1. Theory of the Consumer (30 points} a) The utility function for an individual is given by . If prices for the UGLY) = X'SY'S two goods are and respectively, and income is , derive the ordinary PX PF I (Marshallian) demand functions for the two goods and using the method of X Y Lagrange b) For a small increase in the price of , what is the total change in the quantity X demanded of ? Express your answer in terms of price(s) and income. c) Using the Slutsky decomposition, calculate the income effect for the price change in part (b). Again, express your answer in terms of price(s} and income. d) Is a normal good? Provide any calculation to justify your answer. e) Derive the Expenditure Function, , for this individual. E (P , P ,U)