Spr09MidtermSolutionSketches

Spr09MidtermSolutionSketches - Economics 50 Stanford...

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Unformatted text preview: Economics 50 Stanford, University Spring Quarter 2009 Name: Suggest warm TA. Midterm Exam April 30, 2009 Part I . (Questions 1 through 4; 50 points total) Write your name and your TA’s name (N adeem Karmali, Annika Todd, Takuro Yamashita, or ' Xiaoling Zhou), and sign the statement on the cover of Parts I and ll of the exam. Pace yourself carefully, andlprovide clear, concise answers —- lengthy explanations are not necessary! Write all of your answers in the space provided. If you need extra room, please use the back of each sheet. You can work on Parts I and II in any order. If you must make any additional assumptions in order to answer a question, please state what those assumptions are. At least one member of the Econ 50 staff will be available outside the classroom at ' all times. We usually cannot answer questions, but please notify us if you feel you’ve found a mistake in the exam or if you observe a classmate engaging in suspicious behavior. At the end of the exam, turn in Part I and Part II in the boxes provided. Your numerical answers should be as precise as possible. If you’re pressed for time, don’t worry about simplifying your answers perfectly. Make sure you show your work. You will have a total of 110 minutes to complete this exam. The exam is worth a total of 100 points, so you should allocate approximately one minute per point. Remember that no calculators, notes, books, headphones, or visible cell phones are allowed. Good luck!‘ “The answers written on these pages are entirely my own. I attest that in taking this exam, I am fully complying with all provisions of Stanford’s Fundamental Standard and Honor Code.” Signature: Do not open this exam until it is time to begin.- Page 1 of11 Economics 50 Stanford University Spring Quarter 2009 Question 1: If the curve fits [8 points] _ You are given the following information: o The price elasticity of demand for cigarettes at current prices is —O.5. 0 The current price of cigarettes is $.05 per cigarette. o Cigarettes are being purchased at a rate of 10,000 per year. Find the equation of a linear demand curve that fits this information, and sketch that demand curve in a well-labeled diagram. Show your work. Question 2: Who bears the burden? [4 points] The U.S. government decides to enact a $9 excise tax on each bottle of vodka sold. If, at current ' prices, the price elasticity of demand for vodka is —0.4 and the price elasticity of supply is 0.8, What will be the effect ”of the excise tax on the price paid by consumers who purchase vodka? Be as precise as you can. MA :Ejfigfg Economics 50 . Stanford University Spring Quarter 2009 Question 3: Working out the kinks [14 points] Liberty has a total weekly income of $48, which she devdtes to purchases of string (X, measured in yards) and kibble (Y, measured in pounds). Liberty can purchase kibble (Y) at a price of $3 per pound; she can purchase up to twelve yards of string (X) at a price of $2 per yard; any additional string (beyond twelve yards) will cost $4 per yard. a) Write down a precise expression for Liberty’s budget constraint, and sketch it in a well— labeled diagram. [8 points] «QM 3V 442:7 Xéxa away é 9&7 WV; Suppose we know that Liberty’s preferences over string (X) and kibble (Y) are summarized by a utility function of the form U(X,Y)=X“Y, where a is some positive constant. For parts b) through d), note that you do not have to provide a full, formal solution to Liberty’s utility-maximization problem. b) For what values of a will Liberty consume more than twelve yards of string? Show your work. [2 points] WS @093): ”"é 4iv‘xsstsrgié. %>hg NW 00 22 c) For what values of a will Liberty consume less than twelve yards of string? Show your work. [2 points] 9‘0‘ /-4$/g NM 0k 453— 'd) For what values of a will Liberty consume exactly twelve yards of