E322 Notes (Managerial Economics)

8/13/2019 E322 Notes (Managerial Economics)

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Managerial Economic 322 Class Notes Houston H. Stokes

Version 18 October 2007

Managerial Economics Concerne! "it# t#e a$$lication o% economic $rinci$les an! met#o!s to t#e!ecision making $rocess un!er con!itions o% uncertaint&.

'#eor& 'ools( Micro Economics) Statistics) Econometrics *O+S,

So%t"are an! -ecision Su$$ort 'ools( Ecel) Matlab) /3S

oal( -eelo$ a s&stematic an! re$ro!ucible !ecision making strateg&.

Common 'asks %acing a Mo!ern Manager(

- #et#er to lease or bu& e4ui$ment5

- Ho" to !etermine t#e s#a$e o% t#e cost cure o% a $ro!uction $rocess.

- Ho" to $rice a $ro!uct.

- Ho" to estimate -eman! %or a $ro!uct.

- Ho" to %orecast -eman!.

- Ho" to estimate a $ro!uction %unction.

- Ho" a $ro!uction %unction can be use! to set "ages.

- Ho" to !etermine t#e a$$ro$riate leel o% a!ertising.

- Ho" to estimate t#e cost o% serice o% a utilit&.

- Ho" to !etermine t#e minimum cost o% a !iet.

'#e ke& goal is to %acilitate sensitiit& or 6"#at i% anal&sis. rom t#e class &ou "ill be able tomo!i%& t#e Ecel 9!ecision9 %iles to #an!le &our $roblems.

Manager s#oul! be able to incor$orate business $ractice *suc# as marku$ $ricing, into :$$lie!Managerial Economic '#eor&

Seek to establis# rules an! $rinci$les to %acilitate t#e attainment o% t#e !esire! economic goals o%management.

;ositie Economics( Ho" economic agents o$erate *!escri$tion,.

Normatie Economics( Ho" economic agents s#oul! o$erate *$rescri$tion,.

Managerial Economics( Mostl& normatie.

Mo!els !esigne! %or e$lanator& $ur$oses an! are to be


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Simple Math Toolkit

2


3/59


1

1 2 1 1 2 2

1 2

1 2 1 1 2 2

1 22 1

11 1 2

2

1. = 0

2. =

3. * ,) * ,) =

. ) * ,) =

>. ) * ,) * ,

=

?. ) * ,) * ,

7. ) * ,)

b b

y a dy dx

y ax dy dx bax

dy dzy f z z f x dy dx

dz dx

dzy zx x f z dy dx z xdx

Y y y y f x y f x

dy dydY dx

dx dx

Y y y y f x y f x

dy dy dyy y

dx dx dx

yY y f x y

y

= =

= =

= = =

= = = +

= + = =

= +

= = =

= +

= =

g

g

2

1 22 1

2

2

10

10

10

* ,

@ A @ A

@ A

8. log

log * ,

B* ,

* ,

1 B* ,ln

* ,

. log

1log

ln*10,

log * , 1= ln*10.,

10.

11. l

e

e

u u

bx

bx

f x

dy dyy y

dY dx dx

dx y

Y a bx

dY ab a

dx bx x

Y a f x

dY f xa

dx f xd du

e edt dt

d dV f t V

dt V dt f t

Y a bx

dY abab e

dx X x

e

Y ae

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dx

d

dt

=

=

=

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=

=

=

= =

=

= =

=

=

* , * ,B* ,og * , ) B* , ln* ,* , ln* ,

f t f t

b

f t df t b f t b b

f t b dt= =

3


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'o %in! a ma or min(

1. Set %irst !eriatie D 0.0 an! sole2. Calculate secon! !eriatie. DF min) G DF ma

2

2 2

32 ? 2

= ? 0 ? =

= ma 32 3? = 72 =1? 27.>

y x x

dy dx x x

dy d x

= + = = =

= => = + =

2

2 2

28 8

= 8 2 0

= 2 min 28 32 1? 12

y x x

dy dx x x

dy d x

= +

= + = =

= => + =

2

2 2

28> ?2> >

= ?2> 10 ?2.>

= 10 min 1>2?.2>

y x x

dy dx x x

dy d x

= +

= + =

= => =

2

3

2 2

2

2 2

2>0 3

1>00 >0 2

2>0 3 1>00 >0 2

1>00 200 >

= 200 10 0 20

= 10 ma

TR TC

TR Q Q

TC Q Q

Q Q Q Q

Q Q

d dQ Q Q

d d Q

=

=

= + +

=

= +

= = => == =>

;roblem coul! #ae been sole! b& setting slo$es e4ual an! soling

2>0 ? >0 10 200 20Q Q Q or Q = + => = =


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;roblems to test &our skills.

3

2

2

3

3 2

3 ?

3 ?

2 >

:G2

1. 3? .>

= 13.>2. 8 3

3

8 3* 3 ,

8 3*1? 2 ,

8 8 72 27

= 21? 1?2

y x

y x xy z

z x

y x

x x

x x

y x x x

= +

==

= +

= +

= + +

=

=

2

2

2

2 2 2

2 3

2

3

2 2 3 3

2 3 2 2

2 2 3

3

3. 73 2

7 *3 2 ,

= 7*3 2 , 7 * ,

21 1 28 21 2

. 1? ?

8 ?

3

1? *8 ? , ?* 3 ,= 8*8 ? ,* 12 , 18* 3 , *12 ,

? *8 ? , 21? * 3 ,

7?8 >7

y kxk x

y x x

y x x x x

x x x

y j k

j x

k x

y x xy x x x x x

x x x x

x x

==

=

= +

= =

= +

=

= +

= + + = +

= +

= + 2 > 81 >18 3>?x x x+ 2 2

2 2

2 2

2 2

2 2 2 2

2 2

2 2 2

2

>. 3 * ,) ? 2 ) 2

3* ? 2 ,*,* 2 ,

12* ? 2 ,* 2 ,

* 72 2 ,* 2 ,

= 2* 2 , * 72 2 ,* 8 ,* 2 ,

2* 2 ,** 2 , * 3 ,* 8 ,,

2* 2 ,* 2 2 10 ,

38 11>2 80 23

y m n m x n x

y x x

x x

x x

y x x x x x

x x x x

x x x x

x x

= = + =

= +

= +

= +

= + + = + +

= +

= + + 3

2 2

0 11>2

?* 2,*> 12 2,

x x

x x x

=

>


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2

2

?.

= 8

7. ?log >

= B* , = * ,

= ?*> = > , ? =

x

x

e

y e

y x e

y x

y x af x f x

y x x x

=

=

=

=

= =

Matlab $rograms to calculate roots o% t#ese ans"ers

% Problems in Economics 322 developed by Houston Stokes

% TR-TC

q=linspce!"#$"&

% note '( due to scler

tr = 2)"*q - 3*q'(2&tc = +)"" , )"*q , 2*q'(2&proit=tr-tc&plot!q#tr#q#tcpuse&plot!q#proit

% -2 . +3') * / ( 2.roots!0+3') " "1

% -2 b

.-2+*/(2-+2*/().roots!0-+2#"#"#-2+#"#"1

% -2 c.2+-$2*/(2.roots!0-$2#"#2+1

% -2 d.-4*/,)*/(3-+5$$*/(2,)+4$*/()-3$)*/(4.roots!0-3$)#"#"#)+4$#"#)#-+5$$#-41

% -2 e.$4"*/($-++)2*/(3-++)2*/(2,23"$*/,34$.roots!0$4"#-++)2#-++)2#23"$#34$1

?


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:ns"ers

e3226+ns =+3') * / ( 2

ns = " "ns =-2+*/(2-+2*/()ns = " " -+'+"" "'))"32 , "'5)3+4i "'))"32 - "'5)3+4ins =2+-$2*/(2

ns = "'"++ -"'"++ns =-4*/-+5$$*/(2,)*/(3,)+4$*/()-3$)*/(4ns = "'5$543 , "'+"$")i "'5$543 - "'+"$")i -"'25 , "'422i -"'25 - "'422i -"'+))+ , "'445i -"'+))+ - "'445i -"'33"2ns =

$4"*/($-++)2*/(3-++)2*/(2,23"$*/,34$ns = 2'))) -+'$+$2 +'$+$2 -"'+)$diry o

7


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73$S Solution

b3$se/ec mtri/&89 Problems in Economics 322 developed by Houston Stokes

89 TR-TC

q=:rid!"'#$"'#'+&

tr = 2)"'*q - 3'*q**2'&tc = +)""' , )"'*q , 2'*q**2'&proit=tr-tc&89 cll tbulte!q#tr#tc#proit&cll :rp;!q#proit


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tri/ Commnd' >ersion ?pril 2""+

=@ A=BRD!"'#$"'#'+9

=@ TR = 2)"'*A - 3'*A**2'9

=@ TC = +)""' , )"'*A , 2'*A**2'9

=@ PRFT=TR-TC9

=@ C?GG BR?PH!A#PRFT


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/rie% Statistical notes(

e use O+S to estimate !eman! cures.

