Fall 2011 - Exam 1

Fall 2011 - Exam 1 - ECONOMICS 201 FALL 201 1 EXAM 1...

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Unformatted text preview: ECONOMICS 201 FALL 201 1 EXAM 1 Instructions: Please mark your answers clearly. No class notes or other materials are allowed. 100 points total. Each question is worth 5 points unless indicated otherwise. 1. Dora likes bubbles (good 1) and balloons (good 2). The price of good 1 is $2, and the price of good 2 is $1. Her income is $100. For her birthday, she received a $20 gift card for bubbles (good 1). Draw Dora’s budget set. Label the intercepts and slope. (6 points) and 3 a 3094!! Multiple choice. Lady Gaga is indifferent between bundles (4,9) and (12,3). Which of the following leads us to conclude that her preferences are convex? Lint: The line connecting (4,9) and (12,3) is X 2 = — Z X1 +12; her preferences satisfy monotomcrty and transrt1v1ty. (Please Circle one response.) She strictly prefers (12,4) to (12,3). She strictly prefers (12,3) to (6,6). She strictly prefers (6,6) to (4,10). She strictly prefers (6,6) to (10,3). 999‘?” . Multiple choice. Given that a consumer is indifferent between bundles (3,2) and (2,3), which of the following could not represent her preferences? (Please circle one response.) a. Linear (perfect substitutes) b. Leontief (perfect complements) c. Cobb-Douglas (e.g., u(X1,X2) = XfXé‘”) d. Lexicographic (Godzilla) True or False: Consumption of an inferior good decreases when all prices rise by the same percentage. Explain your answer with a mathematical expression, graph, and/or one or two sentences. . True or False: If goods 1 and 2 satisfy the law of diminishing marginal utility, then MRS decreases as X1 increases. Explain your answer with a mathematical expression, graph, and/or one or two sentences. 6. Matt Ryan likes red (good 1) and black (good 2). Prices are P1 and P2 . His utility function is u(X1,X2) = X105 + X2. (12 points) a. For fixed level of utility ; , what is Matt’s EMP (expenditure minimization problem)? b. What is the Lagrangian? What are the first-order conditions with respect to X1, X 2 , and )u ? c. What is his demand function X1(Pl, P231.) ? 7. Tiger Mom purchases math lessons (good 1), Violin lessons (good 2), and language lessons (good 3). Prices areP1 ,P2 , and P3. Her utility function is u(X1,X2,X3) = arXi + sz + 0X3. (10 points) a. For income m, what is Tiger Mom’s UMP (utility maximization problem)? b. What are the conditions that ensure she spends all of her income on Violin lessons (good 2)? Hint: They are two inequalities involving a, b, c, and prices. 8. True or false: Suppose a consumer spends money on good 2 but not on good 1. The price of good 1 is $3 and the price of good 2 is $2. If the marginal utility of good 2 is 6, the marginal utility of good 1 can be any number greater than 9. 9. True or False: The numerical solutions to the UMP and EMP are the same when the fixed level of utility in the EMP is the same as the maximized level of utility in the UMP. Explain your answer with a mathematical expression, graph, and! or one or two sentences. 1 l 10. Jack Sparrow likes peg legs and parrots. His utility function is u(XPeg,XPa,) = X 2 X 2 . Prices are Peg Par (Pp PM) , and his income is m. On his way to the market, he finds 6 free peg legs! (12 points) Eg’ a. What is his UMP? b. How many parrots does Jack purchase (in terms of prices, income, and (9 )? 11. True or False: If the substitution effect is larger in magnitude than the income effect, it must be that the good is not Giffen. Explain your answer with a mathematical expression, graph, and/or one or two sentences. 