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Munich Personal RePEc Archive

Heterogeneous Consumers, Demand

Regimes, Monetary Policy and

Equilibrium Determinacy

Di Bartolomeo, Giovanni and Rossi, Lorenza

Universita Cattolica del Sacro Cuore, Milano

5 September 2005

Online at

https://mpra.ub.uni-muenchen.de/5100/

(2)

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[

0

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> − , − −

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1

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−β

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(13)

/ $ " , " 0 & $ 1

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)

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2 ( 0 " " /

0 0 β+

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$ " , " 0 0 " "

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(14)

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" <0 %G # %,#& % " # 5%,#&5% "

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8 # B% & " "

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& ( " F 0

( ( ' 0 A 0

(15)

B

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0 ( ( ( ," "

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(16)

>

" & 0 "

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0 "

( 0

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0 "

& " F 0 $ " ,

" 0 "

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0 " " " D ( " &

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" & " (

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( & <

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% & 0 0 0 , "

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0 ( ( $ " , " 0

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( " &

A 7 & "" A A

(17)

4

" " " " " <

( < ( " "

( " "

""

%

&

" A " & # " % " # , " %0

A ( 1

# % β $# # φ# #

{

}

 

+ +

 

=

, , ∈ ,

( β∈

(

,

)

" 0 $ "

0 ( & #

φ & & ( #==

" ( #= 0 φ = ! (

0

( )

. = $+# +κ  − +#  ( χ > " κ >

& 0 & " 1

# %

# #

# % # # # & & $

' φ '

− −

 − + 

= + Π −

 0 ( % (

0 " Π ' (

, " " & 0 " 0 &?

& " 0 ( # " %

"

" " , " F

A & 0 ( & ( , " " 1

# % $ =β

(

+

)

'− ' $+ +

# 5% $ % '

=

# B% " & # B0 >% ( "

" & " & ( &

(18)

# B% % '− =κ$#

(

− #

)

#

{

0

}

+$ # % " # 5% " # ,

+ $ % " , "

#( ( & % +$ # B% G "

& $ # 5% " # B%0 " ,

" A " $ & 0

κ

+

=

"

# >% $ =

(

λ

)

$ +λ$

# 4% =

(

−λ

)

$ # B% " # 4%0 ( & ( 1

# % $ %

(

)

'

κ

= −

, $ # % ( & $ # %0 =$

$ & , $ # % " # 5% ( "1

# C% =

(

−λ ζ

)

+λζ

# E%

(

π

)

+ +

= − − +

# % =(

* $ # C% " $ # E% " # % ( &

$ # %

""

%

&

" A ( " " & (

" , , & ! "

" , " "

"

' 0 " H # B%0 " " & , " " " " " "

(19)

C

" 0 " " " 0 $ # 5%

" # C%0 ( & ζ $ $−

(

υ κ

) (

κ

)

= = + + 0 "

A " &

" " 0 ( " "

0 & " " ( ( & " #

" A & $ % 7 0 ( " "

& # " A " & )

[

0

]

% " " "

" " (

( )

) = # %)

/ " " " & "

/ A 0 " A & 0 0 "

$ <, 1

#& % θ

(

η

)

η−

= −

; 0 "

< 0 "

" " 7 " 0 0

1

#& % *$ % '−

=

$ $ # C% " #& %0 ( & " 1

#& 5% θ κ

(

θ

)

= + 0

( " " "

" & (

θ " κ " " " 0 $ " ,

< & & " θ

(20)

E

""

% $ &

" " & , " " #5%,#4%

( "& < #E%0 ( & 1 5

# % π π β      +            +    

Ω + Ω Ω

   

=

  

   

* & " " , ( A1

# % *

(

β

)

(

β

)

β β β

− −

 + Ω + Ω − 

Ω + Ω Ω

   

=   =  

    

" ( +# %. " !# %. " " 0 ( 1

# 5%

(

)

(

)

# % # % + * ! * β β β − − −  = + Ω +

 

= + Ω + + Ω 

, A * " " ! " " # 51 7 "

9 B% * " " " "

! " " # 5%0 ( " $ " , " 0 "

$ 1 , + *# %> 0 <

(

−β

)

− −  − 0 + *# %±! *# %+ >

, + *# %±! *# %+ <

1

# B% + *# %+! *# %+ =

{

(

)

− Ω

(

)

+ +

(

)

}

β−

 

# >% + *# %−! *# %+ = −Ω

(

−β

)

+

(

)

β−

 