O+S can be estimate! "it# Ecel) /3S) S$eakeas& an! ot#er s&stems.

e& terms( coe%%icient) SE) I2

See !ata on $age 173 on sales) $rice an! a!ertising.

Data from Douglas page173sales price advertisi

ng4.65 0.79 230003.02 0.99 18500

2.15 1.25 246004.4 0.89 26200

6.38 0.59 251005.5 0.45 16800

S!!"#$%&'&

RegressionStatistics

!ultiple

#

0.99295

7#S(uare

0.985963

"d)usted#S(uare

0.976605

Standard *rror

0.238381

%+servations

6

",%-"df SS MS F Significance F

#egression

2 11.97432

5.987162

105.3605

0.001663

#esidual 3 0.170476

0.056825

&otal 5 12.1448

10


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Coefficients

Standard Error

t Stat P-value Lower95%

Upper95%

Lower95!%

Upper95!%

ntercept 5.718022

0.635793

8.993532

0.002902

3.694644

7.7414 3.694644

7.7414

/

-aria+le1

5.80262 0.39974

6

14.5157 0.00070

9

7.07479 4.53045 7.07479 4.53045

/-aria+le2

0.000153

2.98*05

5.139834

0.014269

5.84*05

0.000248

5.84*05

0.000248

Sales rise i% $rice goes !o"n. Sales rise i% a!ertising goes u$. :!


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Iesults

b D

8.00? 20.8 31.2?13 0.02?

/3S setu$ %or $roblem. e use a #ig#er leel comman! as "ell as mat#. ra$#s s#o" results.

/$ Tests OLS for E322

b34sexec data;

input obs y x1 x2 x3;

datacards;

1 149.14 .77667 .21742 .62031

2 167.09 .29961 .9914 .75751

3 151.8 .61454 .50349 .60719

4 135.69 .26693 .11695 .69936

5 166.34 .51311 .65085 .91552

6 145.53 .98985 .16785 .51892 7 167.81 .69008 .93999 .63845

8 130.39 .40984 .37011 .25652

9 138.13 .5172 .40385 .3915

10 141 .78821 .10173 .57355

11 137.09 .75963 .3724 .24666

12 134.19 .33848 .88302 .027473

13 150.58 .53163 .36573 .75816

14 134.03 .73944 .20044 .3554

15 125.97 .94043 .15688 .080885

b34sreturn;

b34srun;

b34sexec reg;

model y=x1 x2 x3;

b34srun;

b34sexec matrix;

call loaddata;

y=vfam(y);

12


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x=matrix(norows(y),4:);

x(,1)=1.;

x(,2)=vfam(x1);

x(,3)=vfam(x2);

x(,4)=vfam(x3);

beta=inv(transpose(x)*x)*transpose(x)*y;yhat=x*beta;

call print(beta);

call tabulate(y yhat);

/$ Do ols using built in commands

call olsq(y x1 x2 x3 :print);

call graph(%res);

call graph(%y,%yhat);

b34srun;

REB Commnd' >ersion + Februry +55

+"""""" double precision slots in spce# 4 re bein: used'

Dependent vrible I- 2?dLusted R**2 = "'55$3225)Stndrd Error o Estimte +'"23)4Sum o Squred Residuls ++')2$22odel Sum o Squres 2)2'+""Totl Sum o Squres 2)43'4$F! 3# ++ 4+4'3)4F Si:niicnce +'"""""""+8Condition o IPI "'33)$E-"2Jumber o bservtions +)Durbin-Mtson +'"+2$$3

>rible Coeicient Std' Error tI+ N "O 2"'4553 +'$+332+2 +$'4$+)

I2 N "O 3+'2+33) +'"3)3)4 3"'+53)+4I3 N "O $"'"2525 +'"2"534 3'334"3CJST?JT N "O 54'5"")4) +'3352344 3'4$43)4

tri/ Commnd' >ersion ?pril 2""+

=@ C?GG G?DD?T?9

=@ =>F?!9

=@ I=?TRI!JRMS!#$


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=@ H?T=I*7ET?9

=@ C?GG PRJT!7ET?9

7ET? = >ector o $ elements

54'5"" 2"'455$ 3+'2+3 $"'"25

=@ C?GG T?7G?TE! H?T9

bs H?T + +$5'+ +$'4 2 +'+ +') 3 +)+'4 +)+'4 $ +3)' +3'+ ) +'3 +' +$)') +$)' +'4 +4'3 4 +3"'$ +25'3

5 +34'+ +34'" +" +$+'" +$+') ++ +3'+ +3'3 +2 +3$'2 +3$' +3 +)"' +)+'4 +$ +3$'" +3$'4 +) +2'" +2'

=@ C?GG GSA! I+ I2 I3 rible G: Coeicient SE tI+ " 2"'4553 +'$+332+2 +$'4$+)I2 " 3+'2+33) +'"3)3)4 3"'+53)+4I3 " $"'"2525 +'"2"534 3'334"3CJST?JT " 54'5"")4) +'3352344 3'4$43)4

=@ C?GG BR?PH!%RES9

=@ C?GG BR?PH!%#%H?T9

73$S tri/ Commnd Endin:' Gst Commnd rec;ed'

Spce vilble in lloctor 44332# pek spce used 32"Jumber vribles used $+# pek number used $+

1

J

2 $ 4 +" +2 +$

bs

2 $ 4 +" +2 +$

+3"

+3)

+$"

+$)

+)"

+))

+"

+)

H

?

T

E322 Test =odel

2 $ 4 +" +2 +$

R

E

S

bs

2 $ 4 +" +2 +$

-+

-')

"

')

+

+')

2

Residuls o ?bove =odel


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Decision Tools

Net ;resent Value

-e%ine Vias %uture reenue an! r D t#e interest rate an! c 0as t#e initial cost. '#e net $resent alueo% a stream o% $a&ments is(

0

1 *1 ,

ni

i ii

FVNPV FV c

r==

+

K% t#e $a&ments are m times a &ear

=

*1 = ,

i

i

FV mPV

r m=

+

'able /3 is %or !ail& $a&ments.

ormulas suggest t#at a lan!lor! "ants mont#l& $a&ments not &earl& $a&ments at t#e en! o% t#e&ear.

irm assigns $robabilities o% arious outcomes.

;roblem 1G 6O%or! E4ui$ment Com$an& is a tem$late case regar!ing lease s bu&. SeeEam$le1.ls %or t#e Ecel Solution

'ro+lem 19 %ford *(uipment ompan nouse vs ontract out

ost pro+a+ilit *- &a+le +2 pvintnperpa

20000.00 0.15 3000.00 pa 1.00

30000.00 0.2 6000.00 interest 0.15

40000.00 0.3 12000.00 nper 1

50000.00 0.25 12500.00 pv 0.8695652

60000.00 0.1 6000.00

*- of n ouse 39500.00 &a+le +1 pa:1;r>> &a+le +3 'resent value +as

pa 1.00

interest 0.15

nper 1

'- 0.92843668

Sum pv 0.92843668

1>


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Consult t#e bottom o% t#is Ecel %ile %or t#e earless :mbition Iacing 'eam ;roblem

Decision Making Under Uncertainty

G K!enti%& courses o% action

G IecogniLe $ossible outcomes %rom eac# actionG :ssign $robabilitiesG :$$l& !ecision criterion

DF ;ro$erl& traine! lea!ers "ill come to t#e same conclusion. '#e !ecision making ste$s can bere$licate! an! im$roe! oer time.

Maximize expected value criterionD i iR P "#erereturn %or eent i) $robabilit& it# eent ll occuri iR P= =

Minimax Criterion +ist t#e "orst outcomes o% all $ro$ose! courses o% action. Select t#e one t#atloses &ou t#e least.

Maximax Criterion +ist t#e best outcomes o% all $ro$ose! courses o% action. Select t#e one t#at"ill gie &ou t#e biggest $a&o%% i% all comes out "ell.

Certainty Equivalent Criterion '#e amount o% mone& t#at "oul! make t#e !ecision makerin!i%%erent bet"een un!ertaking t#e act) or receiing t#at sum o% mone&.

e& $oint E$ecte! alue is an aerage conce$t) not goo! %or one s#ot !eals. or one s#ot !eals t#ecertaint& e4uialent EV

EV not a goo! "a& to !eci!e "#o to marr&.

EV ma& be a "a& to $rocee! to get a !ate.

: %ormer $resi!ents "i%e marrie! a ric# ol! man $resumabl& on t#e basis o% a CEC calculation.

Certaint& e4uialent criterion makes a $erson access attitu!e to"ar! risk.

Decision Treesallo" !ecision making un!er uncertaint&. -ecision trees s#o" cost an! reenueconse4uences o% eac# $ossible !ecision.

Evaluation o! Decisions"or a gien risk "ant to maimiLe return. or a gien return "ant tominimiLe risk. Ealuate !ecisions(

G as su%%icient searc# actiit& un!ertaken5

G as in%ormation obtaine! use! $ro$erl&5

1?


