Currently, the price of consuming housing x1 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 (p1-s) to p1. At the same time, the government lowers the tax on other consumption x2, lowering the price from (p2 + t) to p2.
a) Write down your original budget constraint assuming the consumer has income I.
b) Suppose the utility function u(x1, x2) = (1/3) lnx1 +lnx2 captures your tastes, and suppose I = 10, 000, p1 = 10, p2 = 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? (show process)
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?