Calculate the CV, EV and the change in the Marshallian
consumer surplus for a consumer with...

Question

Calculate the CV, EV and the change in the Marshallian
consumer surplus for a consumer with preferences represented by the utility
function u x1x2 with income M 100, p2 = 1 and
p1 falling from 1 to . Do this consumer’s preferences satisfy the
condition for the change in the Marshallian consumer surplus to be a valid
measure of the change in utility?

Komalavalli · Accepted Answer

U = x1x2
M = 100
P1=1
P2=1
Budget constraint : 100= x1 + x2
Maximize U subject to budget constraint U = x1x2
L= x1x2+ λ(100- x1 -x2)
∂L/∂ x1 = x2- λ = 0
x2 = λ---(1)
∂L/∂ x2 = x1- λ = 0
∂L/∂ λ = 100-x1- x2 = 0
x1 = λ---(2)
100 = x1 + x2 -----------(3)
(1)/(2)
x2/ x1 = 1 
x2 = x1 substitute this  in (3)
100= x1+ x1
2 x1 = 100
x1 =50
Substituting x1 =50 in (3)
We get x2 =50
Utility U =  50*50* = 2500
New Price P1=0.5
Budget constraint : 100= 0.5 x1 +x2 
Maximize U subject to budget constraint U = x1x2
L= x1x2+ λ(100-0.5 x1 -x2)
∂L/∂ x1 = x2-0.5 λ = 0
x2 = 0.5λ---(1)
∂L/∂ x2 = x1- λ = 0
∂L/∂ λ = 100-0.5x1- x2 = 0
x1 = λ---(2)
100 = 0.5x1 + x2 -----------(3)
(1)/(2)
x2/ x1 = 0.

Calculate the CV, EV and the change in the Marshallian consumer surplus for a consumer with preferences represented by the utility function u x 1 x 2 with income M 100, p 2 = 1 and p 1 falling from 1...

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