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G as t#e a$$ro$riate !ecision a$$lie!5

G as sensitiit& anal&sis use! to !etermine "#at assum$tions are most critical. K. e. #o"sensitie is t#e !ecision to t#e assum$tion use!5

'#ings to consi!er(

G '#e more %re4uent one is con%ronte! "it# a !ecision DF can calculate t#e outcome "it#more certaint&.

G Magnitu!e o% t#e gamble G Can &ou a%%or! t#e maimum loss5

G #at is &our attitu!e to"ar!s risk5

Standard Deviation

2

1

* ,n

i i

i

x EPV p=

=

Coe!!icient o! #ariation mean $ Standard Deviation

NonGeconomic actors

G -oes t#e %irm #ae t#e same interests as t#e !ecision maker5 K% t#e CEO is $ai! as a

%unction o% t#e siLe o% t#e com$an& "ill t#e same !ecision be ma!e as i% #e=s#e "as an o"ner5

Value o% Kn%ormation

G -i%%erence bet"een "#at &ou can earn "it# t#e in%ormation &ou alrea!& #ae an! "#at &oucoul! earn i% &ou kne" "it# certainl& t#e outcome $rior to t#e !ecision. '#is is not al"a&s $ossible.

:ssume &ou are consi!ering selling ice cream or #ot !ogs "#ere "eat#er is 1> rain) >> clou!&)an! 30 sunn&.E$ecte! alue o% regret

E$ecte! cost o% not kno"ing eactl& "#at "eat#er con!itions "ill occur. '#e e$ecte!alue o% regret is e4ual to t#e alue o% in%ormation.

Stu!& $ages 33G3 an! look at e3222!1.ls an! e322c#2.ls

'#ese $roi!e a tem$late %or a large=small mac#ine !ecision tree

17


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Characteristics o! Decision Maker

Iisk aersion DF ;s&c#ic !issatis%action or !isutilit& cause! b& uncertaint&.

Iisk $re%erence DF Iisk is ie"e! as utilit& $ro!ucing.

Iisk neutral DF ;erson is in!i%%erent bet"een !i%%erent leels o% risk.

Maimin DF since "orst case %or t#e large mac#ine *G2083, an! t#e "orst case %or t#esmallest mac#ine *8?1, an! bu& t#e smallest mac#ine.

Nee! to resole large s small mac#ine case "it#(

G :lternatie assum$tions on sales = $ro%it

G :lternatie interest rates.

#at are t#e ke& assum$tions5

/asic 'ools to use Micro to uncoer $re%erences(

'#eor& o% Economic Consumer /e#aior(

Kn!i%%erence Cure DF locus o% $oints to "#ic# t#e consumer is in!i%%erent.

/u!get line DF locus o% $oints "#ere e$en!iture is %ie! at x yP X P Y= +

:ssum$tions(

Consumers can rank or!er $re%erences.

;re%erences are trans%erable) or i% : F / an! / F C t#ere%ore : F C

Consumers $re%ers more to less o% a goo! or no satiation.

Consumers e$erience !iminis#ing MP %or all goo!s.

Marginal rate o% substitution *assuming Q on Q aisRR, D =Y X

MIS !ecreases as "e moe !o"n in!i%%erence cure because gie u$ less o% Q an! get more o% toremain at same leel o% #a$$iness.

18


19/59


X

Y

MMR!

M=

Kn general bu!get constraint is1

n

i i

i

PQ=

= or t"o goo! case) x yP X P Y= +

Slo$e o% bu!get constraint is=

=Y X

X Y

P P

P P

=

MISDSlo$e o% bu!get line DFX X

Y Y

M P

M P= or in n goo! case 1 2

1 2

n

n

M M M

P P P= = =L

rom bu!get lines an! in!i%%erence cures "e can obtain a !eman! cure. Once "e kno" t#is cure"e can get a !eman! cure. '#e interce$t o% t#is cure an! t#e su$$l& cure can be c#ange!.

Sole sim$le s&stem(

TsD 1800 20;

T!D 3>>0 G 2??;

Kn e4uilibrium T!D Ts. or 1800 20; D 3>>0 G 2??;

>0?; D 17>0 DF ; D 3.? an! T D 1800 *17>0=>0?,U20 D 2?30

Ecel %ile c#21.ls soles t#is s&stem. Psing t#is tec#nolog&. Sole t#e s&stem assuming(

- :n a!ertising cam$aign raises 3>>0 to 023.

- : lack o% rain%all lo"ers 1800 to 1>00

- : c#ange in taste c#anges 2?? to 280

'#is is t#e basic tem$late %or micro anal&sis o% su$$l& an! !eman!. : ma


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T D 8G2; DF *T=;, D G2

:s T 0 DF E! G

:s ; 0 DF E! 0

K% XE!X F 1 DF ; DF Total %evenue*'I, u$.

'I D ; U T

: %irm s#oul! neer o$erate "#ere XE!X Y 1.

:!ertising is !esigne! to make XE!X !ecrease !or every price. :%ter a success%ul a!ertising cam$aignt#e %irm "ill #ae more $ro!uct !i%%erentiation an! can eit#er raise $rice or increase sales at t#e current$rice. Care%ul anal&sis "ill tell us "#at to !o.

20


21/59


irm starte! "it# !eman! cure a e "#ic# im$lie! $rice ;1 an! T1. : ma


22/59


Since !% D ce an! b! F ac D F at ! X!X is less t#an at c

Note t#at at a !D G"#ile at e ! D 0.

& parallel shi!t right o! a demand curve makes is more inelastic at each price"

'ncome elasticitymeasures t#e $ercent c#ange in t#e 4uantit& o% a goo! %or a $ercent c#ange inincome.

EK K D *T=T,=*K=K, D *T=K,*K=T,

: goo! is normali% KF 0 an! in!eriori% KY 0 . /ake! beans are t#e classic in%erior goo! an! t#e/M car a classic normal goo!.

:ssume an in!ii!ual %aces goo!s a to n. +et ;abe t#e $rice o% goo! a) ;bbe t#e $rice o% goo! b. +et

: be t#e c#ange in t#e amount o% : boug#t an! / be t#e c#ange in t#e amount o% / boug#t. :ssumet#e in!ii!ual gets an increase in income K.

;a: ;b/ W.. ;nN D K

K% "e assume K D 0) t#e aboe e4uation !e%ines t#e (udget line "#ic# "ill be use! in in!i%%erencecure anal&sis.

-ii!e aboe e4uation t#roug# b& K an! t#en multi$l&ing all terms on t#e le%t b& K : = K : gies a ke&

e$ression. Kn ste$s

@ = A @ = A )...)@ = A @ = AP " # P $ # P N # # #a b n + + =

@ = A @ = A )...)@ = A @ = AP " "# # " # P $ $# # $ # P N N# # N # # #a b n + + =

inall&

1a a# b b# n n# % % % + + + =L

Or t#e sum o% t#e "eig#te! income elasticities D 1

'#e cross price elasticity o! demand "P$ measures t#e e%%ect o% t#e $rice o% goo! / on t#e 4uantit&

o% goo! :.

* = , =* = ,b"P $ $

" " P P =

22


23/59


K% : is a substitute %or /) t#en "P$ is F 0 or an increase in t#e $rice o% / DF t#e 4uantit& o% : . K% :

is a com$lement o% / t#en "P$ is Y 0. Coke is a substitute %or ;e$si "#ile gas is a com$lement %or an

auto.

Kn t#e long run !eman! is usuall& more elastic. #en t#e $rice o% gas "ent u$ in t#e 70Bs $eo$le !i! not


24/59


!D *T=;,U*;=T,

T=; G2=20 DF ! D *G.1,U*80=20, D G.0

at 100 ! D *G.1,U*100=18, D G.>?

;roblem 2. ' or 9Since tuition #as !ouble! in real terms in t#e last 1> &ears t#is im$lies t#e !eman!cure %or e!ucation is ertical.9 :+SE ma& be seeing s#i%ts o% bot# su$$l& an! !eman!.

Consumer )ehavior

*ey &ssumptions o! Theory o! Consumer )ehavior+

;re%erences are complete ,- Consumers can rank market baskets"

;re%erences are transitive ,- K% consumer $re%ers basket : to / an! / to C t#en t#e consumer$re%ers : to C.

More o% an& goo! is al"a&s better.

'ndi!!erence CurveG +ocus o% $oints s#o"ing !i%%erent combinations o% goo!s to "#ic# t#e consumeris in!i%%erent.

2


25/59


Consumer starts "it# a o% an! b o% Q. ;oints in K DF more satis%action. ;oints is KKK DF lesssatis%action.

Kn!i%%erence cures must be in KK an! KV.

: straig#t line in!i%%erence cure in KK an! KV DF substitutes: rig#t angle in!i%%erence cure DF com$lements

2>


26/59


Kn!i%%erence cures cannot cross unless t#ere is a c#ange in tastes.

.rdinal ranking DF : is better t#an / but cannot tell b& #o" muc#.

Cardinal ranking DF Can tell #o" muc# better : is t#an /.

