pair是什么意思Chapter1NAME
The Market
Introduction.The problems in this chapter examine some variations on the apartment market described in the text.In most of the problems we work with the true demand curve constructed from the rervation prices of the consumers rather than the“smoothed”demand curve that we ud in the text.
Remember that the rervation price of a consumer is that price where he is just indifferent between renting or not renting the apartment. At anyprice below the rervation price the consumer will demand one apartment,at anyprice above the rervation price the consumer will de-mand zero apartments,and exactlyat the rervation price the consumer will be indifferent between having zero or one apartment.
You should also obrve that when demand curves have the“stair-ca”shape ud here,there will typically be a range of prices where supplyequals demand.Thus we will ask for the the highest and lowest price in the range.
1.1(3)Suppo that we have8people who want to rent an apartment. Their rervation prices are given below.(To keep the numbers small, think of the numbers as being dailyrent pay ments.)
Person=A B C D E F G H
Price=402530351018155
(a)Plot the market demand curve in the following graph.(Hint:When the market price is equal to some consumer i’s rervation price,there will be two different quantities of apartments demanded,since consumer i will be indifferent between having or not having an apartment.)2THE MARKET(Ch.1)
012345678
10
20
30
40
60
50
Price
宁少阳Apartments
(b)Suppo the supplyof apartments isfixed at5units.In this ca there is a whole range of prices that will be equilibrium prices.What is the highest price that would make the demand for apartments equal to5 units?$18.
(c)What is the lowest price that would make the market demand equal to5units?$15.
(d)With a supplyof4apartments,which of the people A–H end up getting apartments?A,B,C,D.
(e)What if the supplyof apartments increas to6units.What is the range of equilibrium prices?$10to$15.
1.2(3)Suppo that there are originally5units in the market and that 1of them is turned into a condominium.
(a)Suppo that person A decides to buythe condominium.What will be the highest price at which the demand for apartments will equal the supplyof apartments?What will be the lowest price?Enter y our an-swers in column A,in the table.Then calculate the equilibrium prices of apartments if B,C,...,decide to buythe condominium.
NAME3
Person A B C D E F G H High price1818181825252525 Low price1515151518151818 (b)Suppo that there were two people at each rervation price and10 apartments.What is the highest price at which demand equals supply?
18.Suppo that one of the apartments was turned into a condo-minium.Is that price still an equilibrium price?Yes.
1.3(2)Suppo now that a monopolist owns all the apartments and that
he is trying to determine which price and quantity maximize his revenues.
(a)Fill in the box with the maximum price and revenue that the monop-
olist can make if he rents1,2,...,8apartments.(Assume that he must charge one price for all apartments.)
Number12345678 Price403530251815105 Revenue40709010090907040
(b)Which of the people A–F would get apartments?A,B,C,D.
(c)If the monopolist were required bylaw to rent exactly5apartments, what price would he charge to maximize his revenue?$18.
美女老虎机(d)Who would get apartments?A,B,C,D,F.
(e)If this landlord could charge each individual a different price,and he
knew the rervation prices of all the individuals,what is the maximum revenue he could make if he r
ented all5apartments?$148.
(f)If5apartments were rented,which individuals would get the apart-ments?A,B,C,D,F.
1.4(2)Suppo that there are5apartments to be rented and that the cityrent-control board ts a maximum rent of$9.Further suppo that people A,B,C,D,and E manage to get an apartment,while F,G,and
turns me on
H are frozen out.4THE MARKET(Ch.1)
(a)If subletting is legal—or,at least,practiced—who will sublet to whom
in equilibrium?(Assume that people who sublet can evade the cityrent-control restrictions.)E,who is willing to payonly
$10for an apartment would sublet to F,
who is willing to pay$18.
(b)What will be the maximum amount that can be charged for the sublet payment?$18.
(c)If you have rent control with unlimited subletting allowed,which of
the consumers described above will end up in the5apartments?A,
B,C,D,F.
(d)How does this compare to the market outcome?It’s the same.
1.5(2)In the text we argued that a tax on landlords would not get
pasd along to the renters.What would happen if instead the tax was
脱蜡
impod on renters?
