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 Əzi Ər₂ дрг - др where, for each i = 1,2, z; denotes the Marshallian demand for good i and p; denotes the price of good i.
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 Əzi Ər₂ дрг - др where, for each i = 1,2, z; denotes the Marshallian demand for good i and p; denotes the price of good i.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![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
where, for eachi = 1,2, z; denotes the Marshallian demand for good i and p; denotes the
price of good i.
Solution: By the Slutsky equation,
Əx₁
Əh₁
Əp₂ Əp₂
Əh₂
II
?х1
ərz
7
дрг - др
II
VI
Әрт
Əh₂
Әрт
Əh₂
əpi
onsumer bag proforang for two gooda
22
22
əri
dw
Əri
Əw
- 21
მე _ მი
=
7
dw əp₁¹
where the second line follows from Slutsky symmetry, the third from normality of good 1, and
the fourth from inferiority of good 2.
poproces
1 bar the utiliter function ala](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc5f3af6a-2abe-4d35-9076-d60b28159552%2Fc8430c3a-a415-4102-b6e7-52498548d1ad%2F0u0mnqf_processed.png&w=3840&q=75)
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
where, for eachi = 1,2, z; denotes the Marshallian demand for good i and p; denotes the
price of good i.
Solution: By the Slutsky equation,
Əx₁
Əh₁
Əp₂ Əp₂
Əh₂
II
?х1
ərz
7
дрг - др
II
VI
Әрт
Əh₂
Әрт
Əh₂
əpi
onsumer bag proforang for two gooda
22
22
əri
dw
Əri
Əw
- 21
მე _ მი
=
7
dw əp₁¹
where the second line follows from Slutsky symmetry, the third from normality of good 1, and
the fourth from inferiority of good 2.
poproces
1 bar the utiliter function ala
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