$ # B% " # >% ( " " # % " # %0

" # 5%0 & 0 "

" & ( A1

# 4% * β

(

5

)

(

5

)

β

 − Ω − Ω − 

=

 

5

(21)

/ + *# % β− 0

= > & $ + *# %±! *# %> −

" + *# %±! *# %< − + *# %±! *# %< − "G & 0

# % # %

+ * ±! * > − $ " # >%

" & ( " "

" " " 0 " $ # % " # %0 &

β   β

 

 

 

− +

− > − −

Ω "

β β + Ω >

+ 0 (

"

β β + Ω >

+ " $ 1 %

β −

> − &%

β           + < − −

Ω β − < − Ω β β + Ω <

+ " $ 1 %

β           +

> − −

Ω &%

β −

< − < −β − Ω

" % " % ( " " "

" & "

( " / "" 0

# % β β

          − +

− > − −

Ω Ω 5β β + Ω < +

# C% −β − > − −β Ω β β − Ω > +

" & & " 5β

β

+ Ω <

+ " " & & "

β β − Ω >

+ 0 " & & "

5 0

β β

β β

 + + 

Ω ∈ 

+ +

  " " & ( & "

(22)

0 β

β + Ω >

+ " $

β −

> − # %

" 0 β 0 5β

β β

 + + 

Ω ∈ 

+ +

  0 $

β −

> − # % β

 

 

 

 

 

+

< − −

Ω #

0 , # %

$ & " %

5 ( 0 β

β

+ Ω <

+ 0

" $ 1 β

 

 

 

 

 

+

> − −

Ω # 0

$ " & $ & " %

β −

(23)

'

7 0 3 " & # 5%0 , , & " ; 8 0

(0 B 1 E ,C5

< 0 " ; ! " " # EE %0 / " ; 8 0

- * . $ / / & 0 B1 4>5,4CB

& 0 D # B%0 / 0 " 7 ; < 8 "

7 "1 + 8 ( <0 $& %

' ' B C

& 0 D # >%0 " 7 ; < 8 0 ; 8 "

#/ "% ) 0 / $ % ' ' E

9 & 0 3 R " ' ; < ( # ECE%0 9 0 / 0 " /

1 * + " 0 & * 0

0 C>, 4

9 & 0 3 R " ' ; < ( # EE %0 8 / 0 9 / 0 " 9 0- & 0 00 / 1 0 00 C1 4>, E

9 & 0 3 R " ' ; < ( # EE %0 9

/ 1 9 , / 0 (0 5>1

5, 4

9 0 3 0 ; + & " 9 + # >%0 ' " "

+ * < ; 8 0 - '

0 51 ,B>

9 " 0 3 H0 " ; # EEE%0 * ; 8 0

- 2 0 5 1 44 ,

+ " * 2 < ? # >%0 ; 8 0 +A "

9 01 / - 0# %

0 3 9 # %0 2 & 9 " / /

; ,8 ; " 0 (0 E 1 54 ,E

0 3 9 " " & # B%0 + + +$ D 0- * 00 > 1 55, >5

H0 3 0 S ,* " 0 3 : T # B%0 , , & 9 "

/ 0 - * $ / / & 0 541

5E, 45

3 0 # EE % ! 9 " 9 " =* + U0 3

- 00 E, 5B

; < (0 ' # %0 * ,* " 8 0

(24)

5

; : 7 0 8 0 " 9 # 4%0 " ; 8

/ ' ( ) ; " ( $ " 9 0

& ** '0 1JJ J & KCC CB

8 < 0 3 # EEE%0 2 " 9 8 " &

9 * * A 0 (0 CE1 E>E,E 5

* 0 3 # EE>%0 = 9 " ,9 J8 ,/

2 0 (0 C>1 C4,

* 0 ' * # EEE%0 2 " 9 / A

" 0 (0 CE1 EB ,E>C

* + D # EEE%0 / ; 8 0

-* 00 B51 4 ,4>B

* + D # 5%0 ! ! ( U = 3 "

; 8 0 - 2 0

B 1 B 4,B

0 3 # EE5%0 : 8 8 0 $

0 $ 1 0 ' ' 0 5E1 E>, B

! " "0 ; # 5%04 0 / ' 05 / 0 ! *

' 0 8 = 8 0 8

! " "0 ; # B%0 " D ; 8 0

(25)

B & V ; " &

8 : 8

EE

4 + & " "

υ > / &

> "

(26)

>

# % #&%

(27)

4

# % #&%

(28)

# % #& %

# % #& %

# 5% #&5%

References

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