(a)To answer this question,consider the group of people in Problem1.1.
What is the maximum that theywould be willing to payto the landlord
if theyeach had to paya$5tax on apartments to the city?Fill in the
box below with the rervation prices.
Person A B C D E F G H Rervation Price35202530513100 (b)Using this information determine the maximum equilibrium price if
there are5apartments to be rented.$13.
(c)Of cour,the total price a renter pays consists of his or her rent plus
the tax.This amount is$18.
(d)How does this compare to what happens if the tax is levied on the landlords?It’s the same.
Chapter 2
NAME
Budget Constraint
Introduction.The workouts are designed to build your skills in de-scribing economic situations with graphs and algebra.Budget ts are a good place to start,becau both the algebra and the graphing are very easy.Where there are just two goods,a consumer who consumes x 1units of good
1and x 2units of good 2is said to consume the consumption bun-dle ,(x 1,x 2).Anyconsumption bundle can be reprented bya point on a two-dimensional graph with quantities of good 1on the horizontal axis and quantities of good 2on the vertical axis.If the prices are p 1for good 1and p 2for good 2,and if the consumer has income m ,then she can afford anyconsumption bundle,(x 1,x 2),such that p 1x 1+p 2x 2≤m .On a graph,the budget line is just the line gment with equation p 1x 1+p 2x 2=m and with x 1and x 2both nonnegative.The budget line is the boundary of the budget t .All of the points that the consumer can afford lie on one side of the line and all of the points that the consumer cannot afford lie on the other.
If you know prices and income,you can construct a consumer’s bud-get line byfinding two commoditybundles that she can “just afford”and drawing the straight line that runs through both points.
Example:Myrtle has 50dollars to spend.She consumes only apples and bananas.Apples cost 2dollars each and bananas cost 1dollar each.You are to graph her budget line,where apples are measured on the horizontal axis and bananas on the vertical axis.Notice that if she spends all of her income on apples,she can afford 25apples and no bananas.Therefore her budget line goes through the point (25,0)on the horizontal axis.If she spends all of her income on bananas,she can afford 50b
ananas and no apples.Therfore her budget line also pass throught the point (0,50)on the vertical axis.Mark the two points on your graph.Then draw a straight line between them.This is Myrtle’s budget line.
What if you are not told prices or income,but you know two com-moditybundles that the consumer can just afford?Then,if there are just two commodities,you know that a unique line can be drawn through two points,so you have enough information to draw the budget line.
Example:Laurel consumes onlyale and bread.If she spends all of her income,she can just afford 20bottles of ale and 5loaves of bread.Another commoditybundle that she can afford if she spends her entire income is 10bottles of ale and 10loaves of bread.If the price of ale is 1dollar per bottle,how much moneydoes she have to spend?You could solve this problem graphically.Measure ale on the horizontal axis and bread on the vertical axis.Plot the two points,(20,5)and (10,10),that you know to be on the budget line.Draw the straight line between the points and extend the line to the horizontal axis.This point denotes the amount of
6BUDGET CONSTRAINT (Ch.2)
ale Laurel can afford if she spends all of her moneyon ale.Since ale costs 1dollar a bottle,her income 菲利普艾斯特中学
in dollars is equal to the largest number of bottles she can afford.Alternatively,you can reason as follows.Since the bundles (20,5)and (10,10)cost the same,it must be that giving up 10bottles of ale makes her able to afford an extra 5loaves of bread.So bread costs twice as much as ale.The price of ale is 1dollar,so the price of bread is 2dollars.The bundle (20,5)costs as much as her income.Therefore her income must be 20×1+5×2=30.
When you have completed this workout,we hope that you will be able to do the following:
•Write an equation for the budget line and draw the budget t on a graph when you are given prices and income or when you are given two points on the budget line.
•Graph the effects of changes in prices and income on budget ts.•Understand the concept of numeraire and know what happens to the budget t when income and all prices are multiplied bythe same positive amount.
•Know what the budget t looks like if one or more of the prices is negative.•See that the idea of a “budget t”can be applied to constrained choices where there are other constraints on what you can have,in addition to a constraint on moneyexpenditure.
