Micro Handouts and Quizes [Weston]

8/2/2019 Micro Handouts and Quizes [Weston]

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ECO 3312WestonSpring 2010

Price Elasticity of Demand - Graphic Representation. f J . %

fi . . . I .. fd d %fJ.Q Q1. De mltton: pnce e asncity 0 eman =E= -- = A D ' / j%M tsr. P

2. Handy algebraic manipulation:

QThe slope of a linear demand curve = fJ.P/fJ.QThe slope of a line Oa= Pa l QaThus, E = [slope ofa line Oa]/[slope of the demand curve].

3. Questions.(a) Why do all linear demand curves have variable elasticity?(b) What will a demand curve with constant elasticity (example: E = -1 at every point)look like?4. E=-1 exact! curve.The form of a linear demand curve is: P =a - b where a =vertical intercept, -b =slope,and alb = horizontal intercept.E = -1 => P /Q = -( fJ.PlfJ.Q) = b = (a-bQ)/Q => a lQ - b = b => a lQ =2b= > Q = al2b = one-half the horizontal intercept.


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EC03312Weston S pri ng 2 00 9E xercise 1Show how the current w orld dem and curve for oil w ill change in response to the event.

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Q1 . A v era ge ho useh old incom es increa se inIn di a a nd C hi na .

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ECO 3312 Fall 2010Weston Exercise 1I. In economics scarcity means f .(a) shortages exist in all markets. P~-~-----r---

(b) there must be poor people in rich nations.(c) there is no opportunity cost in using a good. r


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7. Demand curves are negative sloping because(a) everything has its price.(b) human wants are insatiable.(c) most people use price to judge the quality of goods,~ the higher the price of a good, the less people will buy.(e) False. Demand can be negative or positive sloping depending on elasticity .

. . 'fle 8. What is the error in the following argument? "An increased sales tax on gasoline won't reduce~.,\~~~onsumption, because while the higher price will at first reduce demand, the reduced demand wille~entually bring the price back down again. and consumption will return to its former level."~a.(~\\T 4 J A higher price doesn't reduce demand. oemo..n~ 'i. ~\l.a",\'" O e ' r \ H . ' I ~ A e J(b) A reduced demand does not cause lower prices.

(c) The tax-induced price increase may be greater than the price reduction due to the lower demand . (d) The tax-induced price increase will necessarily be greater than the price reduction due to the

,t'.i~"\ lower demand, because demand is never perfectly inelastic.It\'C\~(\~ (e) There is no error.C' ~",'\-1 ~~I'I 9. The demand for any good is likely to be inelastic when

~consumers have few good substitutes for it.< : 6 ) ' it is a manufactured good rather than an agricultural good.(c) it is a luxury rather than a necessity,(d) there are very many producers of the good.(e) people use price as a measure of the quality ofa good.

10. If the university administration plans to raise tuition charges in the belief that this will cause tuitionrevenues to increase, we know(a) they are assuming an elastic demand.( { 1 ) } ) they are assuming an inelastic demand.(c) they cannot succeed because of the law of demand.(d) they must now be losing money.(e) they will only succeed if more students can be enrolled.

11. The principle of c omp a ra tiv e a d va n ta g e says that you will have an advantage in producing something(a) only if you can do it using less resources than someone else.(b) only if your resource costs (labor, rent, etc.) are comparatively lower than those of your

competitors .. . Y r J . if you take advantage of someone else before they take advantage of you.


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ECD 3312WestonSpring 2010

Exercise 21. In the diagram below, which region of the demand curve is elastic and which isinelastic?How do you know?p

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2. Is the algebraic sign of the price elasticity of demand positive, negative, or either waydepending on circumstances? Why? t-(e ~C I\\ ie ~ ( c..~~.(. ~\who1l5

3. A college decides to raise its tuition in order to increase its total revenue.(a) What is the economic reasoning behind this move?(b) Will it work? Explain.


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Exercise 3

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1. A small liberal arts college wants to increase its enrollment. Can it do this byreducing its tuition fees? Why?

2. A small liberal arts college wants to increase its total revenue. Can it do this byreducing its tuition? Why?

3. Because of perfect weather, US farmers grow a record wheat crop. Is this goodnews for farmers? Why?

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ECO 3312Weston Spring 2010Exercise 5p

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1. As you move from point a to point b in the above diagram does Total Revenue(Expenditure) increase or decrease? How do you know? Is Marginal Revenue positive,negative, or zero? How do you know? Is the demand elastic or inelastic? How do youknow? f u lm ~ -+ b ~T P ,1 ' : & \ ' \ \ \ , , ' T~bft'lo.rtitl4l rt.~~ i& fC.~"\~ ...I~ ~a.I\ ~\o.r,);(.

(vJ~~ T R 1 ' JM~ 't~ - t o )2. As you move form point c to point d inthe above diagram does Total Revenue

(Expenditure) increase or decrease? How do you know? Is Marginal Revenue positive,negative, or zero? How do you know? ~rom C':'d ~ ,R ~IM o . ' f " ' j \ i ( 1 0 . \ ~tx1.\,)el ~::I "'t~{~i~w n e " t ' \ de.l'I\a"'~ i:. ; I\t\CI'.\It.!_t o . G .3. Where on the demand curve above will Total Revenue reach its maximum level? How

do you know? Is the demand elastic or inelastic? How do you know?'W \\9(" e d~o.~~ t~Nt. ~~ ' , \ ( ' 1 , \ ~\o.s\\l

4. How are price elasticity, price changes, total revenue, and marginal revenue() systematically related?


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ECO 3312WestonSpring 2009Exercise 6

A production function is a representation of the quantitative relationship between inputs andoutputs in a productive process. The total product of a factor (say labor) is a short-runproduction function. What makes it "short-run" is that at least one other factor is fixed in itsavailable amount. (For example, what happens to the total product of labor as you add more andmore labor to a fixed amount of land?) The table below represents a total product of laborfunction:Units of labor Units of output Marginal AverageProduct of Product ofLabor Labor0 0 Q 01 20 70 ;_t)2 36 \ < . : , I X3 48;' I! 1':04 56 i < :,I5 62 -' tv I),"/

1. Fill inthe Marginal and Average product data.2. Graph this information inthe space provided, with labor on the horizontal axis and outputon the vertical axis.

