Currently. the price of consuming housing 
is lowered by the fact that home mortgage interest is tax deductible. Suppose the government proposed to eliminate this implicit subsidy of your housing consumption, raising the price from 
to
src="https://sciemce.com/media/3/ppg__cognero__Chapter_07_Income_and_Substitution_Effects_in_Consumer_Goods_Markets__media__9b711c52-06c1-4848-984d-2ca85addf439.PNG" style="vertical-align: -8px;" width="17px" height="28px" align="absmiddle" />. At the same time, the government lowers the tax on other consumption, lowering the price from 
to 
.
a. Write down your original budget constraint assuming the consumer has income I.
b. Suppose the utility function 
captures your tastes, and suppose 
, 
, 
, 
and 
. Write out the utility maximization problem for this consumer prior to any policy change.
c. How much housing and other goods will this consumer consume prior to any policy change?
d. How much would this consumer be willing to pay to get the policy change implemented?
What will be an ideal response?
a. 
b. 
c. 
d. We first have to solve for the bundle the consumer would consume if she paid the maximum amount she is willing to pay to get the policy change implemented. The maximum she is willing to pay is an amount that will leave her with the same utility that she had before the policy --- and that utility is 
. At the post-policy prices, the expenditure necessary to reach this utility level is determined by solving
.
This gives us the bundle 
At the post-policy prices, this bundle costs 
--- which implies that the consumer is willing to pay as much as 
to get the policy implemented. (Without rounding errors, this amount comes out to be $2523.26.)
Economics
src="https://sciemce.com/media/3/ppg__cognero__Chapter_07_Income_and_Substitution_Effects_in_Consumer_Goods_Markets__media__9b711c52-06c1-4848-984d-2ca85addf439.PNG" style="vertical-align: -8px;" width="17px" height="28px" align="absmiddle" />. At the same time, the government lowers the tax on other consumption, lowering the price from to .
a. Write down your original budget constraint assuming the consumer has income I.
b. Suppose the utility function captures your tastes, and suppose , , , and . Write out the utility maximization problem for this consumer prior to any policy change.
c. How much housing and other goods will this consumer consume prior to any policy change?
d. How much would this consumer be willing to pay to get the policy change implemented?
What will be an ideal response?
b.
c.
d. We first have to solve for the bundle the consumer would consume if she paid the maximum amount she is willing to pay to get the policy change implemented. The maximum she is willing to pay is an amount that will leave her with the same utility that she had before the policy --- and that utility is
. At the post-policy prices, the expenditure necessary to reach this utility level is determined by solving.
This gives us the bundle At the post-policy prices, this bundle costs --- which implies that the consumer is willing to pay as much as to get the policy implemented. (Without rounding errors, this amount comes out to be $2523.26.)
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