NAME 72.1(0)You have an income of $40to spend on two commodities.Com-modity1costs $10per unit,and commodity2costs $5per unit.(a)Write down your budget equation.
10x 1+5x 2=40.
(b)If you spent all your income on commodity 1,how much could you buy?
4.
(c)If you spent all of your income on commodity 2,how much could you buy?8.
U blue ink to draw your budget line in the graph
below.
024
6
82
4
6
x1
x28
(d)Suppo that the price of commodity1falls to $5while every thing el stays the same.Write down your new budget equation.
5x 1+5x 2=
40.
On the graph above,u red ink to draw your new budget line.
(e)Suppo that the amount you are allowed to spend falls to $30,while the prices of both commodities remain at $5.Write down your budget equation.5x 1+5x 2=30.
U black ink to draw this budget line.
(f)On your diagram,u blue ink to shade in the area reprenting com-moditybundles that y ou can afford with the budget in Part (e)but could not afford to buywith the budget in Part (a).U black ink or pencil to shade in the area reprenting commoditybundles that y ou could afford with the budget in Part (a)but cannot afford with the budget in Part (e).
2.2(0)On the graph below,draw a budget line for each ca.
8BUDGET CONSTRAINT (Ch.2)
(a)p 1=1,p 2=1,m =15.(U blue ink.)(b)p 1=1,p 2=2,m =20.(U red ink.)(c)p 1=0,p 2=1,m =10.(U black ink.)
(d)p 1=p 2,m =15p 1.(U pencil or black ink.Hint:How much of good 1could
you afford if you spend your entire budget on good 1?)
051015
205
10
15
x1
x220
2.3(0)Your budget is such that if you spend your entire income,you
can afford either 4units of good x and 6units of good y or 12
units of x and 2units of y .
(a)Mark the two consumption bundles and draw the budget line in the graph below.
04812
164
8
12
x
y 16
(b)What is the ratio of the price of x to the price of y ?
1/2.
(c)If you spent all of your income on x ,how much x could you buy?
16.
(d)If you spent all of your income on y ,how much y could you buy?
8.
(e)Write a budget equation that gives you this budget line,where the price of x is 1.
x +2y =16.
(f)Write another budget equation that gives you the same budget line,but where the price of x is 3.
3x +6y =48.
2.4(1)Murphywas consuming 100units of X and 50units of Y .The
price of X ro from 2to 3.The price of Y remained at 4.
(a)How much would Murphy’s income have to ri so that he can still exactlyafford 100units of X and 50units of Y ?
$100.
2.5(1)If Amyspent her entire allowance,she could afford 8candybars and 8comic books a week.She could also just afford 10candybars and 4comic books a week.The price of a candybar is 50cents.Draw her budget line in the box below.What is Amy’s weekly allowance?
$6.
081624
328
16
24
Candy bars
Comic books
32
12 2.6(0)In a small countrynear the Baltic Sea,there are onlythree commodities:potatoes,meatballs,and jam.Prices have been remark-ablystable for the last 50y ears or so.Potatoes cost 2crowns per sack,meatballs cost 4crowns per crock,and jam costs 6crowns per jar.(a)Write down a budget equation for a citizen named Gunnar who has an income of 360crowns per year.Let P stand for the number of sacks of potatoes,M for the number of crocks of meatballs,and J for the number of jars of jam consumed byGunnar in a y ear.
2P +4M +6J =
360.
(b)The citizens of this countryare in general veryclever people,but they are not good at multiplying by 2.This made shopping for potatoes excru-ciatinglydifficult for manycitizens.Therefore it was decided to introduce a new unit of currency,such that potatoes would be the numeraire.A sack of potatoes costs one unit of the new currencywhile the same rel-ative prices applyas in the past.In terms of the new currency ,what is the price of meatballs?
2crowns.
(c)In terms of the new currency,what is the price of jam?
3
crowns.
(d)What would Gunnar’s income in the new currencyhave to be for him to be exactlyable to afford the same commoditybundles that he could afford before the change?
