Jane consumes two goods, shoes, s, and housing, h. Her income is M and the prices = s¾/³h¾/3 of s and h are Ps and Ph, respectively. Jane's utility function is U=S Find the following: a b. Marshallian demand functions Derive the price elasticity for housing. What is the cross price elasticity for housing? Derive the expenditure-income elasticity for housing (that is, the % change in expenditure on h when there is a 1% change in income)? What about the Cobb-Douglas demand functions explains these elasticities.
Jane consumes two goods, shoes, s, and housing, h. Her income is M and the prices = s¾/³h¾/3 of s and h are Ps and Ph, respectively. Jane's utility function is U=S Find the following: a b. Marshallian demand functions Derive the price elasticity for housing. What is the cross price elasticity for housing? Derive the expenditure-income elasticity for housing (that is, the % change in expenditure on h when there is a 1% change in income)? What about the Cobb-Douglas demand functions explains these elasticities.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![1
Jane consumes two goods, shoes, s, and housing, h. Her income is M and the prices
57/317/3
of s and h are Ps and Ph, respectively. Jane's utility function is Us
Find the following:
a
Marshallian demand functions
b.
Derive the price elasticity for housing. What is the cross price elasticity for
housing? Derive the expenditure-income elasticity for housing (that is, the %
change in expenditure on h when there is a 1% change in income)?
What about the Cobb-Douglas demand functions explains these elasticities.
C.
Derive the indirect utility function and expenditure function
d.
Using Shephard's Lemma, derive the Hicksian demand functions
e.
Perform a Slutsky decomposition for housing (that is, what is the total effect
on quantity demanded when there is a change in price and also what is the
income and substitution effect).
Now assume income is $1,500, the price of shoes is $8 and the price of housing is $125.
f.
What is the quantity demanded of housing? Now assume the government
subsidizes housing by giving Jane $25 for every unit of housing she buys.
Using the idea of compensating variation, how much consumer surplus does
she gain from this policy?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fea0084d8-63e7-4f56-975c-add2c9289a98%2F09b8fd14-dc04-4079-8356-604bba47402f%2Fpkz9grs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1
Jane consumes two goods, shoes, s, and housing, h. Her income is M and the prices
57/317/3
of s and h are Ps and Ph, respectively. Jane's utility function is Us
Find the following:
a
Marshallian demand functions
b.
Derive the price elasticity for housing. What is the cross price elasticity for
housing? Derive the expenditure-income elasticity for housing (that is, the %
change in expenditure on h when there is a 1% change in income)?
What about the Cobb-Douglas demand functions explains these elasticities.
C.
Derive the indirect utility function and expenditure function
d.
Using Shephard's Lemma, derive the Hicksian demand functions
e.
Perform a Slutsky decomposition for housing (that is, what is the total effect
on quantity demanded when there is a change in price and also what is the
income and substitution effect).
Now assume income is $1,500, the price of shoes is $8 and the price of housing is $125.
f.
What is the quantity demanded of housing? Now assume the government
subsidizes housing by giving Jane $25 for every unit of housing she buys.
Using the idea of compensating variation, how much consumer surplus does
she gain from this policy?
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