify the question number or post only that question.”

The problem for utility maximization is setup as follows:

U(x, y) is maximized subject to constraint $P_{x} x + P_{y} y = m$

The Lagrange function is setup as follows:

$\begin{array}{rcl} L & = & U (x, y) + λ (m - P_{x} x - P_{y} y) \\ = & \sqrt{x} + 3 y + λ (1 - x - y) \end{array}$

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