Microeconomics Sln Ch 1 - Besanko, 4th edition.pdf
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Besanko & Braeutigam – Microeconomics, 4th editionSolutions Manual
Chapter 1 Analyzing Economic Problems Solutions to Review Review Questions 1.
What Wh at is is the the diff differ eren ence ce bet betwe ween en mic micro roec econ onom omic icss and and macr macroe oeco cono nomi mics cs? ?
Microeconomics studies the economic behavior of individual economic decision makers, such as a consumer, a worker, a firm, firm, or a manager. Macroeconomics studies how an entire national economy performs, eamining such topics as the aggregate levels of income and employment, the levels of interest rates and prices, the rate of inflation, and the nature of business cycles. 2.
Why Wh y is eco econo nomi mics cs oft often en des descr crib ibed ed as as the the scie scienc ncee of con const stra rain ined ed cho choic ice? e?
!hile our wants for goods and services are unlimited, the resources necessary to produce those goods and services, such as labor, managerial talent, capital, and raw materials, are "scarce# because their supply is limited. $his scarcity implies that we are constrained in the choices we can make about which goods and services to produce. $hus, economics is often described described as the science of constrained choice. 3. ow does does the the tool tool of of con constr strain ained ed optim optimiz izati ation on hel help p dec decisi ision on ma!er ma!erss ma!e ma!e choic choices? es? What roles do the ob"ecti#e f$nction and constraints play in a model of constrained optimization?
%onstrained optimiation allows the decision maker to select the best 'optimal( alternative while accounting for any possible limitations limitations or restrictions restrictions on the choices. $he ob)ective function represents the relationship relationship to be maimied or minimied. minimied. *or eample, a firm+s profit might be the ob)ective function and all choices will be evaluated in the profit function to determine which yields the highest profit. profit. $he constraints place limitations limitations on the choice the decision maker can select and defines the set of alternatives from which the best will be chosen. %. &$ppos &$p posee the the mar!e mar!ett for for wheat wheat is compe competit titi# i#e' e' wit with h an an $pw $pward ard(sl (slopi oping ng s$ppl s$pply y c$r c$r#e #e'' a downward(sloping demand c$r#e' and an e)$ilibri$m price of *%.++ per b$shel. Why wo$ld a higher price ,e.g.' *-.++ per b$shel not be an e)$ilibri$m price? Why wo$ld a lower price ,e.g.' *2.-+ per b$shel not be an e)$ilibri$m price?
f the price in the market was above the e-uilibrium price, consumers would be willing to purchase fewer units than suppliers would be willing to sell, creating creating an ecess supply. s suppliers realie they are not selling the units they have made available, sellers will bid down do wn the
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Besanko & Braeutigam – Microeconomics, 4th editionSolutions Manual
price to entice more consumers to purchase their goods or services. By definition, e-uilibrium is a state that will remain unchanged as long as eogenous factors remain remain unchanged. Since in this case suppliers will lower their price, this high price cannot be an e-uilibrium. !hen the price is below the e-uilibrium price, consumers will demand more units than suppliers have made available. $his ecess demand will entice entice consumers to bid up the prices to purchase the limited units available. available. Since the price will change, it cannot be an e-uilibrium. -. What What is is the the diffe differen rence ce betwe between en an e/oge e/ogeno$ no$ss #ar #ariab iable le and and an endog endogen eno$s o$s #ari #ariabl ablee in an economic model? Wo$ld it e#er be $sef$l to constr$ct a model that contained only e/ogeno$s #ariables ,and no endogeno$s #ariables?
5ogenous variables are taken as given in an economic model, i.e., they are determined by some process outside the model, while endogenous variables are determined within the economic model being studied. n economic model that contained no endogenous variables would not be very interesting. !ith no endogenous variables, nothing would be determined by the model so it would not serve much purpose. 0. Why do econo economis mists ts do compa compara rati# ti#ee stat statics ics analys analysis? is? Wh What at role role do endog endogen eno$ o$ss #ariables and e/ogeno$s #ariables play in comparati#e statics analysis?
%omparative statics analyses are performed to determine how the levels of endogenous variables change as some eogenous variable is changed. $his type of analysis analysis is very important since since in the real world the eogenous variables, such as weather, policy tools, etc. are always changing and it is useful to know how changes in these variables affect the levels of other, endogenous, variables. n eample of comparative statics analysis would be asking the -uestion6 -uestion6 f etraordinarily low rainfall 'an eogenous variable( causes a 71 percent reduction in corn supply, by how much will the market price for corn 'an endogenous variable( increase8 . What What is is the the diffe differen rence ce betwe between en posit positi# i#ee and and normat normati#e i#e analy analysis sis? ? Whi Which ch of the the following )$estions wo$ld entail positi#e analysis' and which normati#e analysis? a What effect will nternet a$ction companies ha#e on the profits of local a$tomobile dealerships? b &ho$ld the go#ernment impose special ta/es on sales of merchandise made o#er the nternet?
9ositive analysis attempts to eplain how an economic econo mic system works or to predict how it will change over time by asking eplanatory or predictive predictive -uestions. :ormative analysis focuses on what should be done by asking prescriptive -uestions.