12. Multiple choice. The following graph depicts a rise in P} . Which of the following is not true? (Please circle one response.) ‘9‘ Good 1 is normal 33- Good 2 is normal Good 1 is ordinary Goods 1 and 2 are substitutes 9.0 9‘5» goon l l3. Calculate the coefficient of absolute risk aversion for each of the following Bernoulli utility functions. Say whether preferences are risk averse, risk loving, or risk neutral. 1 a. =1 — u(c) n20 1 b. 11(0) = Scg 14. Multiple choice. Which of the following consumers is more risk averse than the other? (Please circle one response.) 1 15. Suppose a consumer’s Bernoulli utility function is u(c) : c2 . Consider the following lottery. There is a 0.75 chance to win $25 and a 0.25 chance to win $36. (10 points) a. What is the expected utility of playing the lottery? Hint: Your response should be a number or an expression with numbers plugged in. b. What is the expected utility of receiving an amount of money $E with certainty? c. The “certainty equivalent” $E is an amount of money such that a consumer is indifferent between receiving that amount of money with certainty and playing a lottery. What is the certainty equivalent given the above lottery? Hint: Your response should be a number or an expression with numbers plugged in. ECONOMICS 201 FALL 201 1 EXAM 1 Instructions: Please mark your answers clearly. No class notes or other materials are allowed. 100 points total. Each question is worth 5 points unless indicated otherwise. 1. Dora likes bubbles (good 1) and balloons (good 2). The price of good 1 is $2, and the price of good 2 is $1. Her income is $100. For her birthday, she received a $20 gift card for bubbles (good 1). Draw Dora’s budget set. Label the intercepts and slope. (6 points) and 33 we 300:! l . I a so 2. Multiple choice. Lady Gaga is indifferent between bundles (4,9) and (12,3). Which of the following leads us to conclude that her preferences are convex? Hint: The line connecting (4,9) and (12,3) is X 2 = — 3; X1 +12; her preferences satlsfy monotomcrty and transrt1v1ty. (Please cncle one response.) 3.. She strictly prefers (12,4) to (12,3). (8,6) > (6, 6) > (5610) > (‘2‘, 1) b. She strictly prefers (12,3) to (6,6). 0n @ She strictly prefers (6,6) to (4,10). ‘5“ (1. She strictly prefers (6,6) to (10,3). 3. Multiple choice. Given that a consumer is indifferent between bundles (3,2) and (2,3), which of the following could not represent her preferences? (Please circle one response.) a. Linear (perfect substitutes) N o L M Mes awe ,‘h A“ 4 gene“), b. Leontief (perfect complements) wad, [ e I“. w M L“ r 91’” Pm“ c. Cobb-Douglas (e.g., u(X1,X2) = Xf‘Xé‘“) 3 P f ‘ Lexicographic (Godzilla) 4. True or False: Consumption of an inferior good decreases when all prices rise by the same percentage. Explain your answer with a mathematical expression, graph, and/or one or two sentences. False. All was “sing by 44.9 Sty-Me pal-«mirage 1's analPJtn/j‘ 4% ‘K 3908653 in mun-:6- (OHSWv-r‘h'aa. “r q.‘ Afar-{gr Jul! InUQGJeS Nil-Ha 4 deco-ease m facing:- 5. True or False: If goods 1 and 2 satisfy the law of diminishing marginal utility, then MRS decreases as X, increases. Explain your answer with a mathematical expression, graph, and/ or one or two sentences. True. MUIJ, 46 KIT: 9° MRS‘Z—Lul \l' 4‘ K‘T' MU‘L 6. Matt Ryan likes red (good 1) and black (good 2). Prices are Pi and P2 . His utility function is u(X1,X2) : Xlo'5 +X2. (12 points) a. For fixed level of utility ii, what is Matt’s EMP (expenditure minimization problem)? M f n Pl K I 4‘ r1 3(1- x.,x‘ s .+« 9 a r: X to- '* x1. b. What is the Lagrangian? What arse the first-order conditions with respect to X1 ,X2 , and ,u 7 i : P,X,+P;X1-/\4 (Rf + X,_-- E) Focs: ‘9. [x3 Pi v“ °i5 “I [XL-l ‘Dfi-f/u :0 5.7.0 0.! [/0 x. + X; : "F c. What is his demand function X1 (3,3,3) '2 _ .9 3‘ mum-i, u) : ,3. ' 3.91 7. Tiger Morn purchases math lessons (good 1), Violin lessons (good 2), and language lessons (good 3). Prices areiD1 ,P2 , and PS. Her utility function is u(X1,X2,X3) = aX1+ sz + 0X3. (10 points) a. For income m, What is Tiger Mom’s UMP (utility maximization problem)? Max «XH- 51(11- (X3 unit-1)“ 5.4.. f.x,+?.,‘<,_ 4- 73x3 : M b. What are the conditions that ensure she spends all of her income on violin lessons (good 2)? Hint: They are two inequalities involving a, b, c: and prices. 