Suppose that good 1 is normal and good 2 is inferior. Prove that the total effect on demand for good 1 of a marginal increase in the price of good 2 cannot exceed the total effect on demand for good 2 of a marginal increase in the price of good 1. That is, prove that əxi дрг 11 VI ?х1 дрг where, for each i = 1, 2, x; denotes the Marshallian demand for good i and p; denotes the price of good i. Solution: By the Slutsky equation, VI მhu дрг Əh₂ дру მh2 др1 Əh₂ дру S where the second line follows from Slutsky the fourth from inferiority of good 2. əx2 др 12 X2 1 1 əxi dw əri dw əx2 dw Əx₂ др symmetry, the third from normality of good 1, and
Suppose that good 1 is normal and good 2 is inferior. Prove that the total effect on demand for good 1 of a marginal increase in the price of good 2 cannot exceed the total effect on demand for good 2 of a marginal increase in the price of good 1. That is, prove that əxi дрг 11 VI ?х1 дрг where, for each i = 1, 2, x; denotes the Marshallian demand for good i and p; denotes the price of good i. Solution: By the Slutsky equation, VI მhu дрг Əh₂ дру მh2 др1 Əh₂ дру S where the second line follows from Slutsky the fourth from inferiority of good 2. əx2 др 12 X2 1 1 əxi dw əri dw əx2 dw Əx₂ др symmetry, the third from normality of good 1, and
Chapter1: Making Economics Decisions
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please only do: if you can teach explain steps of how to solve each part
for ifererior SE>IE?
Transcribed Image Text:Suppose that good 1 is normal and good 2 is inferior. Prove that the total effect on demand
for good 1 of a marginal increase in the price of good 2 cannot exceed the total effect on
demand for good 2 of a marginal increase in the price of good 1. That is, prove that
?х1
дрг
=
where, for each i = 1,2, zi denotes the Marshallian demand for good i and p; denotes the
price of good i.
Solution: By the Slutsky equation,
VI
əx1
дрг
VI
Əh₁
дрг
Əh₂
др1
Əh₂
др1
Əh₂
<
əx2
api'
where the second line follows from Slutsky
the fourth from inferiority of good 2.
I2
X2
əxi
dw
дх1
dw
Əx₂
əx2
I1
др1 dw др1
symmetry, the third from normality of good 1, and
=
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