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BAUMOLS MODEL

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INTRODUCTIONWilliam J. Baumol developed a model(The

!a"#a$ io"# Dema"d %o! Ca#h& A" I"ve" o!' Theo!e i$App!oa$h )hi$h i# u#uall' u#ed i" I"ve" o!'ma"a*eme" + $a#h ma"a*eme" .I !ade o%% ,e )ee" oppo! u"i ' $o# o! $a!!'i"* $o#o! holdi"* $o# + he !a"#a$ io" $o# .

A# #u$h %i!m a emp # o mi"imi-e he #um o% heholdi"* $a#h + he $o# o% $o"ve! i"* ma! e a,le#e$u!i ie# o $a#h.

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ASSUM/TIONS

0The %i!m i# a,le o %o!e$a# he $a#h "eed#)i h $e! ai" '.0The %i!m# $a#h pa'me" # o$$u!# u"i%o!ml'ove! a pe!iod o% ime.

0The oppo! u"i ' $o# o% holdi"* he $a#h i#"o)" + i doe# "o $ha"*e ove! ime.

0The %i!m )ill i"$u! he #ame !a"#a$ io" $o#)he"eve! i $o"ve! # #e$u!i ie# o $a#h.

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0 le u# a##ume ha he %i!m #ell# #e$u!i ie#a"d # a! # )i h a $a#h ,ala"$e o% C !upee#.Whe" he %i!m #pe"d# $a#h1 i # $a#h

,ala"$e # a! # de$!ea#i"* a"d !ea$he# -e!o.The %i!m a*ai" *e # ,a$ i # mo"e' ,'#elli"* ma! e a,le #e$u!i ie#. A# he $a#h

,ala"$e de$!ea#e# *!aduall'1 he ave!a*e$a#h ,ala"$e )ill ,e& C23. Thi# $a" ,e#ho)" i" %ollo)i"* %i*u!e

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0 The %i!m i"$u!# a $o# "o)" a# holdi"*$o# %o! mai" ai"i"* he $a#h ,ala"$e. I i#

"o)" a# oppo! u"i ' $o# 1 he !e u!"i"evi a,le o" he ma! e a,le #e$u!i ie#. I%he oppo! u"i ' $o# i# 1 he" he %i!m#

holdi"* $o# %o! mai" ai"i"* a" ave!a*e$a#h ,ala"$e i# a# %ollo)#&

0 Holding cost = k (C/2)

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0 Whe"eve! he %i!m $o"ve! # i # ma! e a,le#e$u!i ie# o $a#h1 i i"$u!# a $o# "o)" a#

!a"#a$ io" $o# . To al "um,e! o% !a"#a$ io"# i"a pa! i$ula! 'ea! )ill ,e o al %u"d# !e4ui!ed (T 1divided ,' he $a#h ,ala"$e (C i.e. T2C. Thea##ump io" he!e i# ha he $o# pe! !a"#a$ io" i#$o"# a" . I% he $o# pe! !a"#a$ io" i# $1 he" he

o al !a"#a$ io" $o# )ill ,e&0 Transaction cost = c (T/C)

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5oldi"* $o# + T!a"#a$ io" $o#05oldi"* $o# 6 (C230T!a"#a$ io" $o# 6 $(T2C

0To al $o# 6 (C23 7$(T2C5e!e10 1 i# he oppo! u"i ' $o#

0T i# he o al %u"d# !e4ui!eme"0C i# he $a#h ,ala"$e0 $ i# pe! !a"#a$ io" $o#

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0 Optimum level of cash balance0 A# he dema"d %o! $a#h1 8C i"$!ea#e#1 he

holdi"* $o# )ill al#o i"$!ea#e a"d he !a"#a$ io"$o# )ill !edu$e ,e$au#e o% a de$li"e i" he"um,e! o% !a"#a$ io"#. 5e"$e1 i $a" ,e #aid ha

he!e i# a !ela io"#hip ,e )ee" he holdi"* $o#

a"d he !a"#a$ io" $o# .0 The op imum $a#h ,ala"$e1 C9 i# o, ai"ed )he"

he o al $o# i# mi"imum

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0 :o!mula %o! op imum $a#h ,ala"$e

C9 6 (3$T2;23

0 Whe!e1 C9 i# he op imum $a#h ,ala"$e.T i# he o al $a#h "eeded du!i"* he 'ea!.

i# he oppo! u"i ' $o# o% holdi"* $a#h ,ala"$e#.

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0 Wi h he i"$!ea#e i" he $o# pe!!a"#a$ io" a"d o al %u"d# !e4ui!ed1 he

op imum $a#h ,ala"$e )ill i"$!ea#e.5o)eve!1 )i h a" i"$!ea#e i" heoppo! u"i ' $o# 1 i )ill de$!ea#e

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T)o !a"#a$ io" S !a e*'

;. Whe" he $a#h i"%lo) i# !e$eived i"ve# o"e hal% o% he o al i"%lo)& pu he !emai"i"* o"e hal% i" he di#,u!#me" a$$ou" .

3. Du!i"* he %i!# hal% o% he pe!iod1 pa' di#,u!#me" # %!om hedi#,u!#me" a$$ou" . Thi# a$$ou" )ill ,e d!ai"ed o"e hal% o% he )a'

h!ou*h he pe!iod. A ha ime #ell he i"ve# me" # + pa'

di#,u!#me" a$$ou" i= 3a 5e!e1 a i# he $o# pe! !a"#a$ io"

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Th!ee !a"#a$ io" # !a e*'

0 Whe" he $a#h %lo) i# !e$eived1 i"i iall' i"ve# )o hi!do% i . pla$e !emai"i"* o"e hi!d i" he di#,u!#eme"a$$ou" .

0 B' o"e hi!d o% he pe!iod 1 di#,u!#eme" a$$ .)ill ,ee hau# ed. A hi# ime di#i"ve# o"e hal% o% he %u"d# i"

he i"ve# me" a$$ou" i.e.(;23 (32< =6 (;2< ' 1"o) pui i" he di#,u!#eme" a$$ou" .

0 Thu# hi# # !a e*' i"volve# o"e i"ve# me" !a"#a$ io"a"d )o di#i"ve# me" !a"#a$ io"#.

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S !a e*'

I" e!e# I"$ome 6 (32< (;2< i=7(;2< (;2< i=6 (;2< i=F

/!o%i 6 (;2< i=

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imitations of the !aumol model"

0 ;. I doe# "o allo) $a#h %lo)# o %lu$ ua e.3. Ove!d!a% i# "o $o"#ide!ed.

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