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Besanko & Braeutigam – Microeconomics, 4th editionSolutions Manual
a(
b(
Becau Because se thi thiss -ues -uesti tion on ask askss whet whethe herr deal dealer ersh ship ip pro profi fits ts wil willl go up up or dow down n 'and 'and by by how much( – but refrains from in-uiring as to whether this would be a good thing – it is an eample of positive analysis. ;n the other hand, this -uestion asks whether it is desirable to impose taes on nternet sales, so it is normative analysis. :otably, this -uestion does not ask what the effect of such taes would be.
Solutions to Problems Problems 1.1 isc$s isc$sss the fol follow lowing ing stat statem ement ent44 5&inc 5&incee s$ppl s$pply y and dema demand nd c$r#e c$r#ess are alwa always ys shifting' mar!ets ne#er act$ally reach an e)$ilibri$m. 6herefore' the concept of e)$ilibri$m is $seless.7
!hile the claim that markets never reach an e-uilibrium is probably debatable, even if markets do not ever reach e-uilibrium, the concept is still of central importance. $he concept of e-uilibrium is important because it provides a simple way to predict how market prices and -uantities will change as eogenous variables variables change. $hus, while we may never reach a particular e-uilibrium price, say because a supply or demand schedule shifts as the market moves toward e-uilibrium, we can predict with relative ease, for eample, whether prices will be rising or falling when eogenous market factors factors change as we move toward e-uilibrium. e-uilibrium. s eogenous variables continue to change we can continue predict the direction of change for the endogenous variables, and this is not "useless.# 1.2 n an an arti article cle enti entitle tled' d' 5Corn 5Corn Pric Prices es &$rge &$rge on E/p E/port ort eman emand' d' Crop Crop ata ata'7 '7 The Wall Street Journal identified se#eral e/ogeno$s shoc!s that p$shed 8.&. corn prices sharply higher. 3 &$ppose the 8.&. mar!et for corn is competiti#e' with an $pward(sloping s$pply c$r#e and a downward(sloping demand c$r#e. 9or each of the following scenarios' ill$strate graphically how the e/ogeno$s e#ent described will contrib$te to a higher price of corn in the 8.&. mar!et. a 6he 8.&. epartment of Agric$lt$re anno$nces that e/ports of corn to 6aiwan and :apan were 5s$rprisingly b$llish'7 aro$nd 3+ percent higher than had been e/pected. b &ome analysts pro"ect that the size of the 8.&. corn crop will hit a si/(year low beca$se of dry weather. c 6he strengthening of El ;i' 2++>' the the price price of oil oil on on the the world world mar!et mar!et increase increased' d' hittin hitting g a pea! pea! of abo$t abo$t *1%+ per barrel in :$ly' 2++>. n the second half of 2++>' the price of oil declined' ending the year at "$st o#er *%+ per barrel. &$ppose that the global mar!et for oil can be described by an $pward(sloping s$pply c$r#e and a downward(sloping demand c$r#e. 9or each of the following scenarios' ill$strate graphically how the e/ogeno$s e#ent contrib$ted to a rise or a decline in the price of oil in 2++>4
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Besanko & Braeutigam – Microeconomics, 4th editionSolutions Manual
a. b. c.
A boomi booming ng econ economy omy in China China raise raised d the the globa globall dema demand nd for for oil oil to reco record rd le#el le#elss in 2++>. As a res$lt res$lt of the the financ financia iall crisi crisiss of 2++> 2++>'' the the 8.&. 8.&. and and othe otherr de#e de#elo loped ped econo economie miess pl$nged into a se#ere recession in the latter half of 2++>. @ed$c @ed$ced ed secta sectaria rian n #iol #iolenc encee in in ra ra) ) in in 2++ 2++> > ena enable bled d ra ra) ) to to inc increa rease se its oil oil prod$ction capacity. a.
b.
c.
9rice
Booming economy in %hina shifts the demand curve for oil rightward 'from ?1 to ?2 below(, contributing to an increase in the price of oil. Aecession in the @.S. and other developed economies shifts the demand curve for oil leftward 'from ?1 to ?2 below(, contributing to a decrease in the price of oil. ncrease in oil production capacity in ra- shifts the supply for oil rightward 'from S1 to S2 below(, contributing to a decrease d ecrease in the price of oil. Booming economy in %hina S1
?2 ?1 Cuantity 9rice
Aecession in the @.S. S1
?1 ?2 Cuantity 9rice
More oil production capacity in raS1 S2
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Cuantity %hapter 2
Besanko & Braeutigam – Microeconomics, 4th editionSolutions Manual
1.% A firm firm prod prod$ces $ces cell$lar cell$lar telepho telephone ne ser# ser#ice ice $sing $sing e)$ip e)$ipment ment and labor. labor. When When it $ses $ses E machine(ho$rs of e)$ipment and hires L person(ho$rs of labor' it can pro#ide $p to Q $nits of telephone ser#ice. 6he relationship between Q' E ' and L is as follows4 Q EL . 6he firm m$st always pay PE for each machine(ho$r of e)$ipment it $ses and PL for each person(ho$r of labor it hires. &$ppose the prod$ction manager is told to prod$ce Q 2++ $nits of telephone ser#ice and that she wants to choose E and L to minimize costs while achie#ing that prod$ction target. a What Wh at is the the ob" ob"ec ecti ti#e #e f$nc f$ncti tion on for for thi thiss pro probl blem em? ? b What is the constraint? c Which of the #ariables , Q' E ' L' PE ' and PL are e/ogeno$s? Which are endogeno$s? E/plain. d Writ Wr itee a sta state teme ment nt of the the con const stra rain ined ed opti optimi miza zati tion on prob proble lem. m. a( $hee pro $h produ duct ctio ion n man manag ager er want wantss to to min minim imi iee tot total al cost costss TC = P E *E *E + P L*L. b( $he constraint is to produce Q = 011 units, so the manager must choose E and L so that EL D 011. c( $he endogenous variables are E and L, because those are the variables over which the production manager has control. By contrast, the eogenous variables are Q, P E , and P L because the production manager has no control over their values and must take them as given. d(
1.6hee s$ppl 6h s$pply y of al$m al$min in$m $m in the the 8nit 8nited ed &tat &tates es depe depend ndss on the the pri price ce of al$min al$min$m $m and and the a#erage price of electricity ,a critical inp$t in the prod$ction of al$min$m. Ass$me that an increase in the price of electricity shifts the s$pply c$r#e for al$min$m to the left ,i.e.' a higher a#erage price of electricity decreases the s$pply of al$min$m. 6he demand for al$min$m in the 8nited &tates depends on the price of al$min$m and income shifts the demand c$r#e for al$min$m to the right ,i.e.' higher income increases the demand for al$min$m. n 2++%' national income in the 8nited &tates increased' while the price of electricity fell' as compared to 2++3. ow wo$ld the e)$ilibri$m price of al$min$m in 2++% compare to the e)$ilibri$m price in 2++3? ow wo$ld the e)$ilibri$m )$antity in 2++% compare to the e)$ilibri$m )$antity in 2++3?
