Consider the following utility functions: U(X, Y) = 2X 272 a-) (8 points) For the above utility function, derive the demand functions for X and Y as functions of prices and income. Explain whether these goods are normal goods. Explain whether two goods are complements or substitutes. b-) (6 points) Suppose now that Price of good Y is $12 and income equals 1440. Using three distinct values of price of X (Py = 6, Py = 12, PX = 24), draw Price consumption curve and then using Price Consumption curve draw the demand curve for X. c-) (6 points) Suppose Price of good Y is $12 and price of X is equal to 12. Using three distinct income values ( 10 = 1440, I' = 2880, 12 = 4320), draw Income Consumption curve and then using Income Consumption curve draw the Engel curve for good X. d-) (8 points) Consider initially that Income (1) = $1440, Py =12 and Py = 12. What is the initial optimal consumption levels of X and Y? Suppose that PX rises from $12 to $24. Find the substitution effect, income effect and total effect on good X. Explain the steps carefully and support your result with an explanation and a graph