lecture 2 the microfoundations of money - part 1
TRANSCRIPT
Lecture 2
The Microfoundations of Money - Part 1
Lecture Structure
• The foundations of Classical Monetary theory and the Classical dichotomy
• The invalidity of the Classical dichotomy• neo-Classical monetary theory - the Real
Balance Effect• Evaluation of RBE• The CIA model• macro implications
Marginal Utility of Money
Stock of Money
rate of time preference
M*
D
Classical Interpretation
Cambridge ‘k’
kPyM
P
XPkPXPkM
nAggregatio
PPPXXXMM
d
n
i
iin
iii
d
nn
)3(
)2(
),,..,,,..,()1(
11
2121
• Where the Xs are initial endowments, and the Ps are market prices.
• By aggregation we get (2). Valuing the initial endowments at market prices gives nominal income.
• Dividing by the general price level P gives a measure of real income.
• M is the n+1th good and y is real income.
T h i s f o r m u l a t i o n u n d e r l i e s t h e C a s h - b a l a n c e a p p r o a c h o f t h e C a m b r i d g e ‘ k ’ .
T h e b u d g e t c o n s t r a i n t i s ;
P X Xi id
ii
n
( )
01
S a y ’ s I d e n t i t y ( L a w )
I n e q u i l i b r i u m , a l l m a r k e t s a r e c l e a r e d , a n d b y W a l r a s ’ L a w
P X X M Mi id
id
i
n
( ) ( )
1
T h e p r o b l e m w i t h t h e C l a s s i c a l a p p r o a c h w a s t h a t i t d i d n o t s p e c i f y h o w m o n e y e n t e r s i n t ot h e a n a l y s i s . S o c o n c e r n e d w e r e t h e y a b o u t m a i n t a i n i n g t h e ‘ n e u t r a l i t y o f m o n e y ’ , t h ed e m a n d f o r g o o d s w a s a s s u m e d t o b e h o m o g e n e o u s o f d e g r e e z e r o i n m o n e y p r i c e s - t h eH o m o g e n e i t y p o s t u l a t e .
T h e p r o p o s i t i o n s o f t h e C l a s s i c a l t h e o r y c a n b e s u m m a r i s e d a s f o l l o w s ;l e t x X Xi i
di ( )
( 1 ) M k P yd Q u a n t i t y T h e o r y
( 2 ) x hP
P
P
P
P
P
P X
PXi
di
ni i
i
n
i
1 2 1, , . . . , H o m o g e n e i t y p o s t u l a t e
( 3 ) P w Pi ii
n
1
P r i c e l e v e l
( 4 ) P xi id
i
n
01
S a y ’ s i d e n t i t y
( 5 )
n
i
dnn
dii xPxP
111 W a l r a s ’ l a w
T h i s s y s t e m o f e q u a t i o n s i s i n t e r n a l l y i n c o n s i s t e n t - t h e i n v a l i d C l a s s i c a l D i c h o t o m y
Invalid dichotomy
• Let P rise, then Md > Ms
• by Walras’ law good market must be in ES• by homogeneity postulate rise in P does not
effect relative prices so goods market must be in equilibrium
• thus Say’s law holds• by Walras’ law the money market is in
equilibrium - contradiction!
Patinkin’s solution was;
Max U(X1,X2,....Xn, M/P)
s.t. P
PX X
M
P
M
Pi
i
n
i i
1
( )
P x
P
M
P
M
Pi i
d
i
n
1
Optimisation yields;
x hP
P
P
P
P X
P
M
PXi
di
n i i
i
n
i
1
1
, ... ,
i = 1, 2, ......n
x h
P X
P
M
PX
M
Ph y
M
PM
nd
n
i ii
n
n
xd
ns
1 1
11
1
,
,
Real Balance Effect
• A change in the price level affects goods markets inversely to the money market.
• Inclusion of real balances destroys Say’s identity as all markets in the goods market are affected in the same direction.