Slo$e o% in!i%%erence cure measure marginal rate o! su(stitution (et/een goods. Kn terms o% aboe

eam$le D * = , Y X assuming Q on Q ais. :s * = , * = ,Y X Y X => or in "or!s &ouget more an! more Q %or eer& unit gien u$.

ien &ou #ae relatiel& more t#an Q DF "ill gie less Q %or eer& a!!itional .)udget line , locus o% $oints s#o"ing !i%%erent combinations o% goo!s t#at can be boug#t gienincome. #ere bu!get lines is tangent to #ig#est in!i%%erence cure DF !esire! $oint *e,.

aD K = ;&) b D K = ; an!B=

x

c # P= . :%ter t#e $rice o% %alls moe to #ig#er in!i%%erence cure an! go to

$oint !. :t e MIS D Q= D;= ;&

i% income increases bu!get line moes out an! is $arallel to t#e ol!er bu!get line.

2?


27/59


K% $rice o% %alls bu!get line rotates %rom ab to ac.

'otal s$en!ing %ie! along bu!get line. Ob


28/59


Casae(

:ntonio bu&s 8 ne" college tetbooks at a cost o% >0.00 eac#. Pse! books "ere 30.00 eac#. Net&ear $rices %or ne" books go u$ 20 an! use! books go u$ 10. :ntonioBs -a! sent #im 80.00 more.Ks #e better o%%5

Cost last &ear %or ne" books 8 U >0.00 D 00.00Cost last &ear %or use! books 8 U 30.00 D 20.00

Ielatie $rice o% ne" an! use! books last &ear >0=30 D 1.?7

Ielatie $rice o% ne" an! use! books t#is &ear *>0U1.20,=*30U1.1, D ?0 = 33 D 1.82

Ne" books are relatie more costl&.

Cost t#is &ear %or t#e t"o c#oices "oul! be 8U?0 D 80

8U33 D 2?

-a! gae #im mone& to bu& 8 ne" books t#is &ear. ill #e still bu& t#is bun!le no" t#at $rices o% ne"books are relatiel& #ig#er5

Zane #as a utilit& %unction P*)c, D C. Set u$ a table %or PD12 an! P D 2Su$$ose Zane #as 12.00 to s$en! an! ;%D 1.00 an! ;cD 3.00 S#o" bu!get line#at s#oul! s#e bu&5 *D? C D2 ,.

P*)C, D C ; %oo! 1 ; Clot# 3

PD12 PD2

C Cost C Cost

1 12 37 1 2 73

1.> 8 2>.> 2 12 38

2 ? 20 3 8 27

3 1> ? 22

3 13 ? 18

? 2 12 8 3 17

8 1.> 12.> 12 2 18

12 1 1> 2 1 27

/u!get line is Q D ;%U ;cU C

MIS D G1=3

28


29/59


'ndividual Market Demand

Demand Curve holds constant+

0rices o! other goods

'ncome

Tastes

:ssume Kncome aailable is K(

: D K =;1&) / D K = ;1) C D K = ;2) - D K = ;3

:s ;%alls t#e bu!get line moes %rom :/ to :C to :-. '#e $ossible set o% goo!s increases. '#econsumer increases $urc#ases andQ $urc#ases. '#e aboe !iagram is same as %igure .1.

;oints to remember( :s $rice o% %alls t#ere is a su(stutution e!!ectt#at is !ue to t#e relatie $ricec#ange an! an income e!!ect"#ic# is !ue to t#e increase in real income !ue to t#e $rice !ecrease. K%t#e $rice o% %alls) t#e consum$tion o% Q can increase) or !ecrease.

2


30/59


'ncome Consumption Curve'races out $oints o% consum$tion o% an! Q t#at occurs as incomeincreases.

K% an! Q are bot# su$erior goo!s) as K increases t#e consum$tion o% an! Q increases. DF-eman! cures %or bot# goo!s s#i%t rig#t.

K% is in%erior at #ig# income D F as K increases) consum$tion o% eentuall& %alls.:s Kncome rises consum$tion %irst increases) t#en %alls. :s income rises t#e consum$tion o% Qincreases.

Q is a normal good. is a normal goo! %or lo" incomes) an in!erior good%or #ig# $rices.

Kn an N goo! "orl! all goo!s can be normal goo!s. :s a u$$er limit onl& NG1 can be in%erior. DF Kna 2 goo! "orl! cannot #ae t"o in%erior goo!s.

Kncome an! substitution e%%ects can be !ra"n "a&s %or a $rice %all an! "a&s %or a $rice rise

assuming normal goo!s. or t#e in%erior not gi%%en an! in%erior gi%%en t#ere are 8 ot#er "a&s eac#.'otal number o% cases D 2.

'n!erior not 1i!!enD F goo! is in%erior but not so in%erior t#at t#e income e%%ect out "eig#ssubstitution e%%ect.

our "a&s to !ra" cases(

Hicks met#o! *:merican assum$tions,. DF :ssume base case. ;rices c#ange causing t#ebu!get line to rotate. Hel$ing bu!get line !ra"n tangent to ol! in!i%%erence cure but $arallel to ne"bu!get line.

Slutsk& met#o! *:merican assum$tions, DF :ssume base case. ;rices c#ange causing t#ebu!get line to rotate . Hel$ing bu!get line !ra"n t#roug# ol! basket but $arallel to ne" bu!get line.

Hicks met#o! *Euro$ean :ssum$tions,. DF :ssume base case. ;rices c#ange causing t#ebu!get line to rotate . Hel$ing bu!get line !ra"n tangent to ne" in!i%%erence cure but $arallel to ol!bu!get line.

Slutsk& met#o! *Euro$ean :ssum$tions, DF :ssume base case. ;rices c#ange causing t#ebu!get line to rotate . Hel$ing bu!get line !ra"n t#roug# ne" basket but $arallel to ol! bu!get line.

or a $rice %all Hicks *Slutsk&, met#o! "it# :merican assum$tions looks like a $rice increase %orHicks *Slutsk&, "it# Euro$ean assum$tions.e assume income is %ie!. Original bu!get line is ac. Consumer consumes : o% . ;rice %alls DFbu!get line s#i%ts out to a!. Consumer no" obtains C o% .

Hicks met#o! !ra"s #el$ing bu!get line 1 tangent to ol! in!i%%erence cure K but $arallel tone" bu!get line. :C broken into :/ *Hicks substitution e%%ect, an! /C Hicks income e%%ect.

30


31/59


Slutsk& met#o! !ra"s #el$ing bu!get line 2 t#roug# ol! $oint. Consumer isoercom$ensate! an! substitution e%%ect is no" :/Uan! income e%%ect /UC.

Slutsk& :merican met#o! is #o" +as$erse $rice in!e * P Q P Qjt j j j1 1 1= , is constructe!.

Slutsk& Euro$ean met#o! is #o" ;aasc#e $rice in!e * P Q P Qjt jt j jt= 1 , is constructe!.

:ssume Q on Q ais an! on ais. :long an in!i%%erence cure "e #ae x yX P Y P = . '#is

can be trans%orme!(

y x

y x

xy

y xx y

xy

x xP y yP

x xP y yP

X Y

PP

P X P YX P YP

X Y PPXP YP

% %

=

=

=

=

an! slo"s #o" t#e 9Hicks9 cross elasticities are relate! to t#e $ro$ortion s$ent on t#e goo!Re no" $rocee! to s#o" #o" t#ese can be estimate!R

31


32/59


Start at e. goo! %alls in $rice an! bu!get line moes out. Moe to # "#ere utilit& #as increase!

%rom P1 to P. P1GP allo"s us to measure total e%%ect D * 3 1," " " = . Kncome e%%ect "#ic# is

biase! !o"n"ar! is * 2 3," " " = . Substitution e%%ect) is !etermine! b& t#e s#a$e o% t#ein!i%%erence cure) is

U* 2 1," " " =

rom "#ic# "e !e%ine

U" " " = +

Or t#e total e%%ect D t#e income e%%ect $lus t#e substitution e%%ect.

Marginal $ro$ensit& to s$en!U U

a aa a #

P " P " "#M %

# # #"

= = =

32


33/59


U a

a

M #"

P

=

#ic# "#en "e note t#at a# " P = can be "ritten as

U a a

a

M " P"

P

=

Multi$l& b&a

a

P

" P

U

a a a

a a a

a a a

a a

a

a #

"P "P "P

" P " P " P

M P "P

" P P

M

%

= +

=

=

=

rom elasticit&) an! income elasticit& an! $ro$ortion s$ent on goo! can in!irectl& get in!i%%erencecure.

Can use similar logic to get cross e%%ects.

U

U

U

b b

b b b

b b b

a b baP aP

b b

a b

a

a

b #

" " "

"P "P "P

" P " P " P

M P "P

" P P

M $ P"

P

M

%

= +

= +

=

=

=

=

Since

U U

b bb #a

b

"P $P # "%

" P # #"

= =

33


34/59


Market !eman! D sum o% all $riate !eman!s

;rice : / C Market

1 ? 10 1? 322 8 13 2>3 2 ? 10 18 0 7 11> 0 2 ?

:t $rice F 3 consumer : is out o% t#e market.

:ssuming !eman! cure is elastic *inelastic, DF $rice %all im$lies t#at reenue increases *!ecreases,.

