The Microfoundations of Money, Part 1 - Economics Network

The Microfoundations of Money, Part 1 - Economics Network

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 Classical Interpretation Marginal Utility of Money rate of time preference D M* Stock of Money Cambridge k Where the Xs are initial endowments, and the Ps are market prices. (1) M M ( X 1 , X 2 ,.. X n , P1 , P2 ,..Pn , )

By aggregation we get (2). Valuing the initial Aggregatio n endowments at market prices gives nominal income. n n Pi X i d Dividing by the general (2) M k Pi X i kP P i 1 i 1 price level P gives a measure of real income. (3) M d kPy M is the n+1th good and y is real income. T h is fo r m u la t io n u n d e r lie s t h e C a s h - b a la n c e a p p r o a c h o f t h e C a m b r id g e k . T h e b u d g e t c o n s t r a in t is ; n Pi( X d

i S a y s I d e n tity (L a w ) X i) 0 i1 I n e q u ilib r iu m , a ll m a r k e t s a r e c le a r e d , a n d b y W a lr a s L a w n Pi( X d i X i) (M d M ) i1 T h e p r o b le m w it h t h e C la s s ic a l a p p r o a c h w a s t h a t it d id n o t s p e c if y h o w m o n e y e n t e r s in t o t h e a n a ly s is . 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 in t a in in g t h e n e u t r a lit y o f m o n e y , t h e d e m a n d fo 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 in m o n e y p r ic e s - t h e H o m o g e n e ity p o s tu la te .

T h e p r o p o s it io n s o f t h e C la s s ic a l t h e o r y c a n b e s u m m a r is e d a s f o llo w s ; l e t x i ( X id X i ) (1 ) (2 ) d M xi Q u a n t it y T h e o r y kP y P P P h i 1 , 2 ,... n , P P P d n

i1 Pi X i X P i H o m o g e n e it y p o s t u la t e n (3 ) P w i Pi P r ic e le v e l i 1 n (4 )

P i x id 0 S a y s id e n t it y P i x id P n 1 x nd 1 W a lr a s la w i1 (5 ) n i 1 T h is s y s t e m o f e q u a t io n s is in t e r n a lly in c o n s is 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 Says law holds by Walras law the money market is in

equilibrium - contradiction! Patinkins solution was; Max U(X 1 ,X 2 ,....X n , M /P) n Pi M M ( X X ) i i P P P i 1 n Pi x id M M P P P i 1

s.t. Optimisation yields; P1 Pn n Pi X i M x hi ,... , Xi P i 1 P P P i = 1, 2, ......n d i x nd1 n P X i i M i 1 h n 1 , X n 1 P

P M P xd M h n 1 y , M P s Real Balance Effect A change in the price level affects goods markets inversely to the money market. Inclusion of real balances destroys Says 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 ( X ,X ,....X ) 1 2 n (1 ) n P X M

Y M i i i 1 w h e reM isf in a lh o ld in g so fm o n e y M isin itia

lh o ld in g so fm o n e y Y isn o m in a lin c o m e (2 ) C-I-A continued T h e C a s h - in - A d v a n c e c o n s t r a in t is ; n M

PiX (3 ) i i1 F ro m (2 ) an d (3 ) n (1 ) P i X i Y M i1 s e t t in g u p L a g r a n g e a n n L = U (X 1,...X n) - (1 ) P i X i1 i

Y M L U i ( 1 ) P i 0 X i (4 ) n L (1 ) P i X i1 (5 ) i Y M 0 C-I-A equation (4) determines X1, Xn so Xi = hi(P1,...Pn,Y, M ) and d

n n M PX i i Ph i i (P 1,... P n ,Y, M) i1 so i1 Md hm(P1,... Pn ,Y, M) From(5) 1 M Y M 0 Md Y M 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

general terms as; M1 M0 Max U = U(Z1, , Z2, ) P P B0 M 0 1 B1 M1 s.t. Z1+ = Z1 1 r P P P P B1 M1 Z2 = Z 2 P P 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 fa m ilia r ly a s ; I I (r , y ,W ) Ir 0, I y 0, I w 0 I n v e s t m e n t fu n c t io n S S (r , y ,W ) S r 0 ,1 S y 0 , S W 0

M d L (r , y ,W ) P S a v in g s fu n c t io n D e m a n d fo r M o n e y Lr 0, L y 0, Lw 0 Bd B (r , y ,W ) rP D e m a n d fo r B o n d s B r 0, B y 0, BW 0 W M B P rP W e a lt h c o n s t r a in t B B r P B 2M Br M

r 2P 2P P W it h a n O p e n M a rk et O p e ratio n B r M 2M B r M M 2P 2P P S Real rate of interest S I I Investment and Saving Are government bonds net wealth? L e t the v a lu e o f o the r fina nc ia l a ssets b e g ive n by S (fo r se cu ritie s). T he va lu e o f S w ill be

d ete rm ine d b y the d isc o u n te d e xp e c ted fu tu re n e t inc o m e stre a m . S i 0 y t i (1 ) (1 r ) i if the e xp e c ted in co m e stre am is a c o nsta n t o r fo llo w s a ra n d o m w alk , the n ; S y (1 ) r (1 ) w h e re is th e ta x ra te o n sec u ritie s T he v a lu e o f g o ve rn m e nt b o nd s is g iv e n by; V = B /r, a nd the v alu e o f n o n-m o ne ta ry w e a lth is W = S + V . D e bt in te re st is fina nc e d o u t o f taxatio 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 ro m (1 ) abo ve dS y

d r fr o m t h e d e b t s e r v ic e fin a n c e c o n d it io n ( 2 ) a b o v e dV y d r T h e r e fo r e dS dS d 1 dV d dV 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 is s u e d b y t h e g o v e r n m e n t is o ffs e t b y a n e q u iv a le n t d e c r e a s e in t h e v a lu e o f o t h e r fin 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 .

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