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Miss Sabbah Gueddoudj Researcher at the G.E.K.E.M. Professional address : 54, boulevard Desgranges 92 SCEAUX 00 33 1 40 91 17 32 Private address : 04, rue des maraîchers 95 SANNOIS 00 33 1 34 15 77 70 E-mail : [email protected] Firms’cash in advance contrainst and endogenous growth. Abstract The aim of this article is on the one hand to introduce firms’ C.I.A. constrainst in an endogenous growth model which included money as a good producer and to demonstrate that in this framework the capital accumulation needs cash in advance balances. Money is therefore not superneutral and the monetary policy influences the productive sphere. Keywords : cash in advance contrainst, endogenous growth, inflation, money input, steady equilibrium, superneutrality. JEL : E5, 04. Most of economic monetary theories suppose that householders need cash in advance for their purchases, they often neglect the firms’behaviour. Firms like householders are submitted to cash in advance contrainst. Indeed, there is a postponement between income and purchases. An amount of cash recieved at time t is not spent at once. So one has to take into account delays needed to spend this cash. Several growth theoricians introduce the C.I.A. constrainst in their model but they suppose it only for householders. In this work, one will deal with cash contrainst undergone by firms. This article is organised as fellows. The first section present the frame work of an endogenous growth model included firms’CIA contrainst. The section two analyses the resolution of the model and the last one is consacred to comments. Section I Presentation of the model One assumes that two kind of money exist. The distinction is based on the duration of the money in the portfolio. One will be used to pay salaries (m1) and the other to finance invesments (m2). So two different money velocity are defined (1/v1 for m1 and 1/v2 for m2). Besides, one supposes that householders spend all their income in good and services purchases. The two kind of contrainst submitted by firms are defined as fellows : v1I k m1 (1) v2c m2 (2) Where Ik is the invesments in physical capital c the consumption To simplify, those two money are assumed substituable, so : m(t)=m1(t)+m2(t) (3) The endogenous growth model included firms’cash contrainst is : max W U ( c(t )) e t dt (4) 0 s.c m (t ) y( t ) c (t ) I k ( t ) ( m1 ( t ) m2 ( t )) nk (5) v1 I k (t ) (1 ) m1 (t ) (6) v2 c (t ) (1 )m 2 (t ) (7) k I k (t ) Where (8) c consumption actualisation rate p prices r remuneration of capital (real interest rate) i remuneration of money (nominal rate) m real money balances m money for the acquisition of invesments 1 m money for the salaries 2 v et v duration of the two different money in the portfolio 1 2 I physical capital invesment K 1-μ the share measuring the quantity of cash in advance balances. μЄ]0,1]. The production function is a Cobb Douglas function included three producer goods, efficient labor, capital and real money balances. μ is the share of money reserved to precautionary and speculative motives. ( F ( k ( t ) , h ( t ) , m ( t ) ) A k ( t ) h ( t ) ( m ( t ) ) 9 ) The utility function is a constant intertemporal elasticity of substitution : 1 U (c (t )) c 1 1 1 (10) To solve this model one have to write the Hamiltonian equation. Section II Resolution of the model The constraint of accumulation (5) and the intertemporal consumption function (4) can be rewritten : m (t ) y (1 ) m2 m (1 ) 1 ( m1 m2 ) nk (11) v2 v1 m W U ( 2 ) e t v2 0 (12) The Hamiltonian programm is : U( m2 m m m ) 1( y (1 ) 2 (1 ) 1 nk (m1 m2 ) ) 2 ((1 ) 1 ) (13) v2 v2 v1 v1 With θ1 et θ2 adjoint variables of the accumulation of money and physical capital. The first order conditions are : U m2 1 (1 ) (14) v2 1 (1 v1 ) 2 (1 ) (15) 2 1 ( f k n) 2 2 (16) 1 ( f m ) 1 (17) Along the steady growth equilibrium path, all economic and adjoint variables increase at the same rate, therefore the growth rate prevailing in this economy is defined by the following relation : (1 ) f k n c c (1 v1 ) (18) If one supposes no cash in advance constraint for invesment, one will find the famous Rebelo’s relation : c ( fk n ) c (19) Section III Comments The introduction of cash in advance constraint leads to some interesting remarks. There is a negative link between the growth rate of the economy and the nominal interest. This latter represents a cost for the physical capital accumulation. Indeed, the infation rate measures the gap between the return of capital and the return of money, therefore the economic growth rate is : with f m fk i r (20) (1 ) f k n c c (1 v1(i r )) (21) Thanks to this new expression, it is easy to notice that an important interest rate and/or an increase of this variable have a negative effect on the growth rate. The explication lies in the fact that real money balances supposed to be a good producer has got a cost measured by the nominal interest rate (i). Assuming that capital accumulation needs cash in advance balances, an increase of i discourages firms to hold a part of their wealth in liquid form ; the invesments which need a cash advance constraint are therefore penalized. A decrease of investment reduces the production, the employment and consequently the consumption. Note that the negative relation between production and interest rate has been underlined by several authors and Sims (1992) qualifies it as a stylized fact. If one supposes that only consumption submits cash in advance constraint, so money is superneutral, that is to say that a variation of the monetary growth rate has no impact on the economic growth rate. Because according to Asako (1983) in this precise case capital, real money balances and consumption variables are independant. To finish, inflation reduces the economic growth rate. This point has been so many time study by numerous authors, it is for that reason that one will not emphasize on this topic. The model presented in this short article has a double aim, the first is to consider money as an input, the second is to show that firms have to face cash in advance constraint like householders. The introduction of these hypothesis in an endogenous growth model gives an interesting result. This model demonstrates that money is not superneutral. Since, an increase of interest rate affects the growth rate of the economy. So firms prefer to be « liquid », well invesments require cash in advance balances , an increase of i penalizes this variable and therefore growth. This point is very important for the monetary policy. The formalisation chosen opens to critism. One assumes that all money is held by firms (they preserve a part for the precautionnary and speculation motives, they pay salaries and finance invesments). The householders spend all their income in purchases. these hypothesis are restrictive. But goals of this work are to introduce the real money balances in the productive sphere, evaluate its effect on the growth and contribute to keep the debate going on the question of the monetary superneutrality. References ASAKO, K. The utility function and the superneutrality on money on the transition path, Econometrica, 51(5), 1593-1596. CLOWER, R.J 1967. A Reconsideration of the microfundations of money, Werstern Economic Journal, 6(4 ), 1-9. ORPHANIDES A & SOLOW R. 1990. «Money, Inflation and Growth », Handbook of Monetary Economics, North Holland, 223-261. RAJHI T&VILLIEU P. 1993. Monnaie et Croissance endogène, Revue Economique, 3, 257286. SIMS C.A. 1992. Interpreting the macroeconomic time series : The effects of monetary policy, European Economic Review, 36, 975-1011. SINAI A & STOKES H 1972. Real Money Balances : An Omitted Variable from the Production Function ?, Review of Economics and Statistics, 54, 290-296. TSIANG S.C. 1966. Walras law, Say’s law and liquidity preference in general equilibrium analysis, International Economic Review ,33, 329-345. VILLIEU P. 1993 Les modèles à encaisses préalables : un renouveau des fondements microéconomiques de la macro-économie monétaire, Revue économique et politique, 5(103), 615691.