0oint elasticity D *;=T,U*1=slo$e,

or straig#t line !eman! cures elasticit& D $oint elasticit&. 2ot all demand curves are straightlines"

&rc elasticity , * = ,* = , Q P P Q

&rc 'ncome elasticity , * = ,* = , Q # # Q

-eman! cures #ae kinks as consumers . Sall& #as a current income o% 0)000 $er &ear an! s$en!s 800 $er &ear %or %or gas. '#e current$rice o% gas is 1.00.

a. '#e goernment is concerne! about energ& usage an! is contem$lating an ecise ta"#ic# "ill cause gas $rices to increase to 1.0. #at "ill #a$$en to Sall&Bsconsum$tion5

b. '#e oernment is consi!ering a 200.00 ta rebate. Ho" "ill t#is im$act Sall&5

3


35/59


c. :ssume bot# t#e ta an! t#e rebate are im$lemente!. Ks Sall& "orse o%% or not5

a. Sole arc elasticit& %ormula %or ne" Tb. Psing ne" T an! arc income elasticit& %ormula sub in ne" income an! recalculate T

c. See #o" muc# s#e s$en!s be%ore an! a%ter

= + +. * , = * . . ,** . . , = * ,,8 800 10 100 100 10 8002 2Q Q + = . * , * ,8 800 800 ?2 2Q Q?80 1?02. Q =

Q2 ?11 7? ?12= .

. ** , = * ) ) ,,** , = * ,,> ?12 0 200 0 000 0000 0200 ?123 3= + +Q Q

. * , * ,> ?12 ?12 013 3Q Q+ = 00> 30? 2>123.Q = +

Q3 ?13>3= .

On %inal in!i%%erence cure s#e s$en!s ?13.>3 U 1.0 D 858.94. it# #er income an! t#e rebate s#e"oul! #ae 0200G8>8. D 3)31 to s$en! on goo!s.

K% s#e boug#t ?1 at t#e ol! $rice s#e "oul! #ae #a! 0000G?1 D 338?Sall& is NO' #a$$& "it# t#e goernmentRR

;roblem [ 2

'#e San rancisco C#ronicle re$orte! t#at t#e toll on t#e ol!en gate bri!ge "as raise! %rom 2.00to 3.00. ollo"ing t#e toll increase tra%%ic %ell >.

#at is t#e $oint $rice elasticit& o% !eman!5Stee +eonou!akis c#airmen o% t#e bri!geBs %inance au!iting committee "arne! t#att#e toll increase coul! cause toll reenues to !ecrease b& 2.8 million $er &ear. Ks t#isstatement consistent "it# Economic '#eor&5

Elasticit& D * = ,* = ,Q Q P P D G.0>=.>0 D G.1 or inelastic !eman!

Stee is "rong. Knelastic !eman! DF reenue increases as $rice increases.

0roduction

irms turn inputs or !actors o! production into outputsia a production !unctionTD*)+,"

: $ro!uction %unction im$lies a gien tec#nolog&.

3>


36/59


irm uses eac# in$ut as e%%icientl& as $ossible. 'soquant*$ro!uction in!i%%erence cures, s#o"!i%%erent 4uantities o% in$uts *sa& + an! , suc# t#at out$ut is %ie!.

Kn short runnot all in$uts can be c#ange!. Kn t#e long runall in$uts can be c#ange!.

ien ) &verage productD T=+) Marginal productD T=+. T D Total product.

#en Marginal ;ro!uct F :erage ;ro!uct DF aerage $ro!uct is increasing.

M; reac#es a $eak at $oint o% in%lection on '; cure.

3a/ o! diminishing returns DF "it# ot#er in$uts %ie!) M; o% an in$ut !eclines as t#e amount o%t#at in$ut use! increases.

Malt#us beliee! t#at t#e eart# "oul! not su$$ort $o$ulation gro"t#. 'o !ate #e #as been "rong.

: tec#nological c#ange raises t#e $ro!uction %unction. Here it is occurring oer time.

Q "e ' % t=

Kn an& $articular &ear t#e aggregate alue o% goo!s an! serices $ro!uce! b& en econom& is e4ual tot#e $a&ments ma!e to all %actors o% $ro!uction.

Marginal rate o! technical su(stitutionD % '= %or a gien T * on ertical ais,.

MRT! % ' MP MP' %= = = * = ,

since along iso4uant

* ,* , * ,* ,MP ' MP %' % + = 0

#en in$uts are substitutes DF iso4uants are straig#t lines.

#en in$uts are com$lements DF iso4uants are rig#t angles

:ssuming a CobbG-ouglas $ro!uction %unction sum o% coe%%icients !etermines returns to scale.:ssume all in$uts increase b& . et

Q ae ' % ae ' % Qt a t a a aU * , * ,* , * ,= = =+ +

Eam$le( M;+D >0) MI'S D .2>. #at is M;5 . = =2> >0= =MP MP MP' k k . DFMP%= 200

Eam$le( -etermine "#et#er !ecreasing) constant or increasing returns.

3?


37/59


:. Q %' Q % ' Q Q= = =. ) . * ,* ,) UU> > 2 or increasing returns.

/. U2 3 ) 2 3Q % ' Q % ' Q = + = + = or constant returns.

Eam$le( :ssuming TD100*.8+.2, starting D an! +D s#o" M; o% labor an! are !eclining

% ' Q= = => = = 100 ??0 218 2) ) U U .. .

% ' Q MP%= = => = = => => 100 > 78 2> 12 08 2) ) U U . ) .. .

% ' Q MP%= = => = = => =? 100 ? 131 1238 2) ) U U . ) .. .

% ' Q MP%= = => = = => =7 100 7 10330 11 8>8 2) ) U U . ) .. .

% ' Q= = => = = 100 ??0 218 2) ) U U .. .

% ' Q MP'= = => = = => = >0 100 >0 ??2 8 2 ?88 2) ) U U . ) .. .

% ' Q MP'= = => = = => = >1 100 >1 ??>>2 2 ?38 2) ) U U . ) .. .

% ' Q MP'= = => = = => = >2 100 >2 ??811 2 >8 2) ) U U . ) .. .

37


38/59


Cost o! 0roduction

&ccounting Cost concerne! "it# #istorical e$en!itures.

Economic Cost takes into accountopportunity cost t#at #as to be taken into consi!eration in t#e!ecision $rocess *Kt is more costl& %or a !octor to mo" t#e la"n on Mon!a& at 10(00 t#an a


39/59


Ksocost slo$e

% ' ( r= * = ,=

o% ratio o% "age rate to rental cost o% ca$ital.

ant to maimiLe $ro!uction %or a gien total cost 'C.

'#eMRT! % ' MP MP ' %= = = = . Kn e4uilibrium t#e slo$e o% t#e isocost P P' %= D MI'S

MP MP P P ( r' k ' %= = == =

or

MP ( MP r' %

= ==

3


40/59


Expansion paths#o"s t#e amounts o% labor an! ca$ital use! as %irm gro"s '#is is a long runconce$t.

Economies o! scaleinclu!es increasing returns to scaleas a s$ecial case. Kncreasing returns to

scale re4uires in$uts be use! in %ie! $ro$ortions. Economies o% scale allo"s t#e ratio o% in$uts toc#ange.

:t minimum $oint o% +:C t#e +MC an! SMC intersect.

Economics o% scale DF MC Y :C. -iseconomies o% scale DF MC F :C. -e%ine

EC D elasticity o! total cost

E TC TC Q Q TC Q TC Q MC "CC= = =@ = A = @ = A @ = A = @ = A =

Economics o! scale ,- Ec< 1) o% MC Y :C.

Economies o! scopeare $resent "#en


41/59


:uadratic Modeluse! i% #ae straig#t line MC. MC Q= + 2 .

VC Q Q= + 2

Cu(ic cost !unction use! i% #ae P s#a$e! MC cure o% %orm

MC Q Q= + + 2 3 2

VC Q Q Q= + + 2 3

Can use Ecel an! ot#er so%t"are to estimate t#e MC cure.

Com$uter %irm cost is "C CQ Q= +10 1 3. * , . "#ere CT is cumulatie 4uantit&) an! T is 4uantit& $er&ear.

a. '#ere is a learning cure e%%ect since G.1b. '#ere is !ecreasing returns to scale5

TC Q CQ Q Q= +10 1 3 2. * ,* , .

MC TC Q CQ Q= = + = . * , .10 1 ?Since . .? 3Q Q> DF !ecreasing returns to scale

c. CTtD0)000) Tt D 10)000) Tt1D 12)000 "C "Ct t= + = = + =+10 1 0 3 10 10 1 >0 3 12 8 ?1. * , . * , .) . * , . * , .

:ssume TC a bQ cQ dQ MC TC Q b cQ dQ= + + + = = + +2 3 22 3) * , =

"C a Q b cQ dQ= + + +@ = A 2 . :C not !e%ine! %or TD0. or a P s#a$e! cost cure "e "antcY0 an! !F0. :t minimum $oint o% :C) MCD:C. SetaD0 to normaliLe & ais an! e4uate MCD:C.