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ECO 3312Weston

Spring 2009Exercise 7

The Relationship Between Total, Average, and Marginal MagnitudesSuppose you are putting together a basketball team. Thus far you have four playerswhose heights (in inches) are 70, 72, 74, and 76.1.What is the total height of the team? 2'P- "2. What is the average height of the team? 13"You find a new player who is 80 inches tall.3. What is the new total team height? 31 24. What is the new average team height?You find a sixth player who is only 60 inches tall. L \ 31- "S. What is the total team height now?6. What is the average height now?7. What happened to the average height of the team when you added a player who wastaller than the average? !8. What happened to the average height of the team when you added a player who wasshorter than average?9. What do you expect will happen to the average height of the team if you add a playerwhose height is exactly equal to the team average? ~ ">10. Where does the concept of "marginal height" enter this story? f.. , \ " -, ', , .....S, ,- J .. ,._. r .J 11. Make a general statement about the relationship between the "marginal height" andthe average height of the team.12. Make a general statement about the relationship between the average product of laborand the marginal product of labor.13. Make a general statement about the average cost of production and the marginal costof production.


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ECO 3312Weston

Spring 2010Exercise 7

John Hicks has a budget of $200. The price of food is $4 per unit and the price of clothing is $2per unit.1. Draw Hicks' budget line in the space below. Label the intercepts.2. Draw a normal, well-behaved, convex indifference curve that is tangent to Hicks' budget 1ineat one point.3. Indicate the quantities of food and clothing that Hicks will purchase when he has found hisoptimal, affordable combination. 5 0 ~\O\\\;I'I~, l S t~".\4. The price of food decreases to $2 per unit. Draw Hicks' new budget 1ine.5. Draw an indifference curve with the same shape as the one in question #2, but that is tangentto the new budget line.6. Indicate the new optimal bundle of goods. flo e\o~;,,'t I c o ~ ~ ~7. How could you derive Hicks' individual demand curve for food from the information inquestions #3 and #678. How much of the extra food did Hicks demand due to its reduced price, and how much did hedemand due to having an increased real income? , h,~~t( ;1~1f-'j\tA!.

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clothing\00\lC\'~S

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Exercise 61. The following questions refer to the diagram below.(a) Does this consumer prefer bundle a or b?b(b) Does this consumer prefer bundle a or c?C

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2. William S. Jevons and Alfred Marshall both like tea and coffee; however, Jevonsstrongly prefers tea, while Marshall strongly prefers coffee. Which set of indifferencecurves belongs to which person? How do you know?tea tea

coffeeoffee'W\\~j \'-i '. ,J e . ..~Mo~'t ~ ~< i""";~ \t t~We\!


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sco 3312Weston Exercise 11 Spring 20091. What is a price-taker? ~'j ,~.,._. \",~ r,' ',\. . It'.. , 1 \ : " , . . " " (>'

, , ' I I ) .. . ~ _ _ ~ - , ( ' 1-__ ,_.~ ,:~ '. .....2. If a firm is a price-taker in its output markets, what does the demand curve look

like from the standpoint of that individual firm?

3. In the space below draw the individual firm's demand curve.

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4. If a firm is a price-taker, what is that firm's marginal revenue?5. In the diagram above show the firm's marginal revenue curve.6. What level of output should the firm produce in order to earn the maximumprofit?k "\ .. ,~ '\( - r-

1. Profit is total revenue minus total cost. (T I =TR - TC) Show TR and TC in thediagram above. Show the firm's profit.


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ECO 3312 Spring 2010Weston Exercise 81. A theory that assumes consumers can quantify their preferences, for example, that one prefers Coke3.2 times as much as Pepsi, is using the concept of(a) ordinal utility.@ cardinal utility.

(c) diminishing marginal utility.(d) consumer sovereignty.2. The egui-marginal condition in consumption is attained when

(a) each good gives the same utility.(b) the last unit of each good gives the same marginal utility.( ) the last unit of each good gives the same marginal utility per dollar.(d) the same quantities of each good are purchased. ':>-"

_ 1 " \ '" L-_i\ ~ . . . .3. A single indtfference curve shows

(a) various combinations of two goods that a consumer can afford.(b) the best possible combinations of two goods that a consumer can afford.) various combinations of two goods that are equally preferred by a consumer.(d) which combinations of two goods that are preferred to other combinations.

4. Starting from a position of tangency to a normal, well-behaved, convex indifference curve, movingfrom one point to another on a budget line leaves the consumer(a) better off. worse off.(c) neither better nor worse off.(d) either better or worse off, depending on where on the budget line he goes.

5. When the price of one good decreases, with all other prices and money incomes remaining the same(a) the person's real income decreases. the person's real income increases.(c) the person's real income is unaffected.(d) the person's real income is affected only if the good whose price decreased is an inferior good.

6. Themarginal rate of substitution in consumption is a name for the slope of an indifference curve.~(b) a name for the slope of a budget line.(c) the rate at which one good can be exchanged for another at given market prices.(d) how much the consumer wants to buy of each good.

7. If a person has normal, convex, well-behaved indifference curves, the best affordable combination ofthe two goods is found where(a) the indifference curve crosses one of the axes.(b) the marginal utilities of both goods are equal.(c) the budget line equals the equi-marginal condition.@ ) the budget line is tangent to an indifference curve.


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ECO 3312Weston Spring 2010Exercise 10In the space provided draw the Average and Marginal product curves that conespond tothe Total Product Curve shown.

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ECO 3312Weston Exercise 11Spring 2010

In the space provided draw the Average and Marginal product curves that correspond tothe Total Product Curve shown.

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Exercise 121. Plato is a perfectly competitive producer of rye. His cost curves and the demand curve he

faces are shown in the diagram below.(a) Find the quantity of rye Plato must produce in order to maximize his profits.(b) Show graphicaJly Plato's profits when he has arrived at the optimal level of output.

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2. Suppose other people see Plato making profits in the rye business and decide to enter ryegrowing. 17 1 .(a) What effect will this have on the price of rye? r R'.)~ \__\ ~ Me. = \ \ . e(b) At what price will Plato bejust breaking even? Explain. W'"-U "'-L(c) At what price will Plato shut down? Explain. Is there any reason why a firm should .continue to operate in the short-run if the price is below ATe? \0" ~ 0(-'- \,


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ECO 3312Weston Spring 2009Exercise 14Suppose that two firms in a duopolistic market are each trying to decide whether or not toadvertise. The payoffs resulting from their decisions are shown below.