n 0117, the initial e-uilibrium is at price P 2 and -uantity Q2. s national income increased, demand for aluminum shifted to the right, as depicted in the graph below by the shift from D2 to D0. $he fall in the price of electricity shifted the supply curve to the right, from S 2 to S 0. Both shifts have the effect effect of increasing the e-uilibrium e-uilibrium -uantity, from Q2 to Q0. Eowever, it is unclear whether price will rise or fall – if the demand shift dominates, price would riseF if the supply shift dominates, price wo uld fall.
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Besanko & Braeutigam – Microeconomics, 4th editionSolutions Manual
1.0 Ethanol Ethanol ,i.e.' ,i.e.' ethyl ethyl alcohol alcohol is a color colorless less'' flamma flammable ble li)$id li)$id that' that' when blended blended with gasoline' creates a motor f$el that can ser#e as an alternati#e to gasoline. 6he )$antity of ethanol motor f$el that is demanded depends on the price of ethanol and the price of gasoline. Beca$se ethanol f$el is a s$bstit$te for gasoline' an increase in the price of gasoline shifts the demand c$r#e for ethanol rightward. 6he )$antity of ethanol s$pplied depends on the price of ethanol and the price of corn ,since the primary inp$t $sed to prod$ce ethanol in the 8.&. is corn. An increase in the price of corn shifts the s$pply c$r#e of ethanol leftward. n the first half of 2++>' the price of gasoline in the 8.&. increased significantly as compared to 2++' and the price of corn increased as well. ow wo$ld the e)$ilibri$m price of ethanol motor f$el in the first half of 2++> compare to the price in 2++?
$he increase in the price of gasoline shifted the demand curve for ethanol rightward 'from ?1 to ?2(, while the increase in the price of corn shifted the supply curve for ethanol leftward 'from S1 to S2 below(. Both changes had the impact of increasing the price of ethanol, moving the e-uilibrium from 51 in 011> to 52 in 011H. '$he impact of these changes on -uantity is, in principle, ambiguousF the e-uilibrium -uantity could either go up or down depending on the magnitude of the shifts in the demand and supply curves. $he picture below shows the case in which there is a positive change in the e-uilibrium -uantity.( 9rice of ethanol S2 52
S1
51 ?1
?2 Cuantity of ethanol
1. 6he price price of of gasol gasoline ine in the the 8nite 8nited d &tates &tates dep depend endss on the s$pply s$pply of gasol gasoline ine and the demand for gasoline. asoline is s$pplied by oil companies that sell it on se#eral mar!ets. ence the s$pply of gasoline in the 8nited &tates depends on the price of gasoline in the 8nited &tates and its price on other mar!ets. When the price of gasoline o$tside the 8nited &tates increases' the 8.&. s$pply decreases beca$se firms prefer to sell the gasoline
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Besanko & Braeutigam – Microeconomics, 4th editionSolutions Manual
elsewhere. ow wo$ld an increase in the price of gasoline abroad affect the e)$ilibri$m price of gasoline in the 8nited &tates?
!hen the price of gasoline abroad goes up, the supply on the domestic market decreases. *irms are willing to supply less gasoline for the same price as before. t that price the domestic demand eceeds the supply and therefore the e-uilibrium price in the @S has to increase. !hen this is followed by increase in the demand – consumers are willing to buy more gasoline then before – supply would again be smaller than the demand. Eence the e-uilibrium price of the gasoline would increase even ev en more.
