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.

There are two commodities z and y. Let the consumer's consumption set be R and his preference relation on his consumption set be represented by ufz, 3) = VE+ 3y. When his income is equal to 1 and the prices of good z, pe =1and of good y. Py =1, 1. Solve the utility maximization problem. 2. Does the solution caleulated here obey the "equal bang for buck' condition? Explain.

There are two commodities z and y. Let the consumer's consumption set be R and his preference relation on his consumption set be represented by ufz, 3) = VE+ 3y. When his income is equal to 1 and the prices of good z, pe =1and of good y. Py =1, 1. Solve the utility maximization problem. 2. Does the solution caleulated here obey the "equal bang for buck' condition? Explain.

Micro Economics For Today

10th Edition

ISBN:9781337613064

Author:Tucker, Irvin B.

Publisher:Tucker, Irvin B.

Chapter6: Consumer Choice Theory

Section: Chapter Questions

Problem 11SQ

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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

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.

Expert Solution

Step 1

“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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