A don't advertise Aadvertise..,B don't advertise ~~~ofit: 5 Q O A profit:\750)B profit: 400 B profit: 0B advertise A profit: 0) A profit: 300B profit: 300 B profit: 200

1.Does A have a dominant strategy? u-~ ,,(_".\-, s c'2. Does B have a dominant strategy? thO --> o ( ( v . \ . 'I\ .. '.).\It,., Of3. Assume that both firms know accurately what the payoffs from each strategy are toeach firm. Even if a firm does not have a dominant strategy, does it have a reasonablestrategy to follow, based on its anticipation of what the other firm will do? I . . . - j I.S -.,/I

tl. lV J4. Is there a Nash equilibrium in this game? ~r..c -, A,,~., AA.J-". 'J

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ECO 3312Weston Spring 2010Exercise 12Corresponding to the average and marginal product curves shown, in the space provided raw thefollowing cost curves:(a) average fixed cost(b) average variable cost

(c) average total cost(d) marginal cost

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ECO 3312Weston Exercise 13

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Spring 2010

What's wrong with this picture? (At least 4 things.)(Hint: Some mistakes are logical impossibilities concerning the curves themselves,others are dues to inconsistencies between the curves. Assume that the Total Productof Labor curve is correct.)Q

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ECO 3312Weston Exercise 13 Spring 2010

What's wrong with this picture? (At least 4 things.)(Hint: Some mistakes are logical impossibilities concerning the curves themselves,others are dues to inconsistencies between the curves. Assume that the Total Productof Labor curve is correct.)

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ECO 3312Weston Fall 2010Exercise 141. Is the f irm represented in the diagram below a perfect competitor? How do you k now?( Y - 5 . . . M./Cfnl"!_J At cClI'L (Jr.-it- Q.M._fyt , l -tf,u ~~f,'~ ~ f'~ f:.u .s ...2. W ha t is this firm 's ma rgina l revenue? - n.o Cof~t.rr3. In the graph show the quantity of output the f irm should produce in order to maxim ize its profit.4. In the graph show the firm 's profit when i t i s max im i zed.

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ECO 3312Weston Exercise 15 Spring 2010

I. In the diagrams below is th e individual f inn making an economic profit't If so showthis in the diagram.2. Is the market shown in the diagram in equilibrium? Why?3. If the market is not in equilibrium show what changes will occur to bring equilibriumabout.$/ $1

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J ( J l ~ Lt.\[ _ f / o 1 / t o

Spring 2010

1. Draw the average fixed, average variable, average total and marginal cost curvescorresponding to the average and marginal product curves shown.Q/L

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reo 3312Weston Spring 2010Exercise 171. In the diagram below find the quantity of output that will allow this monopolist tomaximize his profit. Graphically show this profit,$/Q

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Hints1. What does the marginal revenue curve for a straight-line demand curve look like?2. Itcan be shown that MR = P[l + 1/8], where I': = price elasticity of demand.3. Where is MR positive? Where is it zero? Where is it negative?4. When you find the Q that sets MR =MC, how do you find the Price that enablesthe firm to sell this amount?


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ECO 3312Weston Exercise 11. Suppose that Y =A + bY + I +G.

Spring 2012

Solve this equation specifically for Y (i.e. so that Y is alone on the left-hand side.)Y _ A - I - G o t s: g ' " J '1 - A- -I. - '~ ~ A ~ p~ + I T G r -;> g B ~-/ B

-1\ -~-e~Y = 20 - 5X

2. For the following function:

(a) Find the vertical intercept.~ J . .O

set- l< = 0:. ~ =C\

(b) Find the horizontal intercept.


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Suppose aX + bY = c. In order to draw a graph of tins function in a diagram withY on the vertical axis and X on th horizontal

(a) Solve explicitly for Y._ (b) Find the horizontal intercept._. (c) Find the vertical intercept.(d) Find the slope.

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ECO 3312Weston Exercise 1- AnswersI. Suppose that Y = A + bY + I+ G.

Spring 2012

Solve this equation specifically for Y (i.e. so that Y is alone on the left-hand side.)Y-bY=A+l+GY(I-b)=A+I+GY= 1/(1- b)(A+ I +G)2. For the following function:Y=20- 5X

(a) Find the vertical intercept.X=O=>Y=20

(b) Find the horizontal intercept.Y = 0 => 5X = 20 => x = 4

(c) Find the slope. ayay = -sax =>-=-5ax

(d) Graph this function in the space below.y

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2 3 4 5 6 X3. Suppose aX + bY = c. Inorder to draw a graph of this function in a diagram with Y onthe vertical axis and X on the horizontal,

(a) Solve explicitly for Y. bY = c -aX => Y =~- ~X(b) Find the horizontal intercept. Y = 0 => ~X = ~=> X = ~~ = ~(c) Find the vertical intercept. X = 0 => bY = c => y = ~

. a ~y a(d) Fmd the slope.a)" = -ba x => ~x = -b


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US uKA1"~ , :SLUI"~. ANlJ INTJ!:Kl.:I!:Yl~In graphing a function such as y = f (x). x is placed on the horizontal axis and is known as the

independent variable; y is placed on the vertical axis and is called the dependent uariable. The graph of alinear function is a straight. line. The slope of a line measures the change iny (~y) divided by a change inx (ax). The slope indicates the steepness and direction of a line. The greater the absolute value. of theslope, the steeper the line. A positively sloped line moves up from left to. right; a negatively sloped linemoves down. The slope of a horizontal line. for which ~y = 0, is zero. The slope of a vertical line, forwhich ~ =0, is undefined, i.e., does not exist because division .by zero is impossible. The y intercept isthe point where the graph crosses the y axis; it occurs when x = O. The x intercept is the point wherethe line intersects the x axis; it occurs when y =O. See Problem 1.16.EXAMPLE13. To graph a linear equation such as