1.> 6hee dema 6h demand nd for for comp comp$te $terr mon monito itors rs is gi#en gi#en by the e)$ e)$ati ation on Qd ++ P ' while the s$pply is gi#en by the e)$ation Qs 1++ P . n both e)$ations P denotes the mar!et price. 9ill in the following table. 9or what price is the mar!et in e)$ilibri$mDs$pply e)$als to the demand? 0 11 0 1 7 11 7 1 41 1 P d Q Q s
P Qd Qs
0 11 11 3++
0 1 4 1 3-+
71 1 41 1 %++
7 1 7 1 %-+
%++ 3++ -++
1. 6hee dema 6h demand nd for for comp comp$te $terr mem memory ory chips chips is gi#en gi#en by the the e)$ e)$at ation ion Qd -++ F 2 P ' while the s$pply is gi#en by the e)$ation Qs -+ G P . n both e)$ations P denotes denotes the mar!et price. 9or what price is the mar!et in e)$ilibri$m F s$pply e)$als demand? What is the e)$ilibri$m )$antity? 1 21 1 2 1 01 1 0 1 P d Q Q s
s shown in the table below, the e-uilibrium price is 21, and the e-uilibrium -uantity is 011. P Qd Q s
1 %++ 1++
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2 11 3++ 1-+
2 1 2++ 2++
011 1++ 2-+
0 1 + 3++
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Besanko & Braeutigam – Microeconomics, 4th editionSolutions Manual
1.1+ 1.1+
6he deman 6he demand d for for s$ng s$nglas lasse sess is gi# gi#en en by by e)$a e)$atio tion n Qd 1+++ ( % P ' where P denotes the mar!et price. 6he s$pply of s$nglasses is gi#en by e)$ation Qs 1++ G 0 P . 9ill in the following table and find the e)$ilibri$m price.
H1
P Qd Q s
=1
P
H1
=1
Q
GH 1 -> +
G4 1 0% +
d
Qs
21 1
21 1 G1 1 + +
221
22 1 G 1 0 +
20 1
12+ -2+ >2+
1.11 6his year year=s =s s$mmer s$mmer is is e/pecte e/pected d to be #ery #ery s$nny s$nny.. ence ence the deman demand d for s$ngl s$nglasse assess increased and now is gi#en by e)$ation Qd 12++ ( % P . ow is the e)$ilibri$m price going to change compared with the scenario described in problem 1.? E/plain and then fill in the following table to #erify yo$r e/planation.
H1
P Qd Q s
=1
21 1
221
20 1
!hen the demand increases, more people are willing to buy sunglasses at the e-uilibrium price. Eence, the supply is insufficient to satisfy the demand and the e-uilibrium price has to go up. $he table below confirms this. P
H1
=1
Q
HH 1 -> +
H4 1 0% +
d
Qs
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21 1 H1 1 + +
22 1 >G 1 0 +
12+ 2+ >2+
%hapter 2 =
Besanko & Braeutigam – Microeconomics, 4th editionSolutions Manual
P
S 2 S 0
P 2 D0
D2 Q2
Q
Q0
1.12 1.12 &$p &$ppos posee the the s$p s$pply ply c$r c$r#e #e for for wool wool is is gi#e gi#en n by Qs P ' where Qs is the )$antity offered for sale when the price is P . Also s$ppose the demand c$r#e for wool is gi#en by Qd 1+ H P G I ' where Qd is the )$antity of wool demanded when the price is P and the le#el of income is I . Ass$me I is an e/ogeno$s #ariable. a &$ppose the le#el of income is I 2+. raph the s$pply and demand relationships' and indicate the e)$ilibri$m le#els of price and )$antity on yo$r graph. b E/plain why the mar!et for wool wo$ld not be in e)$ilibri$m if the price of wool were 1>. c E/plain why the mar!et for wool wo$ld not be in e)$ilibri$m if the price of wool were 1%.
ssuming I = 01 we have Q s
=
P and Q d = 71 − P . Iraphing these yields6
P 30
Cs
25 20 15 10
Cd
5 0 0
5
10
15
20
25
30
Q
$he e-uilibrium occurs at P =2B , Q s t a price of 2H, Q
>
=2B
.
Q d implying an ecess supply of wool. Because sellers
will not be able to sell all of o f their wool at this price, they will need to reduce price to attract buyers. t the lower price, the suppliers suppliers will offer a lower -uantity of output for sale, and consumers will want to purchase more. %opyright / 0122 3ohn !iley & Sons, nc.
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Besanko & Braeutigam – Microeconomics, 4th editionSolutions Manual
d t a price of 24, Q
>
Q s , implying an ecess demand for wool. Buyers will
begin to bid up the price of wool until the new e-uilibrium is reached. t the higher price, the suppliers will offer a higher -uantity -ua ntity of output for sale, and consumers will want to purchase less.
