Consider an individual with utility of the form: U(x.y)=400+x^ay^b where (a+b) = 1. the price of good x is px and the price of good y is py. The individual faces a budget constraint of I (income).
a) Find the demand functions
b) Suppose the price of each good increases by a factor of T. Prove that the price change doesn't influence the relative amounts purchased, just that the consumer purchases less of each good. How much additional income would the individual need to obtain the same utility as in part a?
c) Suppose consumption of good x has a negative externality, so a policymaker decides to subsidize the production of good y, decreasing its price. Given above utility, will this policy work and why?