Y ea -lx + 3ooe need only find two points which satisfy the equation and connect them by a straight line. Since the graph of alinear function is a straight line, all the points satisfying the equation must lie on the line.To find the y intercept, set x = 0 and solve for y, getting y = -:CO) + 3, y = 3. The y intercept is. the point(x, y) =: (0. 3).To find the x intercept, set y =0 and solve for x,Thus,O = -ix + 3, ix=3, x = 12. The x interceptis the point (x, y) = (12, 0).Then plot the points (0, 3) and (12,0)and connect them by a straight line, as in Fig. I-I,to complete the graph of y =: -ix + 3. See Examples 14 and I S and Problems 1.16to 1.19.

y I I~3

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EXAMPLE14. For a line passing through points (Xl' Yl ) and (x%,y : J , the slope m is calculated as follows:a y Y1 - Ylm=- =.: . . . .: . . . .---=._: .ax x % -Xl

For the line in Fig. 1-1 passing through (0, 3) and (12, 0).a y 0- 3 1m = ax = 12- 0 = - 4

and the vertical intercept can be seen to be the point (0, 3).

GRAPHS, SLOPES, AND INTERCEPTS1.16. Find the x intercept in terms of the parameters of the slope-intercept form of a linear equationy=mx+b. .

Setting Y = 0, O=mx+bmx s -b

bx=--m

Thus, the X intercept of the slope-intercept fonn is (-blm. 0)..

Graph the following equations and indicate their respective slopes and intercepts:(a) 3y + 15x =30 (b) 2y - 6x =12 (el 8y - 2x + 16 = 0 .C d ) 6y + 3x - 18 =0Ex To graph au equation, firs~ set it ~ ..Slo~~~t forin by solving it for y in terms of x: Fromi ample. IS . the ~Iope aud two mtercepts- can then be read directly from the equation, providing threei~ of informatJ~n whereas ?nJy two arc needed to graph a straight line. Sec Fig..I-4and Problems 2.1 to

~'j:: ?b - \6.x~~\t)-5x'

V LV -\-:: ( bh o . . . . . .1, :: - \ - 5 i -:! 0

X - : . d ..


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. .r

c l-~ tilL= Il ""(-) - 81.1' l' (J-)--l- =-= =U1 6- !tl-'9,l l' t - 8 .IX _1:x"1'- =01- = ll-l = I.{ _ 1:.{ =.IU

l~i~A\'1'1~ldDmX3 mOlJ ~tW0J ~ql U! iunnl~ns (D). iSl '~)'( - ,) (;)!(9 ') '(~ l '1-) (q) !(Z'S) '(ZI '17) ( v ) qSnonp StJ!SS8d uop:>Ul lJ . m : J U ! l ~ql )0 a u odo rs ~tp pUH " S I " I

(q)

(0 '9) :lr;b:)nllI! x( '0): lr;b:)J~llI!.{f- =un:lCiIS

+xf-=.{SI + X- =.{9

o = SI - X + .{9 (P )(0 'l-):d~llI! x(9 '0) :ld:lOJ~llI!.{ = III ooolS9 +x={

Z I + X9= A ZZ I = X9-.A, (q)

(0 'S) :l~llI! x(Z- '0) =lcbomlI! Af =III OOOlS'

Z - x f ={91-XZ =.{So = 91+ Xl -AS (!)

(0 ' " z : ) :lcbo~1I! x(01 '0) :lcbonllI! IfS- = IU OOOIS

01 + xS- =O+xSl- =A

O= rSI + A (D )

(p) (.1)I i (z- '0) .~/; I-

X 9 S " ( Z 1 ix 01 I i . . . . . .V" Z(0 '9) . . . . . . . . " "(0'8) X I1 1-' i--.. z ;.:;;;:w ! z -t- = III f"'-.r-.,. Ic E -(f '0) ". s l

(q)


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ECO 3312Weston Spring 2012Exercise 3

-

How do you know?

l.In.the diagram below, which region of the demand curve is elastic and which isinelastic] J')_ ' 1 -.~~- . . . . : : .

~\J a .: f/

Q6

2. Is th: algebr~c sign of the price elasticity of deman~ po~itive, negative, or either way, .r i . \ -depend~~~o~Clrcumstances? Why? t ' l . ~CAl r i~ l0 lo lc ~ -)_ e(_ feo6l. ~ uq\.~\J . / to",~~-r-3. A college decides to raise its tuition i~a-rder to increase its total re~enue. ..(a) Whatis the economic reasoning behind this move? a s P{ z; ( \ ' \ . O R .(b) Will it work? Explain. ,.1Q 0 . -e . ,M(A/\ (jI~

1\ D \ ~( (ol\-{_Ot~uJ..v. '~fV\.fJI",_;a.J (,;o;-.'.()..V'O.. J~'('\Le. -\1\ e.\~L,


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ECO 3312Weston Price Elasticity of Demand - Graphic Representation Spring 2012

I. Definition: price elasticity of demand = e = %L lQ = Ll%%t1P L lP jp 'dQ ,c: I .. IQor lor point e astictty E = dP /p

2. Handy algebraic manipulation:_ dQ /Q _ dQ P PdQ P/QE------------dP /p Q dP - Q dP - dP/dQ - - - - - _ . -

p

o Q JThe general formula for a linear demand curve is P = a - bQ.The slope of a linear demand curve = :~The slope of a line Om= Pm/ QmThus, E =[slope of a line Om]/[slope of the demand curve].3. Questions.(a) Why do all linear demand curves have variable elasticity? ) t F(b) What will a demand curve with constant elasticity (example: E = -1 at every point) look like?4. E = -I exactly halfway along a linear demand curve.The form of a linear demand curve is: P = a - bQ, where a = vertical intercept, -b = slope, and alb= horizontal intercept.dP a-bQ ( a ) a 1e= -I=>P/Q=-dQ=b=-Q -= 'Q-b ~ 'Q=2b~Q=2bwhich is one-half the horizontal intercept.


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ECO 3 312

t~\\~~noSpri ng 2 01 2Weston Exercise 4S uppose y ou h ave a specific dem and f unction: P = 100 - O .5Q .I. Wha t i s the vertica l intercept? --

1002 . Wh at is th e h orizo nta l in terce pt?100,/.5" = :: aoo3 . W ha t is the slope?

