. (25 marks) Consider an individual with utility of the form: U(x,y) = x^ay^b where (a+b)=1. The price of good x is p_x and the price of good y is p_y. The individual faces a budget constraint of I (or income).

Note: For this utility function MU_x = ax^a-1y^b and MU_y = bx^ay^b-1. Where x denotes the consumption of good x, and y denotes the consumption of good y.

A)Find the demand functions for the individual in question. (10 marks)

B)Suppose the price of each good increases by a factor of T (therefore the price of good x is (1+T)p_x and the price of good y is (1+T)p_y). Prove that the increase in price does not change relative amount of each good the individual purchases, however, the individual purchases less of each good. How much additional income would the individual need to obtain the same utility as in part A)? (10 marks)

C)Suppose a policymaker is worried about consumption of good x (suppose production of good x pollutes and creates a negative externality on the environment, for example) and decides to subsidize the production of good y, thereby decreasing its price. The hope of said policymaker is that people will substitute away from the consumption of good x towards good y because it now costs less. If all individuals in the society in question have utility that is representative of parts A) and B), will this policy work? Why or why not? (5 marks)