Part A: Definitions: Define the following (Warning : do NOT use the word(s) you are defining in your definition):

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1 Ecns 300 Midterm 2 November 2, 2016 Parts A and Bare to be done in class; Part C is due on Monday, November 7, 2016 at the beginning of class (8:10 am). Part A: each definition is worth 5 points; Parts B and C: each question is worth 25 points. 250 points total. Part A: Definitions: Define the following (Warning : do NOT use the word(s) you are defining in your definition): 1. Reservation Price :: The maximum amount a person is willing to pay for the first unit of a good; graphically, it is (in the limit) the value of the vertical intercept of a demand curve. 2. Ad Valorem Tax: A government levy against the money value of a transaction. A "Sales Tax" is usually an example of this type of tax. 3. Numeraire: A good that represents the "average" of all other goods for purposes of comparison with the good we are analyzing. The price of the numeraire is defined as 1; money can be thought of as a numeraire good. 4. Indifference Curve: The locus of points that represent combinations of goods that yield the same level of utility to someone. 5. Marginal Utility: The change in well-being that someone gets by increasing the amount of a specific good they acquire by one unit while keeping the amounts of all other goods preferences unchanged. Part B: In class Problems / Short Answers. Answer 3 of the following 4 questions. You MUST choose which 3 you want graded (if you do not, your worst 3 scores will be counted). All graphs MUST be completely labeled and explained. 1. Tom has $100 that he can spend between two goods. The prices of the two goods are: p1 = $2 and P2 = $1. a. What is the budget equation for Tom? $100 = $2 x1 + $1 x2 b. If good 1 is on the horizontal axis and good 2 on the vertical axis, draw the budget constraint line. (Label everything carefully) (b).,. (c) ~ 5'D So c. If the government limits the amount one can purchase a maximum of 30 units of good 1, and a maximum of 80 units of good 2, draw the budget constraint line.

2 d. If, instead of limiting the maximum amounts that can be purchased (as in part c), the government levies a quantity (excise) tax of $1 on purchases of good 1 in excess of 20 units. In other words, there is no tax on the first 20 units of good 1 that Tom can purchase, but after that-for purchases of more than 20 units-there is a $1 tax on each additional unit. There is no tax placed on purchases of good 2. Draw this budget constraint line. ~'Z. /PD -5$1~=- -~ ~ Zl> Llti 5"D 'I' NI 2. Draw a set of 3 indifference curves for each situation listed below: a. Goods x and y are considered to be perfect substitutes with a marginal rate of substitution is 5 (of J ood y for 1 of good x). (b) j (o..) 1 \'1,.J1~el'\C-C. ~Ul"Ve.5 Cl -or,:.. ~ ie,"w" I \YVS IP\~ "!i\opc -:: U u'l-.e u, 3 ~, b. Goods x and y are considered to be complementary goods that are used in the ratio of 3 of good x is best used with 1 of good y. c. Good x is a "good" up to 15 units, after which it is a "bad." Goody is a "good' regardless of how much is consumed. l>3 l>2.. u, 5 I eip<~ of I,, if --ei -o u l5

3 3. Mary has homothetic preferences. When her income was $1,000, she bought 40 books and 60 newspapers. When her income decreased to $500 and prices did not change, how many books and how many newspapers did she buy? Briefly explain your answer in words that refer to a well-label and properly-scaled graph that you draw to illustrate your answer. 1 \ L...L,.,,. fl~ 0 "" ""'-~'* n N1a~c... f, v1"'e-!'\c~ -G rn"-', -ae 1 ~r-. of:fe c t)rre~ ~.-re <o~u--h-v\(. ra..ys t>1.>+ ~ +Ae o ~3 '(\. The..refo'l"!:. ctre_ alw41 s +A~ S,a.mc prt>pr>r-hovt o~ IY1t:o"'1 s, o when \ Y'\c.ome. 1 "'~ I tv-r Ir\ ha.it.j ~t>,+tc) Is 4*c... "'l$v)\,\ 110'\I\ ~ ~O ~~ (14'\.-d Y\t'W'~~:p~ ~t> ~ D r-~~~+we 1'1. 3 ) - - I 4. Margo has 4x and 6y. If her marginal utility of x is 6 and her marginal utility of y is 2, a. What is her marginal rate of substitution? (i.e., how many y is she willing to give up for one more x?) ) M. M ~5~~ =- \J~-=-i:.--~ A"J. MV~ ~ - :;;.AU-= D...J A b. If y is the numeraire and the price of x is 2, is Margo at a consumptive optimum? If your answer is "yes" explain why; if your answer is "no" illustrate the situation in a well-labeled graph and explain why Margo would want to buy more x or more y (state which) to enhance her utility. 4 7 nat-r30 I"=> Nor a.-"t- a, ~~ - t\v-c._ or+ t)'\vw\ a.\- 'Pond-A. ~ e. MRS) ~{vpe 1 Uo IS. -3 o...+ p01d- A whlle. ~t. slc,p~ t,p,. *'e.. bv¾e-+ h"e. ~ -2.. Tue:re+ore "ev\':j pt>\,...,+ VV\ -HA-e... bud5j- l 1V\e. bduleen A i f3 ~w<-.s M~o A.. h\, ~ \.)ti \Tl{ S he LuDl9 fd Wo.~ --\1;> bv y t'y\ore ~