DF b cQ dQ b cQ dQ+ + = + +2 3 2 2 or c dQ= 2 . K% c)G1 an! dD1 t#en TD1=2

1


42/59


*ey :uestion+ ;o/ do /e use this theory to solve a practical pro(lem =

ien t#e $ro!uction %unction

*2, Q "% '0=

*3, @ = A @ = A" % ' " % ' r ( =1 1

*, @ = A = ' % r (=

*>, ' r % (= @ = A

Substituting *>, into t#e $ro!uction %unction *2, gies

*?, 0 @ = AQ "% r % ( =

*7, % ( r Q "* , * = , = + = 0

'#e e4uilibrium amount o% ca$ital is

*8, % ( r Q "= + +@* = , A* = ,=* , =* , 01

K% t#e cost o% ca$ital) r) increases or t#e marginal $ro!uct o% ca$ital) ) %alls "ill %all. -irectsubstitution o% *8, into *>, gies

*, ' r ( Q "= + +

@* = , A* = ,* =* ,, * =* ,,

0

1

K% t#e "age rate) () increases or t#e marginal $ro!uct o% labor) ) %alls t#en less labor "ill be use!.

'#e %irms cost %unction is

*10, C (' r% = +

:t e4uilibrium

2


43/59


*11, C ( r Q "= ++ + + + +* =* ,, * =* ,, * =* ,, * = * ,, * =* ,,@* = , * = , A* = , 1

E4uation *11, s#o"s #o" C is relate! to "ages) () cost o% ca$ital) r) an! returns to scale * , + .*11, is obtaine! b& substituting *8, an! *, in *10,. M:'+:/ can be use! to calculate t#ea$$ro$riate !eriaties. E4uation *11, s#o"s #o" costs are relate! to t#e $ro!uction %unction o% t#e%irm as "ell an! in$ut costs. '#e Ecel %ile sta%%ing.ls "ill allo" use o% t#is t#eor&. *1, can be

sim$li%ie! i% 1 + = .

ost of 'roduction given 'roduction function ? interest and @.

"ssumes outputAconstant


44/59


0ro!it Maximization and Competitive Supply

irms "ant to maimiLe reenue.

Com$etitie su$$l& DF man& %irms) all $rice takers) no $ro!uct !i%%erentiation) %ree entr&

0ro!it is t#e !i%%erence bet"een reenue an! cost %or a gien leel o% out$ut 4.

*1, * , * , * ,& R & C &=

'o maimiLe $ro%it !i%%erentiate an! set to Lero. DF MI*4, D MC*4,

*2, = * , = * , =& TR Q TC Q= = 0

or a com$etitie %irm ; is gien DF d= an! ;DMI. Kt can be $roe! t#at

*3, MR "R P d d= + = +@ * = ,A @ * = ,A1 1 1 1

*, = @* , = A @* , = ATR & &p p& & p &p p& &p = + = +

= + = +p p& &p p d@ * = ,A @ * = ,A1 1 1

Kn long run ne" %irms "ill enter an! %irm "ill earn normal pro!itsor t#ose $ro%its suc# t#at no %irmsenter or no %irms leae in!ustr&.

K% an in$ut increases in $rice DF :C cure s#i%ts u$ DF MC cure s#i%ts u$ an! %irm $ro!uces lessout$ut.

Kn!ustr& su$$l& cure is t#e sum o% %irm MC cures in t#e s#ort run.

0roducer Surplus , area aboe %irm su$$l& cure an! belo" $rice. See %igure 8.11.

Kn long run %irm can alter all in$uts. K% in!ustr& is making etra normal $ro%its in t#e s#ort run DFne" %irms "ill enter suc# t#at in t#e long run all %irms are making normal $ro%its. '#e long runcom$etitie e4uilibrium $oint is ;DSMCD+MC. irm is at t#e minimum $oint o% its :C cure.

ien t#e %irmBs tec#nolog&) it is most e%%icient. Kt earns economic $ro%it *normal $ro%it,.Kn long run %irm tries to e4uate +IMC to $rice )UTne" %irms can enter t#e in!ustr& an! !rie!o"n $rice.

Economic pro!itD I G (+ G r "#ere r is t#e o$$ortunit& cost o% ca$ital. : %irm making Leroeconomic $ro%its ma& still sta& in business.


45/59


Economic rentD return to %actors o% $ro!uction in limite! su$$l&. MZ earns economic rent. Songsan! books are co$&rig#te! to allo" economic rent to be earne! %or a limite! number o% &ears.

'#e long run su$$l& o% a constant cost industryis a straig#t line. '#is is a partial equili(riumargument. :s T increases in$ut $rices "ill increase at some time. 1eneral Equili(rium#as all

assum$tions ariable. Some in!ustries are so small t#at t#e& can be assume! to #ae no e%%ect onin$ut $rices.

'ncreasing Cost CaseDF K% etra normal $ro%its are earne! ne" %irms "ill enter t#e in!ustr& an!in$ut $rices "ill increase.

Taxes. :n output taxraises t#e MC cure. : 3ump Sum Tax*suc# as a li4uor license, !oes notc#ange t#e MC since it is $ai! no matter "#at. '#e e%%ect o% a n out$ut ta in t#e long run is toreduce industry supply.

0er!ectly Competitive Markets &ssume(

- ;rice 'aking

- ;ro!uct Homogeneit&

- ;er%ect Mobilit& o% :ssets

- ;er%ect Kn%ormation

Een i% onl& one %irm in t#e market it ma& $a& to act as i% t#e %irm "as in a com$etitie market sinceetra normal $ro%its DF ot#ers %irms ma& enter to bi! a"a& $ro%it.

;roblem [ 1 '#e Conigan bo com$an& is in a com$etitie market. Kt sells boes in batc#es o% 100

%or 100.00. TC Q= +3 000 000 001 2) ) . .

#at is $ro%it maimiLing out$ut5 ant MCDMID:I. DF 100 002 >0 000= => =. ) )Q Q

#at is $ro%it5

= = + = TR TC) U* , * . U* , >00)100 >0000 3000000 001 >0000 0002

S#oul! %irm sta& in business since :VC Y ;(

"VC TVC Q TVC TC TFC= = == ) )

TVC= => > 00 000 3 000 000 2 >00 000) ) ) ) ) ) )"VC= =* ) ) , = ) >02 >00 000 >0 000

;roblem [ 2 Com$etitie market #as a market !eman! cure o%

P Q= 7> 1>.

an! su$$l& cure o%

>


46/59


P Q= +2> >. .

"#ere T D "#ere a t&$ical %irm #as MC &= +2 > 10. .

#at is market $rice an! rate o% sales5 e set S D - or

2> > 7> 1> 2> 7> 1> 2> >+ = => = = =. . ) ) . U 37.Q Q Q P

Eac# %irm sells "#ere MI D MC . Since $er%ect com$etition MID:ID;D37.>0

37 > 2 > 10 3>. . ) .= + => =& &

Note( K% &ou use c#21.ls tem$late to sole s&stem remember t#at t#e tem$late is set u$ as(U* ,) * , ) >0 2 ) >0 *1=1.>,, d , dQ f P Q f P Q P Q P = = => = + =

?


47/59


Market 0o/er+ Monopoly and Monopsony

Mono$ol& DF One $ro!ucer MI :I.

Mono$son& DF One bu&er

:ssuming ;D?GT

; T 'I MI :I 'I? 0 0 G G G 0> 1 > > > in% > 2 8 3 G 83 3 1 3 G1.> 2 8 G1 2 G.??7 8

1 > > G3 1 G.2> >

e& ormulas( MR "R= +@ * = ,A1 1

= @ = * ,A"R MR "R

K% XX Y 1 DF as 4uantit& increases 'I !ecreases.

E4uilibrium at ma $ro%it re4uires MCDMI "#ere MC #its MI %rom belo".Various $oints(

- K% normal $ro%its are ma!e DF :C cure "ill be tangent to :I cure at a $oint tole%t o% minimum $oint. Normal $ro%its "it# MI Y :I DF operating at less thanoptimum capacity"

- K% MID:I DF $er%ect com$etition. Can #ae t#ree cases( 1. K% making loss ins#ort run DF less t#an o$timum ca$acit&. 2. K% making normal $ro%its DF atminimum $oint o% :C cure. 3. K% making etra normal $ro%its DF o$erating atgreater t#an o$timum ca$acit&.

- K% MI Y :I can

;ossible Cases 'able( Stu!& belo" liste! tables an! be able to !ra" all $ossible cases an! $roe t#att#e K cases are not $ossible.

MID:IMCDMI

7


48/59


MCY:C MCD:C MCF:C:CF:I Case 1 ; Case 2 K Case 3 K

:CD:I Case K Case > ; Case ? K

:CY:I Case 7 K Case 8 K Case ;

MIY:IMCDMI

MCY:C MCD:C MCF:C:CF:I Case 10 ; Case 11 K Case 12 K

:CD:I Case 13 ; Case 1 K Case 1> K

:CY:I Case 1? ; Case 17 ; Case 18 ;

: %irm is at less t#an o$timum ca$acit& *MCY:C,) at o$timum ca$acit& *MCD:C, or greater t#ano$timum ca$acit& *MCF:C,.

