a) Suppose u(x1, x2) = x1^a,x2^(1-a). Given M, PI and P2 derive the demands for the two goods: Solve for MUI,MU2 and the MRS. Now use the tangency condition MRS= -(p1/p2) together with the budget line to solve for Xl (M, PI, P2) and X2 (M, PI, P2).

b)Now suppose a= 1/2. Further, suppose M = 12, PI = 2 and P2= 2. Draw the budget set and show the optimal point chosen by this consumer (using your demands in a)). Include a reasonable sketch of an indifference curve through the optimal point.

c)Keep all parameters as in b) the same except now raise PI to 4. Draw the new budget set and show the new optimal point chosen by this consumer. Include a reasonable sketch of an indifference curve through this optimal point.

d)Now set a = 1/3 but go pack to the original prices and income of b). Draw the budget set and show the optimal point chosen by this consumer. Include a reasonable sketch of an indifference curve through this optimal point.

e)Why are the values of x2 the same in b) and c)? Why are the values of x2 different in b) and d)?