4 Part C: Take-home questions. Make sure you follow the format requirements for homework and take-home assignments. 1. Answer the question from Part B that you did NOT submit for the in-class part of this exam. 2. What does the Engle Curve look like for good x if the income offer curve has a negative slope? Graph it and explain your reasons carefully. (Be careful since there are two different possible implications for good x depending on how you draw the portion of the income offer curve where it has a negative slope. So, if your answer depends on how you draw the income offer curve, provide all possible answers.) CQsei,, ; I ~ '"'~,- 1% -c ot.- htt~ ht~el..+,v t.. sl~~ pa.<e,+ p 'Pl\,\,i- A M1 A' A ~3} I/' I I /1 N)'l. ~¼<t - I / Aj. :!) }/.').~ I,c rri, Im 5 c~~e 1: ja,v.cm rot. h~ "'- ~e.,s ve 4!I \o pa.~t PDl\\1 A M3 r... o.t.. Mz.; / / M, 'A, Y..z_ ~?, M3 1(, 11 \ ~2.. "'3 A' on the /;-~)~ C ur-ve.. C o rre-s\ n J ~ +o po, A -1{t,, rn (:) I,,, ()~ c"

5 3. Sam has the following preferences for x and y: x is a "good" up to consuming 10 x and a "bad" for any consumption of x that is greater than 10 (regardless of the amount of y consumed); y is a "good" up to consuming 15 y and a "bad" for any consumption of y that is greater than 15 (regardless of the amount of x that is consumed). (Assume that x is a "neuter" when exactly 10 are consumed and that y is a "neuter" when exactly 15 are consumed where a "neuter" is neither a "good" nor a "bad", but just between being a "good" and a "bad.")) a. Show on a carefully-drawn, well-labeled graph what a typical set of Sam's indifference curves will look like (draw at least 3 representative indifference curves). b. If the price of x is $3 and the price of y is $2, show Sam's budget constraint if she has $90 to I spend. c. If the budget constraint is as stated in part b, what will be Sam's optimal consumption of x and y? 1.5 ( Ct J IV) J I We~:nce.. ~ v rv e.s cc"""-l s how,, 1"vl b i e '\"' k (b) bud~ + 111'\~ \S IYI pe..hci I (~) e>pt11yl21 Cln'lSVWlrhoV\ 1 A/. ~<ij ls 10-~ a. V\d 15 y ( 5 Cl.VY'I v..,i'll hot _ -spe-l'\d flkt b - ~ - Dr\ 1P si1e. cl P-5.J ~ he. O.~'f ~ o\'er I tu Nj ~ C\.~1 j t:j \le Is O..\l!m..1.,) l,._..._s_ bvj~t..+ ' C.01'\,sto;l1ni" C\O = 3 k + 2y 1{ 4. Suppose goods x and y are perfect substitutes where the marginal rate of substitution is 2x for 1 y. On the other hand, goods y and z are perfect complements in the ratio that 2y complement 1z. On a well-labeled graph, draw three typical indifference curves where x and z are the goods on the two axes. Sol.;,-o-hfv+e :).. 1t -h?r 011e ~ ~ tf1!. are CcmplRmeV\-ii,.~ iv 1.-=c. ~ slope.== t ' { U3 --r ~ v, --- Vz

