teach not just solve Consider a consumer with expenditure function e(p, u) = P2u -√√ Suppose that theconsumer has wealth 4. Initially, prices are (3,2).(a) What value of a would make the consumer indifferent between a fall in prices to (1,1)with wealth remaining at 4 and an increase in wealth of 2 with prices remaining at (3, 2)?How is this conceptually related to the compensating or equivalent variation? (You donot have to do any additional calculations to answer the second part of the question.)(b) Find the substitution and income effects on Good 1 associated with a marginal increasein the price of Good 2 when prices are (3,2).

We are given: Expenditure function : e = P2u - P22P1 Rearranging the expenditure function to get…

Answered: Consider a consumer with expenditure…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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teach not just solve

Consider a consumer with expenditure function e(p, u) = P2u -√√ Suppose that the
consumer has wealth 4. Initially, prices are (3,2).
(a) What value of a would make the consumer indifferent between a fall in prices to (1,1)
with wealth remaining at 4 and an increase in wealth of 2 with prices remaining at (3, 2)?
How is this conceptually related to the compensating or equivalent variation? (You do
not have to do any additional calculations to answer the second part of the question.)
(b) Find the substitution and income effects on Good 1 associated with a marginal increase
in the price of Good 2 when prices are (3,2).

Expert Solution

Part 1

We are given:

$E x p e n d i t u r e f u n c t i o n : e = P_{2} u - \sqrt{\frac{{P_{2}}^{2}}{P_{1}}} R e a r r a n g i n g t h e e x p e n d i t u r e f u n c t i o n t o g e t t h e u t i l i t y a s a f u n c t i o n o f e, P_{2} & P_{1} = > u = \frac{e}{P_{2}} + \sqrt{\frac{1}{P_{1}}} - - (*) I n t h e g i v e n s t a t e m e n t w e a r e g i v e n : u (P 1 = 1, P 2 = 1, e = 4) = u (4 + x, P 1 = 3, P 2 = 2) {I t m e a n s t h e c o n s u m e r i s i n d i f f e r e n t b e t w e e n t h e s e t w o c o n d i t i o n s} = > \frac{4}{1} + \sqrt{\frac{1}{1}} = \frac{4 + x}{2} + \sqrt{\frac{1}{3}} = > 5 = \frac{4 + x}{2} + 0.58 = > (5 - 0.58) * 2 - 4 = x = > x = 4.84 A n s .$

In the compensating variation when the price of goods change we provide some changes to consumer's income so that he will be able to afford the same utility level (as he was getting initially) but at new prices. And in the given statement when the price is (3,2) we are giving some additional income to the consumer so that he will be able to get the same utility level at (P1 = 1, P2 = 1& e =4)

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