1.13 Consider Consider the mar!et mar!et for wool wool descr described ibed by by the s$pp s$pply ly and demand demand e)$ati e)$ations ons in Problem 1.12. &$ppose income rises from I 1 2+ to I 2 2%. a 8sing 8sing comp compar arati ati#e #e stat static icss analy analysis sis'' find find the impac impactt of the change change in inc income ome on the the e)$ilibri$m price of wool. b 8sing 8sing comp compar arati ati#e #e stat static icss analy analysis sis'' find find the impac impactt of the change change in inc income ome on the the e)$ilibri$m )$antity of wool. s d !ith I 2 = 01 , we had Q = P and Q = 71 − P , which implied an e-uilibrium price of 2. !ith I 0 = 04 , we have Q s = P and Q d = 74 − P . *inding the the point where
Q s
=
Q d yields Q s
=
Q d
P = 74 − P
0 P = 74 P = 2>
$hus, a change in income of ∆ I = 4 yields a change in price of ∆ P = 0 . s 9lugging the result from part a( into the e-uation for Q reveals the new e-uilibrium -uantity is Q 2> . $hus, a change in income of ∆ I = 4 yields a change in -uantity of ∆Q = 0 . =
1.1% Io$ are are the Jideo Jideo Ac)$ Ac)$isit isitions ions Kffic Kfficer er for for yo$r yo$r residen residence ce hall. hall. 6he othe otherr officer officerss of yo$r hall will tell yo$ how many #ideos they wo$ld li!e to rent d$ring the year. Io$r "ob is to find the least e/pensi#e way of renting the re)$ired n$mber of #ideos. After researching the options' yo$ ha#e fo$nd that there are three rental plans from which yo$ can choose. Plan A4 Pay *3 per #ideo' with no additional fees. Plan B4 :oin the 9re)$ent Jiewer Cl$b. ere yo$ pay a yearly membership fee of *-+' with an additional charge of *2 for each #ideo rented. Plan C4 :oin the Jery 9re)$ent Jiewer Cl$b. n this cl$b yo$ pay a yearly membership fee of *1-+' with an additional charge of *1 for each #ideo rented. a Which Which plan plan wo$ld wo$ld yo$ yo$ selec selectt if yo$r yo$r inst instr$ r$cti ctions ons are are to rent rent - mo#ie mo#iess a yea yearr at the lowest possible cost? b Which Which plan plan wo$ld wo$ld yo$ yo$ sele select ct if if yo$r yo$r inst instr$ r$cti ctions ons are are to ren rentt 1212- mo#ie mo#iess a year year at the the lowest possible cost? c n this this e/erc e/ercise ise'' is the the n$mb n$mber er of #ide #ideos os ren rented ted endo endogen geno$s o$s or e/o e/ogen geno$s o$s? ? E/pl E/plain ain.. d s the the ccho hoic icee of of plan plan ,A' ,A' B' B' or C end endog ogen eno$ o$ss or e/og e/ogen eno$ o$s? s? E/p E/pla lain in..
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Besanko & Braeutigam – Microeconomics, 4th editionSolutions Manual
e
Are Are tota totall e/pe e/pend ndit it$r $res es on on #ide #ideos os end endog ogen eno$ o$ss or e/o e/oge geno no$s $s? ? E/pl E/plai ain. n.
*ormulate each plan as a function of V , the number of videos to rent. TC A
= 7V
TC B
= B1 + 0V
TC C
=2B1 +V
$hen we have TC A '>B (
= 00B
TC B '>B (
= 011
TC C '>B (
= 00B
9lan B provides the lowest possible cost of J011 if you will purchase > > videos.
TC A '20B (
= 7>B
TC B '20B (
= 711
TC C '20B (
= 0>B
9lan % provides the lowest possible cost of J0> if you will purchase 20 2 0 videos. n this case, the number of videos rented is eogenous because we are choosing a plan given a fied level of videos. Because you may choose the plan, the plans are endogenous. :ote, though, that the details of the individual plans are eogenous. Because you may choose the plan and the plans imply a total cost given a fied level of videos, you are implicitly implicitly choosing the level of total ependiture. $otal ependitures are therefore endogenous.
1.1- @econsid @econsider er the the problem problem of of the Jideo Jideo Ac)$isit Ac)$isitions ions Kffic Kfficer er in Probl Problem em 1.1%. 1.1%. &$ppos &$pposee the officers of yo$r residence hall gi#e yo$ a specified amo$nt of money to spend' and want yo$ to ma/imize the n$mber of #ideos yo$ can rent with that b$dget. Io$ can choose from the same three plans ,A' B' and C a#ailable in Problem 1.1%. a Which plan wo$ld yo$ select if yo$r instr$ctions are to rent the most mo#ies possible while spending *12- per year? b Which plan wo$ld yo$ select if yo$r instr$ctions are to rent the most mo#ies possible while spending *3++ per year? c n this e/ercise' is the n$mber of #ideos rented endogeno$s or e/ogeno$s? E/plain. d s the choice of plan ,A' B' or C endogeno$s or e/ogeno$s? E/plain. e Are total e/pendit$res on #ideos endogeno$s or e/ogeno$s? E/plain.
:ow formulate each plan as a function of TC , the level of total ependiture on videos.
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Besanko & Braeutigam – Microeconomics, 4th editionSolutions Manual
V A
= TC K 7
V B
= TC K 0 − 0B
V C
= TC −2B1
$his gives V A '20B (
= 42 .G>
V B '20B (
= 7> .B
V C '20B (
= −0B
!ith plan you could rent 42 movies, with plan B you could rent 7> movies, and with plan % you would not be able to rent any movies 'because the membership fee eceeds your total budget(. 9lan , therefore, will allow you to rent the most most videos with a budget of J20.
V A '711 (
=211
V B '711 (
=20B
V C '711 (
=2B1
:ow plan % offers the opportunity to rent the most videos. $he number of videos videos rented depends on the the choice of plan. $he number of videos rented is endogenous, then, since you can choose the plan. s before, because you may choose any of the three plans, this choice is endogenous. n this problem total ependiture is eogenous because we are choosing a plan given some fied video rental budget.