180crowns.
(e)Write down Gunnar’s new budget equation.
P +2M +3J =
180.
Is Gunnar’s budget t anydifferent than it was before the change?
No.
2.7(0)Edmund Stench consumes two commodities,namelygarbage and punk rock video casttes.He doesn’t actuallyeat the former but keeps it in his backy ard where it is eaten bybillygoats and assorted vermin.The reason that he accepts the garbage is that people payhim $2per sack for taking it.Edmund can accept as much garbage as he wishes at that price.He has no other source of income.Video casttes cost him $6each.
(a)If Edmund accepts zero sacks of garbage,how manyvideo casttes
can he buy?
0.
NAME 11(b)If he accepts 15sacks of garbage,how manyvideo casttes can he buy?
5.
(c)Write down an equation for his budget line.
6C −2G =0.
(d)Draw Edmund’s budget line and shade in his budget t.
0510
15205
10
15
Video casttes
Garbage 20
2.8(0)If you think Edmund is odd,consider his brother Emmett.Emmett consumes speeches bypoliticians and universityadministrators.He is paid $1per hour for listening to politicians and $2per hour for listening to universityadministrators.(Emmett is in great demand to help fill emptychairs at public lectures becau of his distinguished appearance and his abilityto refrain from making rude nois.)Emmett consumes one good for which he must pay.We have agreed not to disclo what that good is,but we can tell you that it costs $15per unit and we shall call it Good X .In addition
to what he is paid for consuming speeches,Emmett receives a pension of $50per week.
02550
7510025
50
75
Politician speeches
Administrator speeches
100
12BUDGET CONSTRAINT (Ch.2)
(a)Write down a budget equation stating tho combinations of the three commodities,Good X ,hours of speeches bypoliticians (P ),and hours of speeches byuniversityadministrators (A )that Emmett could afford to consume per week.
15X −1P −2A =50.
(b)On the graph above,draw a two-dimensional diagram showing the locus of consumptions of the two kinds of speeches that would be possible for Emmett if he consumed 10units of Good X per week.
2.9(0)Jonathan Livingstone Yuppie is a prosperous lawyer.He has,in his own words,“outgrown tho confining two-commoditylim-its.”Jonathan consumes three goods,unblended Scotch whiskey,de-signer tennis shoes,and meals in French gourmet restaurants.The price of Jonathan’s brand of whiskeyis $20per bottle,the price of designer tennis shoes is $80per pair,and the price of gourmet restaurant meals is $50per meal.After he has paid his taxes and alimony,Jonathan has $400a week to spend.
(a)Write down a budget equation for Jonathan,where W stands for the number of bottles of whiskey,T stands for the number of pairs of tennis shoes,and M for the number of gourmet restaurant meals that he consumes.
20W +80T +50M =400.
(b)Draw a three-dimensional diagram to show his budget t.Label the interctions of the budget t with each axis.
(c)Suppo that he determines that he will buyone pair of designer tennis shoes per week.What equation must be satisfied bythe combinations of restaurant meals and whiskeythat he could afford?
20W +50M =
320.
2.10(0)Martha is preparing for exams in economics and sociology.She has time to read 40pages of economics and 30pages of sociology.In the same amount of time she could also read 30pages of economics and 60pages of sociology.
(a)Assuming that the number of pages per hour that she can read of either subject does not depend on how she allocates her time,how many pages of sociologycould she read if she decided to spend all of her time on sociologyand none on economics?150pages.(Hint:You have two points on her budget line,so you should be able to determine the entire line.)
(b)How manypages of economics could she read if she decided to spend all of her time reading economics?
50pages.
2.11(1)HarryHy pe has $5,000to spend on advertising a new kind of
dehydrated sushi.Market rearch shows that the people most likely to buythis new product are recent recipients of M.B.A.degrees and lawy ers who own hot tubs.Harryis considering advertising in two publications,a boring business magazine and a trendyconsumer publication for people who wish theylived in California.
Fact 1:Ads in the boring business magazine cost $500each and ads in the consumer magazine cost $250each.