6 5. Two goods, x and y, are perfect complements that are consumed together in a 1 :1 ratio. Use the indifference map that shows this as a starting point to demonstrate each of the following: a. Using Slutsky decomposition, show on a carefully labeled accurately drawn graph the income and substitution effects of a price decrease. b. How will the income and substitution effects change (from your answer to part a) if, instead, you use Hicks decomposition? Show and explain your answer. c. Can x or y be inferior goods? Explain. d. Derive the equation for the Engel Curve for good x and graph it. e. Derive the equation for the demand curve for x if Py=1 and m=100. Carefully graph this demand. j / C: C:,:;,rn c e..f+ecf- Sub tduhon -e~d- = 0 b) ~I tcks J e.&>rri~.., 1 t-ui.?v, IV\ th,,; -s, c-ht>y), s,jew+r~) to 5 h.,tsl.t.y d,e_a;m~i hc::ll\ Q.) Jvo..) SJnc..eJ hy dthn;froh/lhe /n<yme...f.>tf'an-91pn pa.hi neverhab a n ff 4 h i-<e. 5 I r(-j e._, d.) The.. b d~& lme ts M = Px ~ + Py y.. Ai Hie ce:ns mp -, trve. opmmvw\"?.1 ~ j Uvee.a..vse... of pe.rted C.i;mpleM~ S v\os-h fvh\t\ 1,\th, the ~ ~e-1- e_d 2-h CV\ J t,u e de-+- M:: p'\'-,y_ + Pj!i- - er -+~) ~ "t';?<-tion -fur -/he_ &gke Q,\JrVe..,. E n:1 le. C" r,e. ( sl E>fe -= P1l- -1- Py ) (_"fj e,,.. I-/ J N r :

7 The bvd~e_j \w1e 1~ 1Db-=f:k'..t+1'\ 0 pr tee. offe.r c l),ve: > \.Ue.- c.a.n -s b~+ufe.. ~+ l'v\l"t> ~~ ~ d&e..i- \ ty"lk: ov\d 3et I DO::= \l,x, + ~ S1V1c.e ~-=Y Dn~e_ 1 OD -;:.(f1'+ i )-¼ ~ I OD =,¼ Is -#,e. d etn"2-\aj -e_b -a_-hbn. ~+i ~ plttt,v:r pi;rpt>ses~ IB,? ca.111 be. reu_,r;fh~l'\ l ~o - i = F;.,_ 4 ljs 1nj Excel -fo c kt, 2 I cte. +-h \~ re 1a.:l-rt)V\<5 h 1p.J tue ~ Me. foobld,~1 '. t1vl'yl b-e,s IY'I Demand forx X... 0 ::J 20 ;:: ~ Quantity of X

8 6. Casper consumes cocoa and cheese. Cocoa is sold in an unusual way. There is only one supplier, and the more cocoa you buy from him, the higher the price you have to pay per unit. In fact y units of cocoa will cost Casper y 2 dollars. Cheese is sold in the usual way at a price of 2 dollars per unit. Casper s income is 20 dollars and his utility function is U(x, y) = x + 2y, where x is his consumption of cheese and y is his consumption of cocoa. a. Draw Casper s budget set and shade it in. b. Draw some of his indifference curves and label the point that he chooses. c. Calculate the amount of cheese and the amount of cocoa that Casper demands at these prices and this income. Cocoa 7 Problem C Budget Constraint 3 Optimum Indifference Curve Cheese The expenditure on a good is the prices of the good multiplied by the quantity of the good. So, if the expenditure on y is y 2 then P y * y = y 2 and P y = y. Therefore the budget line is 20 = 2x + y 2. To graph this, solve the equation for y and get: Y = (20 2x) 1/2 which is another way of writing the square root of (20 2x). That is graphed as the blue line in the graph above; the budget set would be the curve and the area under it. The indifference curves are a set of straight lines with a slope of 1/2. (so drawing a few of these would be a group of parallel lines with a slope of 1/2). The preference direction is up and to the right, so the red indifference curve on the diagram represents the optimal level of utility given this budget constraint. You could have solved this by using calculus: take the derivative of the budget equation given above to find the slope of the budget line and set that equal to the slope of the indifference curve (= 1/2). Solving that for x gives a value of x* = 8 and y* = 2. Alternatively, you could have set this up in Excel (how I graphed it) and you would see the answer is x*=8 and y* = 2.