• Now there are n+1 equations plus the price equation = n+2
• By Walras’ law we have n+1 independent equations
Internal consistency
• Let all prices double, 2P, kPY>Ms = EDm
• rise in P reduces real balances = ESg
• ESg = EDm (Walras’ law)
• ESg drives down P until real value of money restored
• Sine Qua Non
Cash - in - Advance
U = U(X1,X2,....Xn) (1)
PX MYMi ii
n
1
(2)
where M is final holdings of money Mis initial holdings of money Y is nominal income
C-I-A continuedT h e C a s h - i n - A d v a n c e c o n s t r a i n t i s ;
M P Xi ii
n
1
( 3 )
F r o m ( 2 ) a n d ( 3 )
( )11
P X Y Mi ii
n
s e t t i n g u p L a g r a n g e a n
L = U ( X 1 , . . . X n ) - ( )11
P X Y Mi i
i
n
L
XU P
ii i ( )1 0 ( 4 )
L
P X Y Mi ii
n
( )1 01
( 5 )
C-I-Aequation (4) determines X1, Xn so
Xi = hi(P1,...Pn,Y, M)and
M PX Ph P P Y Mdi i i i n
i
n
i
n
( ,... , , )1
11
so M h P P Y Mdm n ( ,... , , )1
From (5)
1
0
M Y M
M Y Md 1
which is homogeneous of degree one in Y and M.
The wealth effect in the sense of Pigou(1943) was specified by Patinkin(1965) in moregeneral terms as;
Max U = U(Z1, M
P1 , Z2,
M
P0 )
s.t. Z1+1
11 1
r
B
P
M
P= Z
B
P
M
P10 0
Z2 = ZB
P
M
P21 1
where Z1, and Z2 are bundles of goods consumed in period 1 and 2 respectively.
T h e m a c r o e c o n o m ic r e p r e s e n t a t io n c a n b e e x p r e s s e d f a m il ia r ly a s ;
I I r y W
I I Ir y w
( , , )
, ,0 0 0I n v e s t m e n t f u n c t io n
S S r y W
S S Sr y W
( , , )
, ,0 1 0 0 S a v in g s f u n c t io n
M
PL r y W
L L L
d
r y w
( , , )
, ,0 0 0
D e m a n d f o r M o n e y
B
r PB r y W
B B B
d
r y W
( , , )
, ,0 0 0
D e m a n d f o r B o n d s
WM
P
B
r P W e a lt h c o n s t r a in t
P
M
P
rB
P
MrB
P
BrB
22
2
W it h a n O p e n M a r k e t O p e r a t io n
P
M
P
MrB
P
MMrB
22
2
Realrate ofinterest
Investment andSaving
I
I’
S
S’
Are government bonds net wealth?
L e t th e v a lu e o f o th e r fin a n c ia l a sse t s b e g iv e n b y S ( fo r se c u r it ie s ) . T h e v a lu e o f S w ill b ed e te rm in e d b y th e d isc o u n te d e x p e c te d fu tu re n e t in c o m e s t re a m .
Sy
rt i
ii
( )
( )
1
10
if th e e x p e c te d in c o m e s t re a m is a c o n s ta n t o r fo llo w s a ra n d o m w a lk , th e n ;
Sy
r
( )1 (1 )
w h e re is th e t a x ra te o n se c u r it ie s
T h e v a lu e o f g o v e rn m e n t b o n d s is g iv e n b y; V = B /r , a n d th e v a lu e o f n o n -m o n e ta ryw e a lth is W = S + V .
D e b t in te re s t is fin a n c e d o u t o f t a x a t io n so th a t ;
rV = y . (2 )
No-not if future tax liabilities are discounted at the same rate as the income from bonds!
F r o m ( 1 ) a b o v ed S
d
y
r
f r o m t h e d e b t s e r v ic e f in a n c e c o n d i t io n ( 2 ) a b o v e
d V
d
y
r
T h e r e f o r e
d S
d V
d S
d
d
d V
1
T h u s a n in c r e a s e in t h e v a lu e o f b o n d s i s s u e d b y t h e g o v e r n m e n t i s o f f s e t b y a n e q u iv a le n td e c r e a s e in t h e v a lu e o f o t h e r f in a n c ia l a s s e t s h e ld b y t h e p r iv a t e s e c t o r .