~'j/A)( -?> .. " S4. T h e tota l revenue f unction (T R ) show s tota l revenue a s a f unction of the level of output Q. T his isconventiona lly dra wn w ith T R on the vertica l a xis a nd Q on the horizonta l. W ha t is the tota l revenue (T R )f un ctio n g en era te d b y th is d em a nd c urv e?

5. T he m argina l revenue is d : : . Wh at is th e m a rg in al re ven ue f un ctio n f or th is d ~m a nd cu rv e?. r., ..6 . D r aw the tota l reven ujfunctio n, the dem and curve a nd the m argina l revenue f unction in the spa cesbelow . \ L7TR:; fC~)s

$/Qo

TRAp)(~)T~: (100- . 5 ~C~ )" T ' f < = - I O O Q - 0 1 5 Q)..

0 -= 101.) :J_Q.o : 100Q z 100


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( J ' J i_~ ) 0 0 ~ - J(a]S/---Ool ~~

.

( J _ O \ - , DU - co \ :: 0~ - 00\ @_'2 'C.S ~'f) G O f > ~ Q-J.C D ) 'G S' - 00 \) ::."(\ 1

( _ y ~ \ _ -X ) 0G ' 2 ~ -1]0(7 l -,oS'

D S~- 00' ~0-- - -_ -


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Spring 2012CO 3312Weston Exercise 4 - AnswersSuppose you have a specific demand function: P = 100 - O.5Q.I. What is the vertical intercept? 1002. What is the horizontal intercept? Set P = O. Then O.5Q = It J, s()Q ~ 2003. What is the slope? :: = -0.54. The total revenue function (TR) shows total revenue as a fun, lion of the level of output Q. This isconventionally drawn with TR on the vertical axis and Q on the aorizontal , What is the total revenue (TR)function generated by this demand curve? TR =100Q _0.5Ql5. The marginal revenue is ~R. What is the marginal revenue imction for this demand curve?

MR=~ = 100 - (2)0. SQZ-l = 100 - QdQ6. Draw the total revenue function, the demand curve and the m rginal revenue function in the spacesbelow.

$ /Q

$

Q


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Itl & . ,~--' / LO bl - S J 'lQ ~ ~ .--A h C j - v "'P~ '-j \-'17 -

" ?~S ~ "t){ "'W"til ~ ""'b~-" / \ " 1 . . .0 " ti t ~ O Q S ; , X 'h \ t 1

po 03 qm~:;lJ O A l!I!ln J RU!3 .mw :;ltp PU !iI (e)Z po03 JO possossod Al!lmmb = 'X1 poof JO posssssod Al!luenb = IX

AlU!ln mOl = n : :; ll: ;lt JA \.:U O!P UllJ Alm ln 3 u!M on oJ: ;l tp Aq P: ;>lU:; lS : ;l ld : ;l l; lq t rao spoof OMl o i p ..m3:; ll lJ l !M S: ;lOU:; ll ;} J :; ll dS, l: ;lwnSUOO V Z

P ' \ < t : " : l t O .9 ~~~ tbes ~ -UOlS:;l.A\

ZI ooa


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ECO 3312 Spring 2012

\

Weston Multi-variable CalculusPartial Derivatives Thus far we have found derivatives of functions with two variables, for example Y = f{X).Sometimes we must consider relationships involving three or more variables. We do this by

us~ng the technique of partial derivatives, written :~ or fx . In order to find a partial derivative treat all variables, except the one with respect to which you

are differentiating, as constants. For example ifZ = 5X2+ 2XY + y3, :~ = lOX + 2Y,and az =2X + 3y2a y .

The Cobb-Douglas Function The general form of a Cobb-Douglas function is Y = AX f x f . This function has many

convenient mathematical properties that cause it to be useful for representing utility functions andproduction functions. V V . Ifwe defme a total utility function as U = Q 1 2Q 2 2, then the marginal utility of good I isau 1 -1/ 1/ au 1 1/ -1/2MU1 = 8Ql = iQ1 2Q 2 2 and the marginal utility of good two is MU2 = aQ z =iQ1 2Q 2 .

Total Differential of a Function The total differential of a function breaks down the change in the dependent variable into the sum

of the changes caused by changes in the independent variables. If Z is a function of X and Y, then dZ = :~ dX + :~dY .

The Slope of an Indifference Curve The total differential ofa total utility function is dU =: : 1 dQ l + :~ dQ 2 =MU1dQI +MU2dQ2. By definition there is no change in total utility on an indifference curve. Therefore dU = o . dU = 0 = MU1dQI +MU2dQ2 = > MU1dQI = - MU2dQ2 = > :~ ~ = - : ~ : . Thus, the slope of an indifference curve is the negative ratio of the marginal utilities of the two

goods.

- z ; ~ ( ' ( / ~ )" Z : ~ ~ '5~ .s .. t o Xj 1- ~ (

:; \D X + Z j


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"

v,~ u,_~-l .... .l. z t'f ~ ~\ "Y \~ < C _ f-r \ . - e e( v . x . ' " ' . f " L " , ' l y )J : : "


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/((; 260 s: 2 . . . Q I --I '2 . .S I . .V Z .Find: D-(a) the vertical intercept. -.-- L \ f\ I I .: !06 S 0p e = - ~(b) the horizontal intercept. o ft f r : _-? 6 . "2 -(c) the slope., ' I. . _ lo t,I ' 'J~-;.-5 ~ Q , - \00 - ~ I q nf )\..(7.

beer-100

Q , 125

7 S

25

25 I 50 75 100 125meat(d) Draw Senior's budget line in the space above. / s: vS--Q ~\,.(e) Find Senior's optimal combination of beer and meat. C--"~(f) Suppose the price of meat decreases to $1.50 per pound. I f = qz, ~ t . S "I

(i) Draw the new budget line. , 1 -(ii) What is Senior's new optimal consumption bundle? - 0 ~e .t> c.. tQ .. (g) How can we go from the above exercise to Senior's individual demand curves?


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Spring 2012

33

u ~~ 1..,0 - - - . _( I . .

