CurrentlyThe Price of Consuming Housing $x _ { 1 }$ Is Lowered by the Fact That Home Mortgage Interest Is

Essay

Currently.the price of consuming housing $x _ { 1 }$ 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 $\left( p _ { 1 } - s \right)$ to $p _ { 1 }$ .At the same time,the government lowers the tax on other consumption,lowering the price from $\left( p _ { 2 } + t \right)$ to $p _ { 2 }$ .
a.Write down your original budget constraint assuming the consumer has income I.
b.Suppose the utility function
$u \left( x _ { 1 } , x _ { 2 } \right) = \frac { 1 } { 3 } \ln x _ { 1 } + \ln x _ { 2 }$ captures your tastes,and suppose
$I = 10,000$ ,
$p _ { 1 } = 10$ ,
$p _ { 2 } = 1$ ,
$s = 6$ and
$t = 1$ .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.When the policy change goes into effect,will this consumer still be able to afford the bundle you derived in (c)?
e.When the policy change goes into effect,what bundle will the consumer consume?