EBK MICROECONOMICS
EBK MICROECONOMICS
5th Edition
ISBN: 9781118883228
Author: David
Publisher: YUZU
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Concept explainers

Question
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Chapter 3, Problem 3.21P
To determine

(A)

To explain:

The given assumption of more is better is sufficient for both goods.

Expert Solution
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Answer to Problem 3.21P

The given assumption more is better is not sufficient for both goods.

Explanation of Solution

Given that −

  U=Axαyβ

  MUx=αAxα1yβ

  MUy=βAxαyβ1

And,

  MUx=dudx=αA(α1)xαyβ>0 

  MUy=dudy=βA(β1)xαyβ>0 

In the above equation both MUx and MUy are greater than zero. Therefore, the given assumption more is better is not sufficient for both goods.

Economics Concept Introduction

Introduction:

Marginal utility shows the additional utility that the consumer is deriving from consuming additional units of that product or service.

To determine

(B)

To explain:

Whether the marginal utility of x decrease, or remain constant or increase with the consumer buying more of x, if the preferences of consumer are represented by the utility function of Cobb Douglas, U=Axαyβ, where A, α and β being positive constants, and the marginal utilities are represented by MUx=αAxα1yβ, and MUy=βAxαyβ1.

Expert Solution
Check Mark

Answer to Problem 3.21P

The marginal utility of x will diminish will not diminish but increases with an increase in the consumption of x by the individual.

Explanation of Solution

The given marginal utility function of x will not diminish but increases, as the individual consumes more of good x.

Economics Concept Introduction

Introduction:

Marginal utility shows the additional utility that the consumer is deriving from consuming additional units of that product or service.

To determine

(C)

Tofind:

The MRSxy.

Expert Solution
Check Mark

Answer to Problem 3.21P

After necessary derivations, the MRSxy is given by αyβx.

Explanation of Solution

Marginal utility shows the additional utility that the consumer is deriving from consuming additional units of that product or service.

Through dividing the marginal utility of x with the marginal utility of y, the marginal rate of substitution can be arrived at.

Implies,

  MRSx,y=MUxMUy=(αAx α1yβ)βAxαy β1=αyβx

Thus, the MRS of x for y will be αyβx.

Now, it can be concluded that the MRSxy will decrease when x increases, and MRSxy also will decrease when y decreases. Since, in both these cases MRSxy decreases, it stays decreasing.

To determine

(D)

To evaluate:

Whether the MRSxy will decrease or increase or remain constant, if the individual decides to substitute x for y along an indifference curve.

Expert Solution
Check Mark

Answer to Problem 3.21P

After necessary observations, it can be said that the MRSxy will be diminishing.

Explanation of Solution

Marginal utility shows the additional utility that the consumer is deriving from consuming additional units of that product or service.

MRSxy, denoting the marginal rate of substitution of x for y, equaling to αyβx will diminish as the individual substitutes x for y, along an indifference curve.

To determine

(E)

To plot:

A graph with x denoted by horizontal axis and y denoted by vertical axis, an indifference curve, and to label the curve U1.

Expert Solution
Check Mark

Answer to Problem 3.21P

As can be seen in the graph plotted in the next section, the indifference curve is bowed towards the origin, owing to the diminishing MRS.

Explanation of Solution

Marginal utility shows the additional utility that the consumer is deriving from consuming additional units of that product or service.

  EBK MICROECONOMICS, Chapter 3, Problem 3.21P , additional homework tip  1

In the graph above, as explained in the requirements, it can be seen that with the diminishing MRS, the indifference curve is bowed towards the origin.

To determine

(F)

Toplot:

On the same graph, with x denoted by horizontal axis and y denoted by vertical axis, another indifference curve, U2, as U2> U1.

Expert Solution
Check Mark

Answer to Problem 3.21P

As can be seen in the graph plotted in the next section, the indifference curves, U1 and U2, as U2> U1.

Explanation of Solution

Marginal utility shows the additional utility that the consumer is deriving from consuming additional units of that product or service.

  EBK MICROECONOMICS, Chapter 3, Problem 3.21P , additional homework tip  2

In the graph above, as explained in the requirements, it can be seen that with the diminishing MRS, the indifference curves are bowed towards the origin, satisfying the rule that U2> U1.

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