UCLA Economics 11 Professor Mazzocco PRACTICE MIDTERM: ANSWER KEY NAME: _______________________________________ID:____________________ TA:__________________________________________________________________ Part 1: Multiple Choices 1. Indifference curves a. are non-intersecting. b. are contour lines of a utility function. c. are negatively sloped. d. all of the above. 2. For an individual who consumes only two goods, X and Y, the opportunity cost of consuming one more unit of X in terms of how much Y must be given up is reflected by a. the individual's marginal rate of substitution. b. the market prices of X and Y. c. the slope of the individual's indifference curve. d. none of the above. 3. The slope of the budget constraint line is a. the ratio of the prices (px/py). b. the negative of the ratio of the prices (px/py). c. the ratio of income divided by price of y (I/py). d. none of the above. 4. If an individual's indifference curves are convex, his or her MRS will a. diminish as X is substituted for Y. b. increase as X is substituted for Y. c. be undefined except in special cases. d. always depend only on the ratio of X to Y.5. If utility is given by U(X, Y) = Min (X, 3Y) then the bundle (3,2) provides the same utility as the bundle a. (1, 3). b. (2, 3). c. (4, 1). d. (4, 2). 6. Suppose that an individual has a constant MRS of shoes for sneakers of 3/4: (that is, he or she is always willing to give up 3 pairs of sneakers to get 4 pairs of shoes). Then, if sneakers and shoes are equally costly, he or she will a. buy only sneakers. b. buy only shoes. c. spend his or her income equally on sneakers and shoes. d. wear sneakers only 3/4 of the time. 7. Suppose an individual's MRS (of steak for beer) is 2:1. That is, at the current consumption choices he or she is willing to give up 2 beers to get an extra steak. Suppose also that the price of a steak is $1 and a beer is 25 cents. Then in order to increase utility the individual should a. buy more steak and less beer. b. buy more beer and less steak. c. continue with current consumption plans. 8. Suppose that at current consumption levels an individual's marginal utility of consuming an extra hot dog is 10 whereas the marginal utility of consuming an extra soft drink is 2. Then the MRS (of soft drinks for hot dogs) -- that is, the number of hot dogs the individual is willing to give up to get one more soft drink—is a. 5. b. 2. c. 1/2. d. 1/5. 9. An increase in an individual's income without changing relative prices will a. rotate the budget constraint about the X-axis. b. shift the indifference curves outward. c. shift the budget constraint outward in a parallel way. d. rotate the budget constraint about the Y axis. 10. If the price of X falls, the budget constraint a. shifts outward in a parallel fashion. b. shifts inward in a parallel fashion. c. rotates outward about the X-intercept. d. rotates outward about the Y-intercept.Part 2: Exercises 1) David likes only peanut butter (P) and toast (T), and he always eats each toast with two ounces of peanut butter. a) Find David’s demand for peanut butter and toast. It is a case of perfect complements. The utility function U(T,PB) = min(2T , P) represents David’s preferences. Indifference curves are L shaped with corners located on the line 2T = P. Since optimal consumption will always take place at the corner of an indifference curve demands can be found as a solution of the system of equation consisting of P = 2T and the budget line: ppP + ptT = I. The solutions of this system are: T = I / (2pp + pt) and P = 2I / (2pp + pt). b) Find the indirect utility function and the expenditure function. U = min{2I / (2pp + pt) ,2I / (2pp + pt)} U = 2I/(2pp + pt) E = U(2pp + pt)/2 c) How much of each good will David consume in a week, if he has $4 of income, the price of peanut butter is $0.02, and the price of a toast is $0.06. Using the demands, T = 4 / (2*0.02 + 0.06) = 40 and P = 2T = 80. Utility is 80 d) Suppose that the price of a toast rises to $0.11. How will his consumption change? T = 4 / (2*0.02 + 0.11) = 26.7 and P = 2T = 53.3. Utility is 53.3. e) How much should David’s income be to compensate for the rise in the price of the toast? David must enjoy a utility of 80 to be back on his indifference curve. This means that he must consume T = 40 with the new prices. Therefore Y’ must solve 40 = Y’ / (2*0.02 + 0.11). Therefore, Y’ = 62) Susan’s utility function is U=XY + X + 2Y. She has a monthly income of I, and the prices of the goods are PX and PY. a) Find Marginal Rate of Substitution. MRS=(Y+1)/(X+2) b) Find Susan’s marshallian demand for X and Y. X= (I-2Px+Py)/2Px Y=(I+2Px-Py)/2Py c) How do changes in PY and I affect the demand for X? What do these results tell us about the properties of this demand function? X/I>0, meaning that X is a normal good, X/Py>0, X and Y are gross substitutes, since demand for X increases when the price of Y increases. d) Find Susan’s Indirect Utility Function. U= (I-2Px+Py) (I+2Px-Py)/4PxPy + (I-2Px+Py)/2Px + (I+2Px-Py)/