Mono$ol& $o"er occurs i% MIY:I. K %irm is in a com$etitie market i% :IDMI. Kn a com$etitiemarket t#e %irm can sell as muc# as it can "it#out t#e $rice %alling.

: %irm al"a&s maimiLes $ro%it i% MCDMI an! MC #its MI %rom belo".

: %irm makes an etra normal $ro%it i% :IF:C) a normal $ro%it i% :ID:C an! a s#ort term loss i%:IY:C.

8


49/59


0ricing /ith Market 0o/er

: %irm t#at $ractices !irstdegree price discriminationc#arges eac# customer #is=#er reservationpriceo% t#e maimum t#at consumer "oul! $a&. Kn t#is "or! all consumer surplus is captured (y

the !irm. Kn $ractice t#is is #ar! to !o. Pniersities tr& to $ractice t#is a$$roac# b& giing=ustenough aidto get t#e stu!ent.

Seconddegree price discriminationoccurs "#en $rice is re!uce! i% a!!itional amounts are boug#t.

Thirddegree price discriminationoccurs "#en %irm $ackages same $ro!uct un!er t"o !i%%erent

labels an! sells at a !i%%erent $rice. Psing %ormula MR Pi i di= +@ * = ,A1 1 an!MC MR MR= =1 2 ) t#en

1 2 2 1@ = A @1 *1= ,A =@1 *1= ,Ad dP P = + +

'#ere is ei!ence to suggest t#at cou$on users #ae #ig#er elasticit& o% !eman! t#an non cou$on

users. :ssume t#e non cou$on users #ae elasticit& o% !eman!d1 " K% P1 DP2) an! V D alue o%

cou$on) t#en in an o$timum "orl!

1 2 2 1@* , = A @1 *1= ,A =@1 *1= ,Ad dP V P = + +

:irlines $rice !iscriminate.

'ntertemporal 0rice Discrimination ,- %irm c#arges %irst consumers more. Har! coer e!ition o% abook comes out %irst. /e%ore too long so%t coer comes out at a lo"er $rice. +ibrar& bu&s #ar!

coer.

0eak3oad 0ricingDF c#arge more at a certain time in t#e !a&.

T/o0art Tari!! ,-$a& to get into reat :merica) t#en) $a& %or eac# ri!e.

;olaroi! Camera cost "as entr& %ee. ilm "as $rice.

)undling. #en customers #ae heterogeneous demands that are negatively correlatedDF $a&sto bun!le $ro!ucts. E%%ectieness o% bun!ling !e$en!s on #o" negatiel& $ro!ucts are relate!.

Mie! bun!ling. Sell as a $ackage or alone. MS O%%ice 7 is sol! t#is "a&. igure 11.18 s#o"s t#at"it# Lero MC t#is is een more $ro%itable.

+uur& cars are sol! "it# stan!ar! o$tions bun!le! into t#e car. Vacation $ackage anot#er eam$le.Iestaurants sell items a la carte an! as !inners.

Tying ,-%orce customer to bu& all items %rom one source. Mc-onal!s at one time re4uire! o"nersto get su$$lies %rom one source. as station #as to carr& %ull range o% $ro!ucts.


50/59


&dvertising. ant marginal reenue o% an a!!itional !ollar s$ent on a!ertising to e4ual %ullmarginal cost o% t#at a!ertising. e !e%ine $ro%it as a %unction o% amount sol! Qan! a!ertising"-

* ) , * ) , * ,Q " PQ P " C Q "=

= * = , * = , 1 0" P Q " MC Q " = =

e rearrange an! get t#e marginal reenue %rom a!ertising.

* = , 1 * = ,a d ,MR P Q " MC Q "= = +

@ A@ = A ) @* , = A@* , = * ,A @ = AP MC Q " P MC P " Q Q " " PQ = => =1

ien elasticit& o% !eman! D @* , = * ,A" Q Q " " = ) in e4uilibrium

t#en

@* , = A @ = A

1 1@1 A @* , = A

a

p p

P MC P " PQ

MC P P MC P

=

= + => =

@ = A @ = A" PQ " P=

'#e more inelastic t#e !eman! %or t#e %irmBs out$ut) t#e more a!ertising. Kn $er%ect com$etition

since p= ) no a!ertising is !one.

Monopolistic Competition and .ligopoly

Monopolistic Competition ,- +arge number o% sellers eac# "it# some market $o"er !ue to sellinga di!!erentiated product. :t t#e mo!el leel in t#e automotie in!ustr& "e #ae mono$olistic

com$etition. d< in mono$olistic com$etition.

- Man& sellers

- Eac# seller selling a slig#tl& !i%%erentiate! $ro!uct

- Entr& b& ne" %irms is NO' restricte!

.ligopolyDF e" sellers eac# "it# market $o"er. K% one %irm in an oligo$ol& market "ere to raise$rice) t#e ot#ers "oul! not %ollo" an! t#at %irm "oul! %in! sales %all o%% ra$i!l&. K% t#e same %irm"ere to lo"er $rice #o$ing to increase sales at t#e e$ense o% t#e ot#er %irms) t#en all ot#er %irms"oul! lo"er $rice an! t#e e$ecte! increase in sales "oul! not be realiLe!.

- e" sellers

- Eac# seller selling a !i%%erentiate! $ro!uct.

>0


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- Eac# "it# substantial market $o"er

- Entr& is restricte! b& barriers *eam$le aircra%t in!ustr&,

Cartel,- irms "ork toget#er. *E in >0Bs until t#e& got caug#t.,

- +ike a mono$ol& /P' members tem$te! to c#eat.

- Cartel usuall& !oes not control com$lete market

Pn!er Mono$olistic Com$etition %ree entr& DF

- No etra normal $ro%its in long run.

- irms in long run o$erate at less t#an o$timum *minimum aerage cost, ca$acit& *seecase 13,.

Kn $er%ect com$etition an! mono$olistic com$etition >hen a market is in equili(rium !irms aredoing the (est they can and have no reason to change their price or output"

Kn oligo$ol& each !irm is doing the (est it can? given /hat its competitors are doing"

0risoners Dilemma

Nas# e4uilibrium is a noncooperative equili(rium. K% &ou #o$e t#at %irm "ill set $rice at collusieleel) t#e ot#er %irm "ill %in! t#at it $a&s NO' to set at t#is leel. Veri%& t#at c#121 s#o"s t#at i%%irm [ 2 sets .00 an! %irm [ 1 sets ?.00 *collusie $rice, t#en %irm [ 2 makes 20.00 an! %irmmakes .00.

Pse t#e tem$late to eri%&

irm [ 2 .00 irm [ 2 ?.00 irm [ 2 8.00irm [ 1 .00 12)12 20) 28)G20irm [ 1 ?.00 )20 1?)1? 28)G.irm [ 1 8.00 G20)28 G)28 12)12

it# ?) ? t#e total $ro%it is #ig#est *32.00,. /ut eac# %irm "ill look at situation as 9K% K c#arge.00 K "ill !o 9best9 *i.e. make 12.00,.9 Eac# %irm !oes not !are trust t#e ot#er %irm to c#arge t#e#ig#er $riceRR

Kn Oligo$ol& t#ere is an incentie to kee$ $rice %ie!. igure 12.7 illustrates t#e kinked demandcurve. MC can moe insi!e !iscontinuous section an! t#ere is no incentie to c#ange $rice or4uantit&. DF .ligopolistic !irms have price rigidity

>1


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0rice signaling %irm suc# as :merican :irlines announces it is raising its $rice. irm #o$es t#atsuc# price leadership"ill result in t#e ot#ers %ollo"ing. *'#is seems to be t#e case in H&!e ;arkbet"een S#ell an! :moco stations "#ic# B$ostB $rices t#at seem to agree all t#e time.,

/anks o$erate using $rice signaling as t#e& 9res$on!9 to c#anges at t#e e!.

Dominant 7irm Model" igure 12. s#o"s !ominant %irm mo!el. -ominant %irm takes !eman!cure --as

--D Market !eman! G ringe irm Su$$l&.

-ominant %irm !ra"s MI on t#is derived demand curvean! sets $rice. ringe %irms take t#is $riceas gien.Oil Cartel "oul! not be legal in t#e PS. igure 12.10 s#o"s situation. Here O;EC !eries a !eman!cure -O;ECan! !ra"s a marginal reenue cure. ;rice is set at ;

U "#ere MIO;ECD MCO;EC. K%O;EC "ere not a cartel) O;EC $rice "oul! be at ;c.

