Question 1 [30 marks] Consider a consumer who has preferences over two goods, x and y, represented by the utility function u(x, y) = x 3/5 y 2/5 . a) [5 marks] Find equations for this consumers indifference curves for utility levels u = 1 and u = 2, and represent them graphically.

b) [5 marks] Find this consumers marginal rate of substitution (MRS). Then, using this result and supposing that this consumer has money income m, and faces prices px and py, solve the system of equations consisting of the optimization principle and the budget constraint to find functions x(px, py, m) and y(px, py, m). These two equations, relating quantities bought of both goods to prices and income, are Marshallian demands.