Question

VER s DULU .) Question (2): Consider a consumer with perfect substitute) utility function u(x) = a11 + Dy; a > 0. Suppose the consumer has income of 20 and faces a price change from (2, 2) to (1,2). What is the Equivalent Variation of this price change? (Note that you can and should use any needed functions we have derived in previous assignments. You do not have to compute those from scratch.)

Answer 1

MRS = MU1/MU2 = a

As P1/P2 = 1

So if, MRS > P1/P2

Only X1 is Consumed

Then, a > 1

Only X1 is Consumed , X1= 20/2 = 10

If a< 1 , only X2 is Consumed ,

.

Price change,

P1'/P2 = 1/2

Then at eqm, if, a> P1'/P2

a > 1/2 , only X1 is Consumed

X1* = 20/P1' = 20

U' = a*20 = 20a

.

If a< 1/2 , only X2 is Consumed

X2* = 20/P2 = 10

U' = 10

so new Utility : U' = { 20a, if a> .5

= { 10, if a< .5

.

so for EV , new Utility at original prices

Let new income level at original prices M"

If a>1, only X1 is Consumed

( If a> 1, then a is also greater than .5)

then, M"/2 = U' = 20a

M" = 40a

then EV = M"-M = 40a - 20

.

If a < 1, but a> .5

Then , at original prices , only X2 is Consumed

So, M"/2 = 20a

M" = 40a

EV = 40a - 20

.

if a< 1 & a< .5

then M"/2 = 10

M" = 20

then EV = 20-20 = 0

.

so EV = { 40a - 20 , if a>.5

{ 0 , if a<.5

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