Fact 2:Each ad in the business magazine will be read by1,000recent M.B.A.’s and 300lawyers with hot tubs.
Fact 3:Each ad in the consumer publication will be read by300recent M.B.A.’s and 250lawyers who own hot tubs.
Fact 4:Nobodyreads more than one ad,and nobodywho reads one magazine reads the other.
(a)If Harryspends his entire advertising budget on the business pub-lication,his ad will be read by
10,000
recent M.B.A.’s and by
3,000
lawyers with hot tubs.
(b)If he spends his entire advertising budget on the consumer publication,his ad will be read by 6,000
won
recent M.B.A.’s and by
5,000
lawyers with hot tubs.
(c)Suppo he spent half of his advertising budget on each publication.His ad would be read by 8,000
recent M.B.A.’s and by
4,000
lawyers with hot tubs.
上海美高学校(d)Draw a “budget line”showing the combinations of number of readings byrecent M.B.A.’s and bylawy ers with hot tubs that he can obtain if he spends his entire advertising budget.Does this line extend all the way to the axes?No.Sketch,shade in,and label the budget t,which includes all the combinations of MBA’s and lawyers he can reach if he spends no more than his budget.
(e)Let M stand for the number of instances of an ad being read byan M.B.A.and L stand for the number of instances of an ad being read by a lawyer.This budget line is a line gment that lies on the line with equation M +2L =16.With a fixed advertising budget,how manyreadings byM.B.A.’s must he sacrifice to get an additional reading bya lawy er with a hot tub?
2.
04
8
12164
812Lawyers x 1000
MBA's x 100016
102
62.12(0)On the planet Mungo,theyhave two kinds of money ,blue moneyand red money .Everycommodityhas two prices—a red-money price and a blue-moneyprice.EveryMungoan has two incomes—a red income and a blue income.
In order to buyan object,a Mungoan has to paythat object’s red-moneyprice in red moneyand its blue-moneyprice in blue money .(The shops simplyhave two cash registers,and y ou have to payat both registers to buyan object.)It is forbidden to trade one kind of moneyfor the other,and this prohibition is strictlyenforced byMungo’s ruthless and efficient monetarypolice.
•There are just two consumer goods on Mungo,ambrosia and bubble gum.All Mungoans prefer more of each good to less.
•The blue prices are 1bcu (bcu stands for blue currencyunit)per unit of ambrosia and 1bcu per unit of bubble gum.
•The red prices are 2rcus (red currencyunits)per unit of ambrosia and 6rcus per unit of bubble gum.(a)On the graph below,draw the red budget (with red ink)and the blue budget (with blue ink)for a Mu
ngoan named Harold who blue income is 10and who red income is 30.Shade in the “budget t”containing all of the commoditybundles that Harold can afford,given
NAME 15its ∗two budget constraints.Remember,Harold has to have enough blue money and enough red moneyto payboth the blue-moneycost and the red-moneycost of a bundle of
goods.
0510
15205
10
15
Ambrosia
Gum 20(b)Another Mungoan,Gladys,faces the same prices that Harold faces and has the same red income as Harold,but Gladys has a blue income of 20.Explain how it is that Gladys will not spend its entire blue income no matter what its tastes maybe.(Hint Draw Glady s’s budget lines.)
The blue budget line lies strictlyoutside the red budget line,so to satisfyboth budgets,one must be strictlyinside the red budget line.
(c)A group of radical economic reformers on Mungo believe that the currencyrules are unfair.“Whyshould every one have to paytwo prices for every thing?”theyask.Theypropo the following scheme.Mungo will continue to have two currencies,everygood will have a blue price and a red price,and everyMungoan will have a blue income and a red income.But nobodyhas to payboth prices.Instead,every one on Mungo must declare itlf to be either a Blue-MoneyPurchar (a “Blue”)
or a Red-Money Purchar (a “Red”)before it buys anything at all.Blues must make all of their purchas in blue moneyat the blue prices,spending onlytheir blue incomes.Reds must make all of their purchas in red money,spending only their red incomes.