1.10 A ma"or ma"or a$tomob a$tomobile ile man$ man$fact fact$rer $rer is consid consideri ering ng how how to alloc allocate ate a *2 millio million n ad#ertising b$dget between two types of tele#ision programs4 ;9L football games and PA to$r professional golf to$rnaments. 6he following table shows the new sports $tility #ehicles ,&8Js that are sold when a gi#en amo$nt of money is spent on ad#ertising d$ring an ;9L football game and a PA to$r golf e#ent.
%opyright / 0122 3ohn !iley & Sons, nc.
%hapter 2 27
Besanko & Braeutigam – Microeconomics, 4th editionSolutions Manual
6he man$fact$rer=s goal is to allocate its *2 million ad#ertising b$dget to ma/imize the n$mber of &8Js sold. Let F be the amo$nt of money de#oted to ad#ertising on ;9L football games' G the amo$nt of money spent on ad#ertising on PA to$r golf e#ents' and C ,F 'G the n$mber of new #ehicles sold. a What Wh at is the the ob" ob"ec ecti ti#e #e f$nc f$ncti tion on for for thi thiss pro probl blem em? ? b What is the constraint? c Writ Wr itee a stat statem emen entt of of the the cons constr trai aine ned d opt optim imiz izat atio ion n pro probl blem em.. d n lig light ht of of the the info informa rmatio tion n in the the table table'' how how sho$ sho$ld ld the the man man$f $fact act$re $rerr alloc allocat atee its its ad#ertising b$dget?
a(
$he ob)e $he ob)ect ctiv ivee funct functio ion n is is the the num number ber of new new S@L S@Lss ssol old, d, whi which ch we we can can denot denotee by Q' F, F, G(.
b(
$he constraint is that total spending must be less than or e-ual to J0million, or TS ≤ J0 million.
c(
$hee cons $h constr trai aine ned d opti optimi mia attion prob probllem is
ma Q( F , G ) ( F ,G )
d(
sub)ect to TS ( F , G )
≤ J0
million
$he foll $he follow owin ing g tabl tablee shows shows all all poss possib ible le com combi binat natio ions ns of of spen spendi ding ng on on foot footba ball ll games and golf events6
' F, F, G(
:ew sales from F
:ew sales from G
$otal new sales
'1, 0(
1
=
=
'1., 2.(
21
H
2H
'2, 2(
2
G
02
'2., 1.(
2=
H
0>
%opyright / 0122 3ohn !iley & Sons, nc.
%hapter 2 24
Besanko & Braeutigam – Microeconomics, 4th editionSolutions Manual
'0, 1(
01
1
01
$he table indicates that new S@L sales are maimied when ' F, F, G( D '2., 1.(, that is, when the manufacturer spends J2. million on football and J1. million on golf.
1.1 An electri electricity city prod prod$cer $cer has has two power power plants' plants' each each of of which which emits emits carbon carbon dio/ide dio/ide ,CK2' a greenho$se gas. Each plant is c$rrently emitting 1'+++'+++ metric tons of CK 2 per year. owe#er' new emissions r$les restrict the firm=s emissions to 1'+++'+++ metric tons of CK2 per year from both plants ombined . 6he cost of operating a power plant goes $p as it c$rtails its emissions. 6he table below shows the cost of operating each plant for different emissions le#els4 Emissions of CK 2 by a plant ,metric tons per year + 2-+'+++ -++'+++ -+'+++ 1'+++'+++
Ann$al cost of operating plant 1 ,millions
Ann$al cost of operating plant 2 ,millions
*%+ *30+ *2-+ *10+ *+
*2-+ *10+ *+ *%+ *1+
6he firm=s goal is to choose emissions le#els at each plant that minimize its total cost of operating its plants' s$b"ect to meeting its emissions target of 1'+++'+++ metric tons of CK 2 per year from both plants combined. Let ! denote denote the )$antity of emissions from plant 1 and " denote denote the )$antity of emissions from plant 2. Let TC , ! '" denote the total operating cost of the firm when the )$antity of emissions from plant 1 is ! and and the )$antity of emissions from plant 2 is " . a. What Wh at is the the ob" ob"ec ecti ti#e #e f$nc f$ncti tion on for for thi thiss pro probl blem em? ? b. What is the constraint? c. Writ Wr itee a stat statem emen entt of the the cons constr trai aine ned d opti optimi miza zati tion on prob proble lem. m. d. n lig light ht of of the the info informa rmatio tion n in the the table table'' what what emis emissio sions ns le# le#el elss from from each each plant plant sho sho$ld $ld the firm choose? a. b.
c.
$he ob)ective function is TC ' X (. X ,Y (. $he constraint is X Y D D 2,111,111 $he st statement of of the problem is6 min' X X ,Y ( X ,Y ( TC ' X Sub)ect to6 X Y D D 2,111,111
%opyright / 0122 3ohn !iley & Sons, nc.
%hapter 2 2
Besanko & Braeutigam – Microeconomics, 4th editionSolutions Manual
$he solution to the problem is6 X D D >1,111 and Y D D 01,111. !e can see this by creating a table that shows various combinations of X and and Y that that add up to 2,111,111 and computing the level of total operating cost associated with each feasible combination of emissions.
d.