string? Show your work. [2 points] Q>4 am 0x49. \ <04 (‘1 Page 3 ofll Economics 50 » , Stanford University Spring Quarter 2009 Question 4: Do these go together? [24 points] Bo’s preferences over nachos (X) and cream Cheese (Y) are summarized by the utility function U(x,y)=xy+10(x+y). Bo has an income of $1; he can purchase nachos and cream cheese at the market prices PX and Py, respectively. a) Write down an expression for Bo’s Marginal Utility from each good and for his Marginal Rate of Substitution of x for y. Sketch a representative indifference curve on the following axes. Label the axes. [8 points] ‘33 MUX= meta W \O H MRS = [@325 tow >>< ', b) Derive expressions for Bo’s utility-maximizing demands for nachos and cream cheese, XD(PX, Py, I) and YD(PX, Py, I). Be precise, and show your work. [8 points] . 1+;Pigflopx CD '- "EA—{692’ ‘09:; , ® ‘2 X :- )K o . c9 ‘3 1’93 C?) «I W <9 0 (3 CD I > MOL‘X {\OPx—KDPU‘ \093-i09xg_ @ 16:10 934091) \oWedei Omd PX‘> ()3 ‘ ® 1-e§\OQX’\OQ:) I \O (93» IOOXQS amok it)? PX Page 4 of 11 Economics 50 Stanford University Spring Quarter 2009 0) Write down Bo’s optimal consumption bundle (X: Y*) for the case Where Px=$2, PY=$3, and I=$60. [2 points] (1) Write down Bo’s optimal consumption bundle (X: Y*) for the case Where Px=$2, Py=$3, and I=$6. [2 points] ‘ V Och >6: (3. 0> 6) Are nachos and cream cheese complements, substitutes, or neither for Bo — or does it “depend?” (and if so, on What?) Be as specific as you can.- [4 points] HWM cm @,@ em. (a) iw®r mm :3 are MW Q3) \Wé) mot® mm W W M ' name/u We» WWW Page 5 ofll Economics 50 Stanford University Spring Quarter 2009 Name: iAW%W Lay TA: Midterm Exam April 30, 2009 Part 11 (Questions 5 through 9; 50 points total) “The answers written on these pages are entirely my own. I attest that in taking this exam, I am fully complying With all provisions of Stanford’s Fundamental Standard and Honor Code.” Signature: Do not open this exam until it is time to begin. Page 6 ofll Economics 50 Stanford University _ Spring Quarter 2009 Question 5: Sketch it [4 points each; 12 points total] For parts a) through c), sketch a curve with the appropriate shape for the given information. Be as specific as you can, and label your axes a) A demand curve for X for a consumer with utility function U(X, Y)= (X+2Y), Where income is I: 60 and each unit of Y costs PY=$6. 11/: 11: 3.11:1 1 11121 «1 b) An income consumption curve for a consumer with utility function U(X,Y), where Y is a normal good for lower levels of income and an inferior good for higher levels of income: Page 7 ofll Economics 50 Stanford University Spring Quarter 2009 Question 6: Decompose it [10 points] Millie is a utility-maximizing consumer. Her preferences over fish (X) and cheese (Y) are strictly monotonic and strictly conyex. Sketch a Slutsky diagram showing how Millie’s utility—maximization decision will change if there is an increase in the price of fish, for a set of prices and income such that cheese is an inferior good for Millie. Make sure you draw and label all necessary curves. Label the key points A, B, and C, such that the total effect is fiom A to B, the substitution effect is from A to C, and the income effect is from C to B. And then answer the additional (brief) question at the bottom of the page. El What do you know about the income elasticity of demand for fish, for the prices and income analyzed above? Be as specific as you can. «FivéTA-F 3 as mate/«W W ma z Mgr at Mm “ll/ms, ELL '> D . (”WWW/v fiat}: rxl7&f%1)+ faiéagfet,f7m1):1i we have; Pig”? 