Suppose you are given the following Information for a particular individual consuming two goods, a and b: P. = $3, P. = $4, MUA = 100, MU. = 200, and income (m) = $200. a) Sketch the budget set. What is the slope of the Budget Line? What are maximal possible consumptions of a and b? b) What is the MRSat for the two goods? c) Is this person maximizing her utility? How can you tell? d) Should she consume more of good a or of b? Explain. e) Why can't you tell what her optimal bundle is? Explain. Q2: Consider the following consumer's problem: U(x,y) = X1/4 Y34. Prices are P. = $10, Px = $10 and Income is m = $1000. a) Sketch the budget set. What is the slope of the Budget Line? What are maximal possible consumptions of X and Y? b) Show that the MRSxy = Y/[3X). c) Show that the optimality condition implies that Y = 3P.X/P, Graph this relationship onto your budget set in (a). d) Find the consumer's optimal consumption bundle (X,Y*) given these prices and income. e) Suppose the price of good X falls to $5. Find the new optimum. Are goods X and Y substitutes or complements? Explain.
