QB. Sam's utility function is U = x yl'z. Her budget constraint is given by: Px. x + Py. y = I. a) Derive Sam's demand curve for x and y as a function of the prices, Py and I. How are x and y related? Explain. b) Calculate the optimal basket when Px = 1 , Py = 2 and I = 24. Call this basket A. What is Sam's utility at basket A? Now assume, the Py decrease to 0.5, calculate her optimal basket and call this basket C. What is Sam's utility at basket C? c) Decompose the total change (From A to C) into income and substitution effects d) Graph these effects. (Say take a point B on the graph. The graph should clearly show the substitution effect from A to B and income effect from B to C to receive credit)