393(312( 1) «Mai Moe Fara” <31 >i 0% QEE<QJ it MulTIPiyi/w; tom :05; 5]? flag {“fiwui‘tjy, Ly F cm W scram ML >L f I Pita? $6 (91'. F136;!” MW LHS' 2): I cwet RHS> l (_/ ”x 43 kat EXT 7 E Q Page80f11 f.» Economics 50 Stanford University Spring Quarter 2009 Question 7: ,Reveal it [8 points] Rex buys two goods, clothing (X) and food (Y). He likes both clothing and food, and his preferences for the goods do not change from month to month — although his income does fluctuate, as do the prices of the goods. We learn the following about Rex’s recent choices: 0 In February, Rex purchased ten units of clothing and twenty-five units of food, when the prevailing market prices were Px=$15 (for each unit of clothing) and Py=$2 (for each unit of food). We will refer to this bundle as Bundle A. o In March, Rex purchased eighteen units of clothing and twenty units of food, when the prevailing market prices were Px=$10 and PY=$3. We will refer to this bundle as Bundle B. a) Using revealed preference analysis, what can you say about Rex’s preferences for Bundles A and B (i.e. how does he rank them? Or do his choices contradict each other?) Show your work. [4 points] a I'm Feb : ’ . P2362; EPLmlgp—f 1 l? (0+ 1: 1g": loo W. 1;“ m 242.0 :- 3w (we), 15 «.5 Warmth u (Tau n In [Howrah Pass/S Lady? :1 to-lfg’i— 3” 20 e 240‘ since he" 10+ 3. 2:2 {wkm'}, A :9 mean age (m a c m...) ,. Tween, e (am) Wu were: i». Awanga. b) Write down a utility function U(X,Y) that is consistent with Rex’s choices — or indicate that no reasonable utility function can rationalize these choices. In either case, briefly explain your reasoning. [4 points] . '~ Nofim ‘tLa‘T Riga/vibe; sf (finial) , We haw; . {7.11 )C I 3 W3 . . «Tl/J‘s ”(Wife/[7’ "as” safiff‘iQ/i if ilk” ha; a {131$th imam my, I?“ Z {3 - Page 9 ofll Economics 50 Stanford University Spring Quarter 2009 Question 8: Consuming in three dimensions {14 points] Buddy is a utility—maximizing consumer, with preferences described bythe utility function U(X,Y,Z)=X+Min(Y,Z). He faces an ordinary budget constraint of the form PXX + PYY + PZZ = I. 3) Write down Buddy’s utility—maximizing consumption bundle, (X*,Y*,Z*), when the market prices are Px=$4, PY=$3, and Pz=$2, and his income is I=$60. Show your work and/or explain your reasoning. Also write down the level of “maximized utility,” U: he is able to attain. [6 points] ' " Y amt % ova/‘3 €2ng CMMYJ’LM "aw/if? fin“; [#32: ‘~ 36 \wioi y if; FWQGQ/Wi , Mama: 1+ V} ‘ Sleigegi "to 475 "9 (Ml) 3' g €3.63 " (iii, if“? 2*) :2 0 , week :awtw Mir—{3* if Tbmfirfg ,7 b) Beginning with the prices and income outlined in part a), what would be Buddy’s compensating variation if the price of good X increased to PX=$6? Show your work. [4 points] UM?” “th ‘NZ’v’ 53’2“”? “Wei I 66-},- DWJJY twmmm similar fié—liz) wt ewes Wide. ‘ Ta Okla—1m Ufa: {9 (Maia/v Tm iota/v. ‘ 95’ W ‘> SSW-0L4 \f heeyiS I 3' “Tirf‘f $19 flail Buci 61y Cam» ioni- “1:25: ‘ "Tina/xx CV"‘=‘¥£‘»— éa:[§ 0) Compute the equivalent variation corresponding to the same price change described in part b). Show your work. [4 points] W. x K a 6L :22“. $44 ‘P‘V‘l 2:! { l Utxgijyt/ Th 95"? £9 if: M! BLLL‘i‘i. L/ Whiz/COL; . 1 '3'— [ii 8",. (>70 fact-r BUCLXV {M14 L“? ' ‘ll [M bro}. .. We Ev: @4942, Page 10 of11 Economics 50 Stanford University Spring Quarter 2009 Question 9: Analyze it'[2 points each; 6 points total] Your research assistant, Heidi, has just finished a theoretical paper in which she analyzed the utility— maximizing behavior of a consumer who purchases two goods, X and Y, and faces a simple linear budget constraint. Among Heidi’s results are the following Hicksian demand function and expenditure function: uyl/ZP 1/2 XH(PX,P,,u)_ — —— 2PX1/2 f(PX,Py,u) = 111/21.0,{1’ZPYI’2 a) Write down this consumer’s indirect utility function. * P71 111 11:11:15? 11511117“ fiwrcam Mi? £71,? *1 U b) Write down this consumer’s ordinary (Marshallian) demand function for X i F” Na?“ iii-M iifitiwm'i :T:***c'i§m~1 fiffii @711) W91 i111 1*(?119®)~ 3C" ([21 1 F11 W7 €1,351; 1):) F1 F31 F83 ‘DL‘ 1. (I % PX c) Write down this consumer’s utility function, U(X, Y). . 8? 1,2 {0111,11 Mai/1.11.1 we 1111:1111 1; 11113111311 (7 111:1 ?1“:F::Z/‘/~ c‘r' Times, \4 \KTFX'P ((3 £>ZT§ ”Unma’fii’f 11A may (i796 F“; 1) ‘vme, in mg; M111 2:111 1111111 1M1; That’s all! See you next week, as we begin Producer Theory! 476 V - Page 11 ofll ...
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