Suppose you are given the following information for a particular individual consuming two goods, a and b: Pa = $3, Pb = $4, MUa = 100, MUb = 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 MRSab 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. Consider the following consumer's problem: U(x,y) = X1/4 Y3/4. Prices are Px = $10, Py = $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 = 3PXX/PY . 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. Consider the following consumer's problem: U(X,Y) = 3X + 2Y. Prices are Px = $5, Py = $10 and Income is m = $500. 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 = -3/2. c) Sketch the indifference curves onto the budget set and show that, given these prices, optimal consumption implies Y = 0. d) Find the consumer's optimal consumption bundle (X*, Y*) given these prices and income. e) How high would the price of X have rise for the consumer to choose Y > 0? Explain. Are goods X and Y substitutes or complements? Explain