UCLAEconomics 11 - Fall 2016Professor MazzoccoMIDTERM 1, Version 2NAME: ID:TA:Part I: Multiple Choice Questions (3.5 points each):1. If U(X1, X2) = X31+ 23X2, the MRS:(a) depends on the values of X1and X2(b) depends only on the values of X1(c) depends only on the values of X2(d) is always constant2. If U(z, r) = 4z + 6r, then the bundle (4, 2) provides the same utility as:(a) (4, 3)(b) (3, 2)(c) (2.5, 3)(d) (3.5, 1)3. If a function f(x, y) is homogeneous of degree 3, then which of the following is true?(a) f(2x, 2y) = 9f (x, y).(b) f(2x, 2y) = 6f (x, y).(c) f(2x, 2y) = 8f (x, y).(d) None of the above.14. What does the transitivity assumption on preferences imply?(a) Indifference curves never cross.(b) Indifference curves are convex.(c) Indifference curves have diminishing MRS.(d) All of the above.5. Suppose Peter’s MRS (of cake for tofu) is 2. That is, at the current consumption bundlehe is willing to give up 2 pounds of tofu to get an extra piece of cake. Suppose also thatthe price of a pound of tofu is $6 and a piece of cake is $3. Then in order to increasehis utility Peter should(a) Buy more tofu and less cake(b) Buy more cake and less tofu(c) Continue with the current bundle(d) None of the above6. An individual has a utility function for tennis rackets (x) and tennis balls (y) of the formU(x, y) = min(x, y). She wants to achieve the utility level U. Then, her expenditurefunction is given by(a) E (px, py, U) = (px+ py) U(b) E (px, py, U) =U(px+ py)(c) E (px, py, U) = (2px+ 3py) U(d) E (px, py, U) =(px+ py)U7. Which of the following utility functions represent the same preferences as U(x, y) =α ln(x) + β ln(y)?(a) U(x, y) =√xy(b) U(x, y) = α ln(x) ∗ β ln(y)(c) U(x, y) = xαyβ(d) U(x, y) = αβlnxy28. 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 cost twice as much as shoes, 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.9. Bob spends his income buying tomatoes (T) and juices (J). The price of each poundof tomatoes is 8 dollars; the price of each juice is 4 dollars. His utility is given byU=lnT+lnJ. What is the minimum income Bob needs to obtain a utility level equal toln(8)?(a) 40(b) 32(c) 64(d) 10010. An individual has a utility function for skis (x) and ski boots (y) of the form U(x, y) =min(2x, y). His or her indirect utility function is given by:(a) V =Ipx+py(b) V =2px+pyI(c) V = (2px+ py)I(d) V =2Ipx+2py3Part II: Essay QuestionsQuestion 1 (34 Points)1. Janet loves eating large salads (S) while drinking Odwalla juices (J). Drinking the juicesimproves the taste of salads. Therefore, her utility function has the following form:U(S, J) = JS + 3S(a) For a given income I and prices psand pj, find Janet’s Marshallian demands forS and J. (8 Points)(b) Find the indirect utility function. (8 Points)(c) Suppose Janet has 50 dollars of income to spend on salads and juices, and theprices of these goods are ps= 4 and pj= 2. What is her optimal consumptionbundle? What is her utility at that consumption bundle? (5 Points)Janet’s mother is really proud of her daughter’s healthy diet. She therefore wantsto find a way to improve her daughter’s happiness (utility). To do this she comesup with two possible plans:i. The first plan is to increase Janet’s income by 10% from its current value of50.ii. The second plan is to subsidize Janet’s consumption of juices by paying 20%of the price of each juice she buys.(d) Which of the two plans should Janet’s mother choose if she wants to maximizeJanet’s utility? (To obtain the points, show the calculation that enables you tochoose the plan) (8 points)(e) How much money does Janet’s mother have to spend to implement each plan? (5points)4Question 2 (31 Points)1. Janet got tired of eating salads and drinking juices and she decides that from now onshe will only eat steaks (s) and drink red wine (w). Her preferences for those two goodsare such that she always wants to eat one steak with 4 glasses of wine. Her utility isthereforeU(s, w) = min{4s, w}.The prices of steak and wine are psand pw.(a) Find Janet’s Hicksian demand functions for s and w. (7 Points)(b) Find her expenditure function. (7 Points)(c) Suppose that ps= 10, pw= 5. How much income does Janet needs to achieve theutility level U = 200? (4 Points)A new scientific article has provided evidence that excessive consumption of redmeat reduces life expectancy. As a consequence, the government has decided toimpose a sale tax of 20% on steaks.(d) If Janet wants to stay at the same utility level U = 200, how much income doesshe need to spend after the introduction of the tax? (6 Points)(e) Janet realizes that she cannot afford to spend that much and decides to spend thesame amount she was spending before the introduction of the tax. What will hernew level of utility be after the introduction of the tax? (Hint: use the expenditurefunction and its economic meaning/definition; but, if you prefer, you can use othermethods.) (7