Suppo that Harold has the same income after this reform,and that prices do not change.Before declaring which kind of purchar it will be,
∗
We refer to all Mungoans bythe gender-neutral pronoun,“it.”Al-though Mungo has two xes,neither of them is remotelylike either of ours.
16BUDGET CONSTRAINT (Ch.2)
Harold contemplates the t of commoditybundles that it could afford bymaking one declaration or the other.Let us call a commoditybundle “attainable”if Harold can afford it bydeclaring itlf to be a “Blue”and buying the bundle with blue money or if Harold can afford the bundle bydeclaring itlf to be a “Red”and buy ing it with red money .On the diagram below,shade in all of the attainable bundles.
0510
1520
5
10
15
Ambrosia
Gum
20
2.13(0)Are Mungoan budgets reallyso fanciful?Can y ou think of sit-uations on earth where people must simultaneouslysatisfymore than one
budget constraint?Is moneythe onlyscarce resource that people u up when consuming?
Consumption of manycommodities
takes time as well as money.People have to simultaneouslysatisfya time budget and a moneybudget.Other examples--people mayhave a calorie budget or a cholesterol budget or an alcohol-intake budget.
Chapter 3
NAME
Preferences
Introduction.In the previous ction you learned how to u graphs to
show the t of commoditybundles that a consumer can afford.In this ction,you learn to put information about the consumer’s preferences on the same kind of graph.Most of the problems ask you to draw indifference curves.
Sometimes we give you a formula for the indifference curve.Then all you have to do is graph a known equation.But in some problems,we give you only “qualitative”information about the consumer’s preferences and ask you to sketch indifference curves that are consistent with this information.This requires a little more thought.Don’t be surprid or disappointed if you cannot imme
diately e the answer when you look at a problem,and don’t expect that you will find the answers hiding somewhere in your textbook.The best way we know to find answers is to “think and doodle.”Draw some axes on scratch paper and label them,then mark a point on your graph and ask yourlf,“What other points on the graph would the consumer find indifferent to this point?”If possible,draw a curve connecting such points,making sure that the shape of the line you draw reflects the features required by the problem.This gives you one indifference curve.Now pick another point that is preferred to the first one you drew and draw an indifference curve through it.
Example:Jocasta loves to dance and hates houcleaning.She has strictly convex preferences.She prefers dancing to anyother activityand never gets tired of dancing,but the more time she spends cleaning hou,the less happyshe is.Let us tryto draw an indifference curve that is consistent with her preferences.There is not enough information here to tell us exactlywhere her indifference curves go,but there is enough information to determine some things about their shape.Take a piece of scratch paper and draw a pair of axes.Label the horizontal axis “Hours per dayof houcleaning.”Label the vertical axis “Hours per dayof dancing.”Mark a point a little ways up the vertical axis and write a 4next to it.At this point,she spends 4hours a daydancing and no time houcleaning.Other points that would be indifferent to this point would have to be points where she
did more dancing and more houcleaning.The pain of the extra houkeeping should just compensate for the pleasure of the extra dancing.So an indifference curve for Jocasta must be upward sloping.Becau she loves dancing and hates houcleaning,it must be that she prefers all the points above this indifference curve to all of the points on or below it.If Jocasta has strictlyconvex preferences,then it must be that if you draw a line between any two points on the same indifference curve,all the points on the line (except the endpoints)are preferred to the endpoints.For this to be the ca,it must be that the indifference curve slopes upward ever more steeplyas y ou move to the right along it.You should convince yourlf of this by making some drawings on scratch
口语奇招18PREFERENCES (Ch.3)
paper.Draw an upward-sloping curve passing through the point (0,4)and getting steeper as one moves to the right.