"3.5 '\~ 'L -- ),_ ... ./

John Hicks has a budget of $200. The price of food is $4 per unit and the price ofclothing is $2 per unit. Q t .. . : : 7.O~ _ '- f n

'Z - '-\' (1. Find the best affordable combination of the tw~oods, given Hicks' preferences, inthe diagram below. How much food will Hicks purchase? (0 c) 7 . C) .I ,I2. Show how Hicks' best affordable combination changes when the price of food

decreases to $2 per unit. How much food will he buy now? r- Z~ ~. a ::> I ' 2. . \c.. ~ -~ 0,3. Draw a budget line that shows the price ratio in problem #2, but that permits Hicksonly the same teal income he had in problem #1. Why would you want to do this? Howmuch food wilt'HickS'pur


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ECO 3312Weston

Spring 2012Quiz2

1. Which ofthe following best describes the concept of marginal?) erage.

tal.important.. cremental.

2. Diminishing marginal utility means that as a consumer obtains more ofa goodhe total utility decreases.he marginal utility decreases.he total utility becomes negative.e...,marginalutility becomes negative.

3. Assume that the marginal cost of clean air increases, as the air gets cleaner, while the marginal benefitdecreases. The optimal level of clean air occurs where the(a) marginal benefit is zero.(b) m~_ i"halcost is zero.(c) th difference between marginal cost and marginal benefit is maximized.@).1 arginal cost equals the marginal benefit.(er total cost equals the total benefit.

4. Which of the/following is the best explanation for the fact that an ounce of diamonds is usually morevaluable ~~ an ounce of water?(a) Dia fonds are intrinsically valuable, while water is not.(b) Di monds give more total utility than water.

re diamonds that people buy give a higher marginal utility than most of the water that they buy,ecause water is much more plentiful.

(d) People have an irrational desire for diamonds./(e) People fail to appreciate the importance of water.


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ECO 3312Weston Spring 2012Quiz 31. A line representing all the possible combinations that a consumer can afford to buy, given herincome and prices of the two goods, is called(a) an indi erence curve.a b get line.

(c e marginal rate of substitution.(d) the income-consumption line.(e) the price-consumption line.

2. If th equi-marginal condition is satisfied we know thatthe marginal utility of the last unit acquired of each good is equal.e total utility of each good is equal.

(C l it 1 ot possible for the consumer to obtain a better affordable combination of goods.-1he consumer must be spending her entire budget on one good; hence, the best affordablecombination is found on the margin of the graph.

(e) this situation will not last very long because it creates an arbitrage opportunity.3. When the price of one good decreases, with all other prices and money income remaining thesame,

the c nsumer must buy more of the good whose price decreased in order to satisfy thee i-marginal condition.

(b) the consumer must buy less of the good whose price decreased in order to satisfy theequi-marginal condition:(c) the consumer will but more of the good whose price decreased only ifher demand for

that good is price elastic.(d) it is impossible to know what the consumer will do, since preferences are subjective.

4. Indifference curves further from the origin are preferred to indifference curves closer to theorigin because economists generally assume

diminishing marginal utility.more is preferred to less.) that most goods can substitute to some degree for most other goods.preferences can be ranked but not quantified._..e) lse. Distance from the origin has nothing to do with whether on indifference curve ispre erred to another.


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ECO 3312Weston

~ \ \ ~ Y v v Spring 2012

Simple Derivative RulesNotationThe first derivative ofa function is the slope of that function at a point. IfY is a function of X

:~= lim M~ O ::. This can also be written f' (X ) or fx.The Rules1. Constant: Y = cdY dY- =0 Ex.) Y = 4 - = 0dX 'dX

2. Linear function: Y =a + bX/dY---~ dY( - = b) Ex.) Y =200 + lOX, - = 10dX~ dX3. Power function Y =aXP

dY = paXP-l Ex.) Y =42X3 dY = 126X2dX 'dX4. Sums and Differences: Y = f(x) + g(x)

dY = { , (X) + g ' (X)dXThe following are part of the standard toolkit of simple derivatives, though we are unlikely to usethem in this course.5. Products: Y =f(X)g(X)

: : = f (X )g ' (X) + { ' (X)g (X)6. Chain Rule: Y = feZ) where Z = g(X) => Y = f[g(X)]

dY dY dZ-=--dX dZdX7. Quotient Rule: Y = f(X)/g(X)

dY g(X)f' (X)- f(X)g' (X)dX = g(X)2

Higher Order DerivativesSince the derivative of a function is itself a function, it is also possible to find the derivative ofthe derivative. This is called the second derivative, it is written ::~. It is also possible to findthird, fourth, etc. derivatives.Example: Y =25X3

dY =75X2 d2y = 150X d3y = 150 d4y =0dX dX2 dX3 dX4


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ECO 3312Weston Spring 2012Quiz 11. A demand function is given by the equation: P =200 - SQ.

(a) Find the slope of this demand curve.

t r f z;L Q = hoI: 't. iAi " 0 = "1 '0 - Sq Q . : : : "leo!t;5Q:~~ /

(b) The total revenue associated with a demand curve is the total amount received by sellers ofthe product. TR =PQ. Find the total revenue function that is generated by the above demandfunction.

:::.'z DCO :: !-'\()! \:cQ ". - b= = - S . e . .t p~6oc : bQQ _ z: (Alb

-- -n_ ' ) o e ( y C c 6 ' ~ )t v ~G ~ 0 1 \


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J J~U~J _ de 'U _,vf(x) Vl dx\Q~fQ.

v e h , t L = _LV\- P - I - ~ h 9~ [ e _ ~ -r~J u \ CtnfJ d [Lr-\Q]- 0\.+ =: r d+ + d . - - I_ ~ zr' y p c~+ l' ' / G ( 1 - l ~~ J - \ J~ ~: (' % ~ f )

r J j 6 ~ ~ ? '1 o ~ r; i f~ \1 6 b~ \ ~ \C f o ~ f )% 6.~ ).()


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ECO 3312 Spring 2012Weston Things to Look For: Chapter 4,6Chapter 6 . . I ~e - _".r" ,.../ p~......Jmer1ca. ,.. t.f'l__ oi l ' >3. Draw a perfectly elastic demand curve. ~ L_,

~ 4. Is elasticity the same as the slope of a demand curve?5. Why does a linear demand curve have variable elasticity? E"er~\IC'\wr d2mond c.cwe i~ 1/,2 e'Qdi(.-~~;I6. Why must a demand curve with constant elasticity be curved?7. How do you calculate total revenue (expenditure)?8. How can you graphically represent the total expenditure (revenue) in a demand curve

diagram if you know the price ofa good?9. Describe the relationship between price elasticity and total revenue for a linear demand

curve as you move from the origin in the direction of larger quantities.10. What determines whether demand for a good is elastic or inelastic?11. What is the cross-price elasticity of demand?12. What is the income elasticity of demand?13. What is the price elasticity of supply?14. Draw a supply curve that is perfectly inelastic with respect to price.15. Why would the supply of a good be price inelastic?16. How does price elasticity affect a store's ability to pass the increase in the cigarette tax on

to consumers?Chapter 4

I. What is consumer surplus?2. What does consumer surplus have to do with people's willingness to pay for something?3. How does a price increase for a good affect consumer surplus?4. What is producer surplus?5. What does cost have to do with producer surplus?6. Will a price ceiling increase total consumer surplus? Explain.7. Will a price floor increase total producer surplus? Explain.