3):: a :1 :71”. at 13‘ c f3 8. True or false: Suppose a consumer spends money on good 2 but not on good 1. The price of good 1 is $3 and the price of good 2 is $2. If the marginal utility of good 2 is 6, the marginal utility of good 1 can be any number greater than 9. i w mva‘ mu 6 MU. MU. Mus-P Be 52. I _... > _._.,_. Fail P1 7 T u- $3 $3 . 1835 4.144,, ‘i. 9. True or False: The numerical solutions to the UMP and EMP are the same when the fixed level of utility in the EMP is the same as the maximized level of utility in the UMP. Explain your answer with a mathematical expression, graph, and/or one or two sentences. 80H. “birch: True - ‘ «Re '19,,“qu I :3 "v haw p33,, 3 hum 7:6 4+ u' ' Emp u m P W“ 1 1 10. Jack Sparrow likes peg legs and parrots. His utility function is u(XPeg,XPa,) = X fiegX 3a, . Prices are (Ppeg,PPar) , and his income’is m. On his way to the market, he finds (9 free peg legS! (EDD—fills) I.. $ l a. Whatis his UMP? max (Xpes+ e)1X,:, 3‘9”, “par 5.+. P“: chs 4' ?far~XP"‘ 2" M b. How many parrots does Jack purchase (in terms of prices, income, and 9 )7 11. True or False: If the substitution effect is larger in magnitude than the income effect, it must be that the good is not Giffen. Explain your answer with a mathematical expression, graph, and/or one or two sentences. ‘ I qu- A Bid-11ers (decal m°5+ Lave am Income CHM-1' “Hm-t :5 19:33:» a»; in are wow; drama“ - 12. Multiple choice. The following graph depicts a rise in P1 . Which of the following is not true? (Please circle one response.) “It a. Good 1 is normal 3 Good 2 is normal c. Good 1 is ordinary d. Goods 1 and 2 are substitutes 300’. I 13. Calculate the coefficient of absolute risk aversion for each of the following Bernoulli utility functions. Say whether preferences are risk averse, risk loving, or risk neutral. ‘ - I ‘ I n -l _, ., (1. _L ‘ .1 ‘-‘ I «u- r c - fl—H ' ’ Q“ I a. u(c)=lnlc u C I u (1' - J— - C 4U 52 2 _( . V Q "g A; I“ " ’ a: 5 . 1 u‘ICE «Edie? mos» s : ——— Rusk b. “(C)=505 "' f s o 6% 5c (“Verse 14. Multiple choice. Which of the following consumers is more risk averse than the other? (Please circle one response.) ’J’ u ,3 _ 45 g? 1 u(c)=2c% “25-1: “Salicqp' a“): H 3:, 12 "c "I I f‘(<)”'!" b. u(c)=§c U “ 1 H ‘ 1" ' C ‘ 1 15. Suppose a consumer’s Bernoulli utility function is u(c) == (:2 . Consider the following lottery. There is a 0.75 chance to win $25 and a 0.25 chance to win $36. ( 10 points) a. What is the expected utility of playing the lottery? Hint: Your response should be a number or an expression with numbers plugged in. 11“ MC.) + 1T1 “(5‘) 0.15 (asfi 4» 0.8.5 (3031‘: o.1s(s)+ 0-As(6) :: 5-35 b. What is the expected utility of receiving an amount of money $15 with certainty? L u(<) 1. E c. The “certainty equivalent” $13 is an amount of money such that a consumer is indifferent between receiving that amount of money with certainty and playing a lottery. What is the certainty equivalent given the above lottery? Hint: Your response should be a number or an expression with numbers plugged in. .- Eq' 1' 5.15 L__.J L__’I «Insular Amsflc’ 44 I. +0 A E a; 31.9 or ...
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This note was uploaded on 02/23/2012 for the course ECON 201 taught by Professor Ninkovic during the Spring '08 term at Emory.

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Fall 2011 - Exam 1 - ECONOMICS 201 FALL 201 1 EXAM 1...

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