5missions in plant 2
$otal operating cost, plant 2
5missions in plant 0
$otal operating cost, plant 0
$otal emissions
1 01,111 11,111 -+'+++ 2,111,111
J4 =1 J 7G 1 J 0 1 *10+ J=1
2,111,111 > 1 ,1 1 1 1 1 ,1 1 1 2-+'+++ 1
J2 1 J4 1 J= 1 *10+ J0 1
2,111,111 2,111,111 2,111,111 1'+++'+++ 2,111,111
$otal operating cost, plants 2 and 0 combined J1 1 J41 1 J74 1 *32+ J74 1
1.1> 1.1> 6h 6hee deman demand d c$r#e c$r#e for for peach peaches es is gi# gi#en en by the the e)$at e)$atio ion n Qd 1++ H % P ' where P is the price of peaches e/pressed in cents per po$nd and Qd is the )$antity of peaches demanded ,e/pressed in tho$sands of b$shels per year. 6he s$pply c$r#e for peaches is gi#en by Qs RP ' where R is the amo$nt of rainfall ,inches per month d$ring the growing season and Qs is the )$antity of peaches s$pplied ,e/pressed in tho$sands of b$shels per year. Let P M denote the mar!et e)$ilibri$m price and QM denote the mar!et e)$ilibri$m )$antity. Complete the following table showing how the e)$ilibri$m )$antity and price #ary with the amo$nt of rainfall. Jerify that when R 1' the e)$ilibri$m price is 2+ cents per po$nd and the e)$ilibri$m )$antity is 2+'+++ b$shels per year.
R QN P N
2 01 01
0
4
H
2G
2G.G>
!hen R = 2, the e-uilibrium occurs where Qd D Q s, or 211 – 4 P * = P *, or P * = 01. $he e-uilibrium -uantity can be found from either supply or demandF using the latter we have Q* = 211 – 4'01( D 01. !hen R = 0, Qd = Q s implies 211 – 4 P * D 0 P * or P * D 2G.G> and the table6 Q* D 77.77. Similarly, we can fill out the rest of the 2 0 4 H 2G R * 01 77.77 1 H.77 H1 Q * 01 2G.G> 2 0 . GG.G> P
1.1 1.1 6h 6hee world( world(wid widee demand demand c$r# c$r#ee for pis pistac tachio hioss is gi#en gi#en by by Qd 1+ F P ' where P is is the price of pistachios in 8.&. dollars' and Qd is the )$antity in millions of !ilograms per year.
%opyright / 0122 3ohn !iley & Sons, nc.
%hapter 2 2G
Besanko & Braeutigam – Microeconomics, 4th editionSolutions Manual
6he world s$pply c$r#e for pistachios is gi#en by
' where T is is the a#erage
temperat$re ,meas$red in degrees 9ahrenheit in pistachio(growing regions s$ch as ran. 6he s$pply c$r#e implies that as the temperat$re de#iates from the ideal growing temperat$re of + o' the )$antity of pistachios s$pplied goes down. Let P M denote the e)$ilibri$m price and QM denote the e)$ilibri$m )$antity. Complete the following table showing how the e)$ilibri$m )$antity and price #ary with the a#erage temperat$re. Jerify that when T +' the e)$ilibri$m price is *1 per !ilogram and the e)$ilibri$m )$antity is million !ilograms per year. 3+
T QM,millions of !ilograms per year P M ,* per !ilogram
-+
0-
+
>+
1
$o fill in the table, one could create a set of tables, each corresponding to a particular level of $, that shows Qd and Q s for various prices, where Qd and Q s are computed using the formulas in the problem. T QN'millions of kilograms per year( P N 'J per kilogram(
71 2 =
1 7 >
G H 0
>1 = 2
H1 G 4
D 71 T D P
Qd
Qs
1
9.00
0.11
2
8.00
0.22
3
7.00
0.33
4
6.00
0.44
5
5.00
0.56
6
4.00
0.67
7
3.00
0.78
8
2.00
0.89
9
1.00
1.00
10
0.00
1.11
D 1 T D P
Qd
Qs
1
9.00
0.43
2
8.00
0.86
3
7.00
1.29
4
6.00
1.71
%opyright / 0122 3ohn !iley & Sons, nc.
%hapter 2 2>
Besanko & Braeutigam – Microeconomics, 4th editionSolutions Manual
5
5.00
2.14
6
4.00
2.57
7
3.00
3.00
8
2.00
3.43
9
1.00
3.86
10
0.00
4.29
T= 65 P
Qd
Qs
1
9.00
4.00
2
8.00
8.00
3
7.00
12.00
4
6.00
16.00
5
5.00
20.00
6
4.00
24.00
7
3.00
28.00
8
2.00
32.00
9
1.00
36.00
10
0.00
40.00
T= 70 P
Qd
Qs
1
9.00
9.00
2
8.00
18.00
3
7.00
27.00
4
6.00
36.00
5
5.00
45.00
6
4.00
54.00
7
3.00
63.00
8
2.00
72.00
9
1.00
81.00
10
0.00
90.00
T= 80 P
Qd
Qs
1
9.00
1.50
2
8.00
3.00
%opyright / 0122 3ohn !iley & Sons, nc.
