Answered: Consider the following 2-period model…

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 the following 2-period model U(C1,C2) = min{3C1,4C2}

C1 + S = Y1 – T1

C2 = Y2 – T2 + (1+r)S

Where

C1 : first period consumption

C2 : second period consumption

S : first period saving

Y1 = 20 : first period income

T1 = 5 : first period lump-sum tax

Y2 = 50 : second period income

T2 = 10 : second period lump-sum tax r = 0.05 : real interest rate

Find the optimal saving, S*

Expert Solution

Step 1

Considering the model:

$C_{1} + S = Y_{1} - T_{1} C_{2} = Y_{2} - T_{2} + (1 + r) S$

$T a k i n g t h e v a l u e o f S f r o m C_{2} & s u b s t i t u t i n g i n p e r i o d 1 o f B u d g e t \cos t r a i n t : S = \frac{C_{2} - Y_{2} + T_{2}}{1 + r} S o, C_{1} + \frac{C_{2}}{1 + r} = Y_{1} - T_{1} + \frac{Y_{2} - T_{2}}{1 + r} C_{1} + \frac{C_{2}}{1.05} = 20 - 5 + \frac{50 - 10}{1.05} 1.05 C_{1} + C_{2} = 55.75$

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