When you have completed this workout,we hope that you will be able to do the following:
•Given the formula for an indifference curve,draw this curve,and find its slope at anypoint on the curve.•Determine whether a consumer prefers one bundle to another or is indifferent between them,given specific indifference curves.•Draw indifference curves for the special cas of perfect sub
stitutes and perfect complements.•Draw indifference curves for someone who dislikes one or both com-modities.•Draw indifference curves for someone who likes goods up to a point but who can get “too much”of one or more goods.•Identifyweaklypreferred ts and determine whether the are con-vex ts and whether preferences are convex.•Know what the marginal rate of substitution is and be able to deter-mine whether an indifference curve exhibits “diminishing marginal rate of substitution.”•Determine whether a preference relation or anyother relation be-tween pairs of things is transitive,whether it is reflexive,and whether it is complete.3.1(0)Charlie likes both apples and bananas.He consumes nothing el.The consumption bundle where Charlie consumes x A bushels of apples per year and x B bushels of bananas per year is written as (x A ,x B ).Last year,Charlie consumed 20bushels of apples and 5bushels of bananas.It happens that the t of consumption bundles (x A ,x B )such that Charlie is indifferent between (x A ,x B )and (20,5)is the t of all bundles such that x B =100/x A .The t of bundles (x A ,x B )such that Charlie is just indifferent between (x A ,x B )and the bundle (10,15)is the t of bundles such that x B =150/x A .
(a)On the graph below,plot veral points that lie on the indifference curve that pass through the point (20,5),and sketch this curve,using blue ink.Do the same,using red ink,for the indifference curve passing through the point (10,15).
(b)U pencil to shade in the t of commoditybundles that Charlie weaklyprefers to the bundle (10,15).U blue ink to shade in the t of commoditybundles such that Charlie weaklyprefers (20,5)to the bundles.
NAME 190102030
40
10
20
30
Apples
Bananas 40
For each of the following statements about Charlie’s preferences,write “true”or “fal.”(c)(30,5)∼(10,15).True.(d)(10,15) (20,5).True.(e)(20,5) (10,10).True.(f)(24,4) (11,9.1).Fal.(g)(11,14) (2,49).
experienced
True.
(h)A t is convex if for anytwo points in the t,the line gment between them is also in the t.Is the t of bundles that Charlie weakly prefers to (20,5)a convex t?
Yes.
(i)Is the t of bundles that Charlie considers inferior to (20,5)a convex t?
No.
(j)The slope of Charlie’s indifference curve through a point,(x A ,x B ),is known as his marginal
rate
of
substitution
at that point.
20PREFERENCES (Ch.3)
(k)Remember that Charlie’s indifference curve through the point (10,10)
has the equation x B =100/x A .Tho of you who know calculus will remember that the slope of a curve is just its derivative,which in this ca is −100/x 2A .(If you don’t know calculus,you will have to take our word for this.)Find Charlie’s marginal rate of substitution at the point,(10,10).
−1.
(l)What is his marginal rate of substitution at the point (5,20)?
−4.
(m)What is his marginal rate of substitution at the point (20,5)?
(−.25).
(n)Do the indifference curves you have drawn for Charlie exhibit dimin-ishing marginal rate of substitution?
Yes.
3.2(0)Ambro consumes onlynuts and berries.Fortunately ,he likes both goods.The consumption bundle where Ambro consumes x 1units of nuts per week and x 2units of berries per week is written as (x 1,x 2).The t of consumption bundles (x 1,x 2)such that Ambro is indifferent between (x 1,x 2)and (1,16)is the t of bundles such that x 1≥0,x 2≥0,
and x 2=20−4√
x 1.The t of bundles (x 1,x 2)such that (x 1,x 2)∼
(36,0)is the t of bundles such that x 1≥0,x 2≥0and x 2=24−4√
x 1.(a)On the graph below,plot veral points that lie on the indifference curve that pass through the point (1,16),and sketch this curve,using blue ink.Do the same,using red ink,for the indifference curve passing through the point (36,0).
(b)U pencil to shade in the t of commoditybundles that Ambro weaklyprefers to the bundle (1,16).U red ink to shade in the t of all commoditybundles (x 1,x 2)such that Ambro weaklyprefers (36,0)to the bundles.Is the t of bundles that Ambro prefers to (1,16)a convex t?
Yes.
(c)What is the slope of Ambro’s indifference curve at the point (9,8)?(Hint Recall from calculus the wayto calculate the slope of a curve.If you don’t know calculus,you will have to draw your diagram carefully and estimate the slope.)
−2/3.