%hapter 2 2H
Besanko & Braeutigam – Microeconomics, 4th editionSolutions Manual
3
7.00
4.50
4
6.00
6.00
5
5.00
7.50
6
4.00
9.00
7
3.00
10.50
8
2.00
12.00
9
1.00
13.50
10
0.00
15.00
1.2+ Consider Consider the the compara comparati#e ti#e stati statics cs of the farme farmer=s r=s fencin fencing g problem problem in Learni Learning(B ng(By( y( oing E/ercise 1.%' where L is the length of the pen' W is the width' and # LW is the area. a &$pp &$ ppos osee the the n n$m $mbe berr of feet feet of of fe fenc ncee gi#e gi#en n to the the farm farmer er was was init initia iall lly y F 1 2++. Complete the following table. Jerify that the optimal design of the fence ,the one yielding the largest area with a perimeter of 2++ feet wo$ld be a s)$are. 1+ + ++
L W #
2+ >+
3+
%+
-+
0+
+
>+
+
b ;ow ;ow s$p s$ppo pose se the the far farme merr is is ins inste tead ad gi#e gi#en n 2%+ 2%+ feet feet of fenc fencee , F 2 2%+. Complete the following table. By how m$ch wo$ld the length L of the optimally designed pen increase? 2+ 1++ 2+++
L W #
3+ +
%+
-+
0+
+
>+
+
1++
c When Wh en the the amo amo$n $ntt of of fen fence ce is incr increa ease sed d ffro rom m 2++ 2++ to 2%+ 2%+ , $F %+' what is the change in the optimal length , $L? d When Wh en the the amo$ amo$nt nt of fenc fencee is is inc incre reas ased ed from from 2++ 2++ to 2%+ 2%+ , $F %+' what is the change in the optimal area , $#? s the area # endogeno$s or e/ogeno$s in this e/ample? E/plain.
< !
21 =1 =1 1
01 H1 2G1 1
71 >1 021 1
41 G1 041 1
1 1 01 1
G1 41 041 1
>1 71 021 1
H1 01 2G1 1
=1 21 =11
b( < !
01 21 1 011 1
71 =1 0>1 1
41 H1 701 1
%opyright / 0122 3ohn !iley & Sons, nc.
1 >1 71 1
G1 G1 7G1 1
>1 1 71 1
H1 41 701 1
=1 71 0>1 1
2 11 01 0111
%hapter 2 2=
Besanko & Braeutigam – Microeconomics, 4th editionSolutions Manual
$he length < of the optimally designed fence increases by 21 ' ∆ F K 4 (. c(
s in b(, b(, the the leng length th < of of the the opti optima mall lly y des desig igned ned fence fence incr increa ease sess by by 21 21 '∆ F K 4 (.
d(
!hen ∆ F = 41 , ∆ A = 2211 . $he area in this this problem is an endogenous variable. $he farmer may choose values for < and ! and choices for these variables imply a value for . So, implicitly, the farmer farmer is choosing the area of the pen.
1.21 Which Which of the the followi following ng stateme statements nts s$gges s$ggestt a positi# positi#ee analysis analysis and and which which a normat normati#e i#e analysis? a f the the 8nited 8nited &tate &tatess lifts lifts the the proh prohibi ibitio tion n on import importss of C$ban C$ban cigar cigars' s' the the price price of of cigars will fall. b A free freeze ze in 9lor 9lorida ida will will lea lead d to to an an inc incre rease ase in the price price of orang orangee "$ic "$ice. e. c 6o pro#id pro#idee re#e re#en$e n$ess for for p$b p$blic lic schoo schools' ls' ta/es ta/es on on alcoh alcohol ol'' tobac tobacco co'' and and gambl gambling ing casinos sho$ld be raised instead of increasing income ta/es. d 6elep 6e lephon honee comp compan anie iess sho$l sho$ld d be be allo allowed wed to offer offer cable cable 6J ser#i ser#ice ce as well well as as telephone ser#ice. e f tel teleph ephone one compa companie niess are are allo allowed wed to offer offer cab cable le 6J 6J ser# ser#ic ice' e' the the price price of of both both type typess of ser#ice will fall. f o#er o#ernme nment nt s$bsi s$bsidi dies es to farme farmers rs are too high high and and sho$l sho$ld d be be pha phased sed o$t o$t o#e o#err the the ne/t decade. g f the the ta/ on ciga cigare rette ttess is incr increas eased ed by by -+ cents cents per per pac! pac!'' the the e)$il e)$ilibr ibri$ i$m m price price of cigarettes will rise by 3+ cents per pac!.
9ositive analysis – this statement indicates what the conse-uences of the @.S. action will be, ignoring any value )udgment when making the claim. 9ositive analysis – again this statement simply indicates the conse-u ences of a change in an eogenous variable on the market, ignoring any value )udgments. :ormative analysis – here the author implies that there are two possible solutions solutions to providing additional revenues for public schools and suggests, based on a value )udgment, which of the alternatives is better. :ormative analysis – again the author makes a claim based upon his own value )udgment, namely that telephone companies offering cable $L service would be a good thing. 9ositive analysis – $he author is is making a positive statement. statement. $he author is predicting the effect of a policy change on the price in a market. :ormative analysis – here the author is making a prescriptive statement about what should be done. $his is a value )udgment about the policy to subsidie farmers.
%opyright / 0122 3ohn !iley & Sons, nc.
%hapter 2 01
Besanko & Braeutigam – Microeconomics, 4th editionSolutions Manual
9ositive analysis – the author is making a prediction about what will happen if the ta on cigarettes is increased. !hile the claim may not be accurate, the statement is predictive and made without the author imposing any value )udgments on the prediction.
%opyright / 0122 3ohn !iley & Sons, nc.
%hapter 2 02
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