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r , f I O , . r - demo."d cvr\lQ_P : : r 0.. .. '0 ~

6. ~0/o l : JQ% ~ P ~

l tA ~ \ - \ c . \ ~ \ > :i~\ V\ e,\ C l S 4 I c \ - t \ s : :L

? I < . - ( - \ N . . _ . J...o~ ' " ' a ou C \ _ v - e _~t\. CO II e_ ~c .... - -\- V u- . . Q . c . . -1l.--\(\STt(" ctno\W'\J. Curve

Q~ (Ct.Sti~i~ 4 RQ _ " . e ~ . J e .-7TR = ~Q: : : 20 >


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EC D 3312Weston Spring 2012Things to Look For: Chapter 111. What are indifference curves? If two commodity bundles a and b are on the sameindifference curve, what can you say about the consumer's preferences with respect tothese two bundles?2. Inan indifference curve diagram how do you show that one bundle is preferred overanother?3. Why are indifference curves negatively sloped? What would a positive slopingindifference curve represent?4. Why do indifference curves have a convex shape?? Why is the slope of an indifference curve called the "marginal rate of substitution"?6. How do you locate the consumer's optimum affordable consumption bundle in adiagram ~howing her indifference curves and budget constraint?.., MU MU MU7. The book (p.261) defines the o ptim a l co nsumptio n ru le as:__ I = __ 2 = . . . = _ _ n~ P 2 P nThis is also known as the equ i-ma rg in a l c onditio n in con sump tio n.Why must the (MU/P) ratio for each good purchased be equal for a consumption bundleto be optimal? How do you know that improvement is possible if they are not equal?8. Use the optimal consumption rule to explain why demand curves are negative sloping.9. Draw a set of indifference curves for a consumer who is neutral toward the goodrepresented on the vertical axis. (That is, obtaining more of the good or giving up someof the good does not place him on a more preferred indifference c.urve.) Repeat the'exercise for a consumer who is neutral toward the good represented on the horizontalaxis.10. Joan Robinson and Henry Sidgwick both like wine and beer; however Joan stronglyprefers wine while Henry strongly prefers beer. Draw Joan and Henry's indifferencecurves.


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"UMOqS ~A.l11;) lonpoJd pno 1 . ~1.{ loi puodsorroo ltlql S~A.l110 ionpord reu !8 .mw pu a :}8tU~AV~1pM,lUP popixord aosds ~1p U J11 ~S!OJ~XH UOlS~M.

Z I O ;)H

~c' C..:::: c. p{~IXJ c )\ !~)J\-0 .1

.~\)\'}I ,) - Y - .. . J ) \ .r

-,~f\ ,?y pnFXJJd bl\v ~\.j\. \\\(Y)


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IIf' n i!)p _ 1 " ' ' ' ' ' Il}J-.?vJ16/?/\ _ > 1 ~ " "~ 4 '9~ ~\Ol?d - DiJX,~ L l l \ . l , ; { 1h/J ). - If ' '2} (J.j. ~ (\~ I

1(""\" J/\ - ~ \ q " , , ? , I 7 J ~ ~ I'>1J.:r ').::1 _ pa-)(.I:!il~')\ 11"10.1 I,~"",n"'1.l. II

I,iI

~ ~ - - - - - - - - - - - - ~

7;(\)() :J-J("(l~ Q } \ O d . t " O \ o ~hp5A()(\ \J 1 - - u f \ J oj - + S O U I

" "c:Ll ~ o d Q \ s = if1 6 'f ::;S 3 b \A I " v ;J V \ I 'J . , - v o u v . .~ ~ L 9 - ' J \l C ) .. . o ( ] - \ - \J~ ~

.Pq'Q") ~ -+" ,"~~eld ~'\J ~ - a '\ ' ) w -p~",~cr~:" \ ~~~~"

~?vc:} vP,'t?I"I,\?OJd U('l~~JQ,-\~ 0(11)1)t ,,~ ,/' 1)00"' 9-" +:>0 l"C>ld 1 r " " - "OJ -

-;;'1\ .)(Y-;) +')'(\oOGld


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Questions: Ch.12 and 171. What is aproductionfunction?2. What is the difference betweenflxed and variable inputs?3. What defines the long-run and the short-run?4. What relationship does the total product curve represent? What are the variables on

the axes of a graph of a total product curve?5. Define the marginal product of labor. What are the variables on the axes ofa graphof a marginal product curve?6. What does it mean for a production function to exhibit diminishing returns to labor?Draw a total product of labor curve with diminishing returns to labor. Draw a

marginal product of labor curve With diminishing returns to labor.7. Define: average fixed cost (AFC), average variable cost (AVC), average total cost

(ATe), marginal cost (MC).8. What does an AFC curve look like? Why? What are the variables on the axes of an

AFCcurve?9. If wages are the only variable cost and the marginal product of labor decreases asmore labor is added to the production process, what will the marginal cost curve look

like? Why?10. Why are ATC curves usually U-shaped?11. What is the difference between short-run and long-run costs?12. What are economies of scalel How do economies of scale affect cost curves?Chapter 17: pp.451-4541. What are network externalities? Give some examples of products in which network

externalities are significant.2. What is positive feedback? What role does positive feedback play in network

externalities?3. How might network externalities be a basis for a natural monopoly?


