Microeconomic Theory
Microeconomic Theory
12th Edition
ISBN: 9781337517942
Author: NICHOLSON
Publisher: Cengage
Question
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Chapter 17, Problem 17.1P

a)

To determine

To find:

MRS = 1+r

a)

Expert Solution
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Explanation of Solution

Given utility function:

U(c1,c2)

Budget constraint :

W=c1+c21+r

The above equations are put in Langrange equation:

L=U(c1,c2)+λ(Wc1+c21+r)

Taking the fisrt order derivative and equating it to 0.

Lc1=Uc1λ=0

Lc2=c1r<0λ11+r=0

Divide the above two equations, we get:

MRS=11+r

Economics Concept Introduction

Introduction:

b)

To determine

To know:

Price eslaticity of demand of c2.

b)

Expert Solution
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Explanation of Solution

Substitution effect is always negative which implies that any increase in value of 11+r leads to fall in c2 .

While income effect is positive in case of normal good, so it implies c2 and r are positively related. Numerically,

c2r>0

However, c1r has no specific sign as substitution and income effect has both opposite result.

It is assumed that substitution effect has more impact than income effect, that is, c1r<0

Economics Concept Introduction

Introduction: Envelop theorem states that changes in exogeneous variables must be considered for profit maximizing equations, ignoring the change in endogeneous variable.

c)

To determine

To ascertain:

Changes in part b due to change in budget constraint.

c)

Expert Solution
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Explanation of Solution

Budget constraint is given as: y1c1+y2c21+r=0

Rearranging the terms:

y1+y21+r=c1+c21+r

The above equation is a slope of budget line.

When c1>y1 , consumption is greater than income, it implies the consumer borrows and repay in period 2 and vice-versa.

Economics Concept Introduction

Introduction:

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Microeconomic Theory
Economics
ISBN:9781337517942
Author:NICHOLSON
Publisher:Cengage