Pniersities "ork toget#er to kee$ at#letics 9amateur9 b& $a&ing $la&ers nothing. Some#o" t#e&get a"a& "it# itRR

>2


53/59


1ame Theory

1ame Theory9K% K beliee t#at m& com$etitors are rational an! act to maimiLe t#eor o"n $ro%its)#o" s#oul! K take t#eir be#aior into account "#en making m& O"n $ro%itGmaimiLing !ecisions59

Cooperative gameDF $la&ers can negotiate bin!ing contracts an! en%orce t#em

2oncooperative gameDF $la&ers cannot negotiate an! cannot en%orce contracts

>ant to understand your opponent@s point o! vie/ and assuming your opponent is rational

deduce ho/ he or she is likely to respond to your actions"

;roblem. Com$an& : *ac4uirer, consi!ering bi!!ing %or Com$an& ' *target,. Com$an& ' ise$loring %or oil an! kno"s "#at it #as %oun!. Kt is assume! t#at a s#are $rice o% 0.00 G 100.00 %orcom$an& ' un!er its o"n management is e4uall& likel&. K% : bu&s ') ' "ill make >0 more mone&.

: t#us can make an o%%er bet"een 0G1>0 a s#are an! ' "ill acce$t i% t#e o%%er is greater t#an ore4ual to t#e current s#are $rice. #at is t#e o$timum o%%er5

:ns"er. O%%er 0.00. :ssume : o%%ers >0.00. '#is suggests t#at t#e s#are $rice is bet"een 0G>0.Kts e$ecte! alue is 2>.00. it# :Bs management t#e alue "ill rise to 37.>0 *1.>U2>, "#ic# isless t#an t#e o%%erRR

Dominant Strategy one t#at is o$timal %or a $la&er no matter "#at an o$$onent !oes

irm / :!ertise irm / No :!irm : :!ertise 10)> 1>)0

irm : No :! ?)8 10)2

-ominant tGstrateg& is %or : an! / is to a!ertise

irm / :!ertise irm / No :!irm : :!ertise 10)> 1>)0irm : No :! ?)8 20)2

Here : !oes not #ae a !ominant strateg&. -e$en!ing on "#at / !oes) : "ill eit#er a!ertise an!get 1> or not a!ertise an! get 20. /ut / #as a !ominant strateg& "#ic# si to a!ertise. DF : "ill

%igure t#at / "ill !etermine t#is an! "ill a!ertise.

2ash equili(rium ' am doing the (est ' can given /hat you are doing" Aou are doing the (est

you can given /hat ' am doing"

Dominant Strategy ' am doing the (est ' can no matter /hat you do? Aou are doing the (est

you can no matter /hat ' do"

>3


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Markets !or 7actor 'nputs

irms !eman!s %or in$uts are 9!erie!9 in t#at t#e& are t#e result o% $ro!uction !ecisions !ue tomarket !eman! %or t#e %inal $ro!uct.

Marginal revenue productD a!!e! reenue %rom one more unit o% in$ut K in t#e $ro!uction o%goo! . Kn general case

MRP MPP MRi i x=

Kn $er%ect com$etition since %irm %aces x x xMR P= => =) .'#eor& suggests t#at !eman! %or labor o% a %irm "it# mono$ol& "it# #ae a lo"er MI; t#an a$er%ectl& com$etitie %irm. Kn e4uilibrium "#ere i D labor

MRP (i =

or

MR ( MPPx i= =

:s ot#er in$uts increase) M;;+increases "#ic# s#i%ts t#e MI; cure to t#e rig#t

Eac# %irm takes t#e su$$l& $rice o% in$uts as gien. :s a grou$ i% aggregate !eman! increases t#e

$rice o% in$uts "ill increase.

'#e su$$l& o% labor is usuall& u$"ar! slo$ing. K% "ages increase) more labor "ill be su$$lie!. :boesome "age) t#e number o% #ours su$$lie! ma& !ecrease as $otential "orkers c#ose leisure oer"ork.

Economic rent ,- !i%%erence bet"een t#e $a&ments ma!e to a %actor o% $ro!uction an! t#eminimum amount t#at must be s$ent to obtain t#e use o% t#at %actor.

Monopsony 0o/er occurs "#en a %irm #as $o"er oer t#e cost on an in$ut. Kn a com$etitie markett#e marginal expenditure 4ME5%or an in$ut is e4ual to t#e average expenditure 4&E5. it#mono$son&

"E MEi i


55/59


"#ere MRPix D marginal reenue $ro!uct o% in$ut K in t#e $ro!uction o% goo! .

K% unions restrict t#e number o% "orkers) t#en t#e "ages o% t#ose in t#e tra!e "ill be aboe t#e "aget#at "oul! occur i% t#ere "as %ree entr&. '#e "ages o% "orkers in t#e non union labor market "ill%all !ue to t#e increase! "orkers looking %or "ork. Kn realit& man& union "orkers "ork o%% t#e books

on t#e "eeken!s an! nig#ts. :t uniersit& tenure! %acult& are not allo"e! to lo"er t#eir "ages %ort#e summer.

Kn $erio! t#e relatie [Bs o% union "orkers #ae !ecrease!. ages #ae not risen as e$ecte! !ue tot#e increase! substitution o% ca$ital %or labor.

:ssuming a $ro!uction %unction o% t#e %orm

Q e ' % t=

t#en MPP e ' % Q ''t

= =

1

=

'#ere "ill be increasing returns) constant returns or !ecreasing returns !e$en!ing on "#et#er

* , ) * , ) * , + > + = +


56/59


Setu$

Max C M

, t C M

C M

C M

C M

= +

+

+

+

+

. .

. . . .

. .

. .

. .

80 70

22 78 13?7 20>

10 ?0 883 10?

1 ? 17 0 188

>00 >00 ?>

'#e b3s setu$ %or t#is $roblem *comments begin "it# =, is(

/$ b34s program to solve

/$ Fish Packing Problem

/$

/$ Max .80C + .70M

/$ st

/$

/$ 22.78C + 13.67M LE 205

/$ 10.60C + 8.83M LE 106

/$ 14.46C + 17.09M LE 188

/$ 5.00 + 5.00M LE 65

/$

b34sexec lpmax n=2,m1=4,m2=0;

amatrix(22.78, 13.67,

10.60, 8.83,

14.46, 17.09,

5.00, 5.00 );

bvector(205., 106., 188., 65.);

cvector( .80, .70 );

b34srun;

With answers:

LPMAX Command. Version 1 September 1997

Of 2000000 double precision slots in space, 93 are being used.

Number of activities (X) 2

Number of constraints (m1+m2) 4

Number of inquality constraints (m1) 4

Number of equality constraints (m2) 0

Constraint Matrix (A)

1 2

1 22.7800 13.6700

2 10.6000 8.83000

3 14.4600 17.0900

4 5.00000 5.00000

>?


57/59


Constraint vector (B)

205.000 106.000 188.000 65.0000

Cost vector (C)

0.800000 0.700000

Objective function maximized at 8.288942665534615

Primal values

2.83325 8.60335

Dual values

0.00000 0.663896E-01 0.665767E-02 0.00000

'#e ans"ers in!icate t#at $ro%it D 8)288. an! t#e $ro!uction o% %is# cakes an! %is# meal s#oul!

be 2.8332> an! 8.?033> t#ousan! $oun!s res$ectiel&. Since t#e s#a!o" $rice o% se$arating laboran! canning labor "as 0.0) t#is suggests t#at a!!ing more labor in t#is area is not nee!e!. -e$en!ingon t#e $rices o% labor in s#re!!ing an! $acking) more labor coul! be a!!e! $roi!e! t#at t#e cost o%t#e labor is less t#an t#e s#a!o" $rice.

ien t#e base case D 8.2882??>>3?1>. K% one more #our o% s#re!!ing is allo"e!) D 8.3>>332303>1723. Note t#at $ro%it #as increase! b& t#e s#a!o" $rice o% .0??38. K% onemore #our o% canning is a!!e!) t#en t#e ob7?7 to8.2>?00330?30. '#e rea!er is encourage! to run t#e


58/59


Max x z

, t x z

x z

= +

+

+

> 3

3 > 1>

> 2 10

.

Veri%& t#at at t#e solution

= 12.3?8210>2?31>8)

D 1.0>2?3 2.3?82

" D 0.2?31>8 0.8210>

: linear $rogramming setu$ can #ae a number o% $roblems.

'#ere "ill be no unique solutioni% a constraint is $arallel to t#e ob3 > 1>

3 2 10

.. .

: minimum $roblem suc# as

Min V x y

x y

x y

x y

x

y

can be (ritten a,

Max V x y

x y

x y

x y

x

y

= +

+

+

+

= +

+

2 3

? 2 8

>

3

3

2 3

? 2 8

>

3

3

Veri%& t#at at t#e solution V D G.0) t#e $rimal is * 1.128? ) 0.>712, an!t#e !ual is * 0.0) 0.2>) 0.>0) 0.0) 0.0,.

>8


59/59


-i%%iculties t#at in!icate an error "as ma!e in setting u$ a +; $roblem inclu!e inconsistentconstraints? no !easi(le solution and un(ounded solution"Kt is be&on! t#is course to !iscuss t#ese$roblems at t#is time.

Summar&( +; anal&sis can be use! to allo" micro t#eor& to be use! to sole real "orl! $roblems. Kn

t#e oil in!ustr& an! t#e airline in!ustr&) $roblems "it# F t#an >0)000 ariables are common.

Documents

E322 Notes (Managerial Economics)