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ECO 3312Weston Spring 2012Exercise 9The Relationship Between Total, Average, and Marginal MagnitudesSuppose you are putting together a basketball team. Thus far you have four playerswhose heights (in inches) are 70, 72, 74, and 76.1. What is the total height of the team? a q a iY' \2. What is the average height of the team? 73 , Y)You fmd a new player who is 80 inches tall.3. What is the new total team height?3"12.4. What is the new average team height?

7Lf, ," t ;1 )You fmd a sixth player who is only 60 inches tall.5. What is the total team height now?

'-f3l i'"6. What is the average height now?7 d . _ ; f " )

7. What happened to the average height of the team when you added a player who wastaller than the average? T h A . . 0. \ . I 1 j i1\ c1"eC~~ec. \8. What happened to the average height of the team when you added a player who wasshorter than average? IT~ c,vlj c .\ e c . reed; eo-9. What do you expect will happen to the average height of the team if you add a playerwhose height is exactly equal to the team average?

~ O \ J : J _ 1 . ) '- \" \ \ s t - t A ' 1 (M("J. . . (A.V\." 'r10.Where does the concept of "margmal height" enter this story?'VIe c. (Y\~, - \ 1 t \ Q . . . 0.v3. ' c.5


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ECO 3312 Spring 2012Weston Exercise 10In the space provided draw the Average and Marginal product curves that correspond tothe Total Product Curve shown.

QIL

Q

L

L


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EC03312 Spring 2012Weston Exam 1 - AnswersMultiple Choice (percentage of class who missed)1. a (17) 2.e (6S) 3.b (17) 4.c (21) 5.a (7) 6.a (24)7.b (10) S.b (10) 9.d (3) IO.b (10) l1.d (0) 12.b (24)13.d (45) 14.c (17) 15.d (17) 16.e (10) 17.a (24) lS.c (21)19.d (28) 20.a (66)Questions Missed with Alarming Frequency2. The price elasticity of demand is defined as: E =::~.By the law of demand P and Q always move in opposite directions; that is to say. if %LlP 0 and vice versa. Thus price elasticity of demand is always negative.13. To say that an individual is indifferent among two or more combinations of two goods is the same assaying that the total utility of all the combinations on an indifference curve is the same.20. When a price decreases, with the other price and the consumer's income remaining constant, theconsumer experiences an increase in real income. If the good whose price decreased is normal, both theprice decrease and the income increase cause the consumer to demand more of the good. If the good isinferior, the income effect of a price decrease is negative. Thus it is possible for the negative incomeeffect to outweigh the positive substitution effect of a price decrease. This is what happens in the case ofa Giffen good. Most goods are not Giffen goods. So it must be the case the positive substitution effect ofa price decrease generally outweighs the negative income effect. (See pp.263-265; 292-297.)Problems and Short Essays1. The idea of a budget is that the sum of one's expenditures must be less than or equal to the amount onehas to spend. or: B ::;;P i Qi + P2 Q2, where expenditure for each good is the number of units of the goodtimes the price of the good, and we have simplified to include only two goods. The budget line is thelimit of possible expenditures and is written B =P1QI + P2~' Since, by convention, we draw the budgetline and indifference curves in a space with Q I on the horizontal axis and Q 2 on the vertical, in order towrite the budget equation in a form that allows us easily to graph it, we want to show Qz as a function ofQt. A little algebra gives us:

Distribution of Scores90s-3 i i lo80s-13 '"70s-6 J0s-5 {~50s-2

The slope is

Alternatively, ifone is on the budget line the only way to get more of one good is to give up some of theother. The negative of the price ratio tells the rate at which this can be done. If, for example, theconsumer wants more of good 1, she must sacrifice some of good 2. If the price of good 1 is $2 a unitand the price of good 2 is $4 a unit, then she must sacrifice ~ units of good 2 for every additional unit ofgood 1 she obtains.

dP2. (a) slope =dQ = -2.(b) TR = PQ = (100 - 2Q)Q = 100Q - 2Q2 .d TR(c)MR= -=100-4Q.dQ


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(d)$/Q10 0

25 a03 . E xp la in w hy a lin ea r d em a nd c urv e m us t h av e v aria ble p ric e ela sticity .

D e fin itio n o f th e p rice ela sticity o f d em a nd : = %6Q = : : , 1 Q %dP PH a nd y m a nip ula tio n s o th at ela sticity is ex press ed in term s o f tw o slo pes th at Ian see in a dema nd curve d.QIQ p /Qdiagram: E = 7 I P I , =srr=P IdQ

P/Q is the slope of a line dra wn from the origin to a ny point on the dem and curve. dP/dQ is the slope of thed emand c urve .H th e d em a nd cu rv e is lin ea r dP/dQ i s cons tan t.F or a ny nega tive sloping dem and curve, a s you m ove from the origin to the right, P is decrea sing a nd Q isi ncreas i ng ; the re fore P/Q i s decreasing .

dQ, P, . hSo if : E = Q = IQ = slope of a line from the origin = uarlable that decreases as you moue to the Tlg t ' " " i I P J ; dP IdQ slope Of the demand rune constantthen ela sticity of a linea r dem and curve m ust va ry f rom point to point.F or p rice e la sticity to be consta nt, the slope of the dem and curve m ust va ry a s P/Q v a ri es f or d : ~ to

IdQ

r ema in cons tan t.S ee the h an do ut " Price E la stic ity o f D em an d - G r a ph ic R ep re sen ta tio n"4. U tility is a function of two goods: U = f (Q . .Q : z ).

T he tota l dif ferentia l of a function decom poses the tota l cha nge of a function into the com ponent cha ngesca used by cha nges of the tw o independent va ria bles. In this ca se:au audU = aQ l dQ l + a Q2 dQ 2 = M U1dQ l + MU2dQ2 ' B y convention indif ference curves a re drawn in a spa ce w ith Q z o n the vertica l axis a nd Q I on thehorizontal . Any slope in a space w ith Qz on the vertica l a nd Q I on the horizonta l w ill ha ve a rise/run in term s of

dQ 2/ dQt' B y definition there is no cha nge in tota l utility a long a n indifference curve. T o pla ce ourselves on a nin dif feren ce cu rv e w e s et d U =O. HdU=O=M UtdQt +M U2dQ 2 th en MU1dQ I= -MUldQ z. Solving for the slope:

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