Key words: financial intermediation, entrepreneurship, economic growth

Transcription

1 DEPARTMENT OF ECONOMICS ISSN DISCUSSION PAPER 18/07 FINANCIA INTERMEDIATION, ENTREPRENEURSHIP AND ECONOMIC GROWTH Wenli Cheng * Abstract: This paper presents a simple general equilibrium moel of financial intermeiation, entrepreneurship an economic growth. In this moel, the role of financial intermeiation is to pool savings an to len the poole funs to an entrepreneur, who in turn invests the funs in a new prouction technology. The aoption of the new prouction technology improves iniviual real income. Thus financial intermeiation promotes economic growth through affecting iniviuals saving behaviour an enabling the aoption of a new prouction technology. Key wors: financial intermeiation, entrepreneurship, economic growth JE classification: G21, D90, O40 * The author is grateful to Professors Yew-Kwang Ng an Xiangkang Yin for their helpful comments. Department of Economics, Monash University, June Wenli Cheng All rights reserve. No part of this paper may be reprouce in any form, or store in a retrieval system, without the prior written permission of the author.

2 FINANCIA INTERMEDIATION, ENTREPRENEURSHIP AND ECONOMIC GROWTH 1. Introuction There is a growing theoretical an empirical literature suggesting that financial evelopment plays a positive role in economic growth (see, for example, Greenwoo an Jovanovic, 1990, Bencivenga an Smith, 1991, King an evine 1993a, 1993b, Greenwoo an Smith, 1997, evine, 1997, evine an Zervos, 1998, McCaig an Stengos, 2005). But how oes financial evelopment enhance growth? This paper evelops a simple general equilibrium moel in which financial intermeiation enhances income growth by influencing the rate of capital formation an technological innovation (evine 1997). In particular, the function of financial intermeiation in our moel is to pool savings to fun an entrepreneur s investment in a new prouction technology. The new technology is assume to be available but its implementation requires a sum of capital that is larger than personal savings achievable by an entrepreneur. Thus financial intermeiation enables a technological innovation rather than an invention. Our moel formalises two often-neglecte insights. First, by pooling funs, financial intermeiaries play an important role in permitting the implementation of new technologies, as pointe out by Bagehot (1873, p10) We have entirely lost the iea that any unertaking likely to pay, an seen to be likely, can perish for want of money; A citizen of onon in Queen Elizabeth s time woul have thought that it was no use inventing railways (if he coul have unerstoo what a railway meant), for you woul have not been able to collect the capital with which to make them. Secon, capital rather than technological avance per se is often the bining constraint on economic growth. Inee, most of the proucts that were first manufacture uring the early perios of the Inustrial Revolution ha been invente much earlier; an what cause the elay in the implementation of many of the existing inventions were the large capital requirements (Hicks, 1969). In our moel, the availability of financial intermeiation is a eterminant of technological choice, an the entrepreneur is the initiator of the implementation of new technology. In this sense our moel is relate to the literature that links 1

3 technological choice to the cost of traing in financial markets (Bencivenga et al., 1995), an also relate to the literature that emphasises the entrepreneur s innovative activities in the presence of financial intermeiation (King an evine, 1993b). Our moel however has two istinctive technical features. First, it is methoologically iniviualistic as it treats all iniviuals as consumerproucers an explicitly an simultaneously moels iniviual consumption, prouction, an saving ecisions for all agents in the economy. Seconly, financial intermeiation is enogenise in the sense that only uner certain conitions (namely that the new technology is sufficiently more prouctive relative to the ol technology; capital goos associate with the new technology can be easily converte from savings; an that time preference is sufficiently weak), will financial intermeiation occur in general equilibrium. If these conitions o not hol, the equilibrium involves financial autarky. We present our moel in section 2 below an offer some concluing remarks in section A Moel of Intermeiation, Entrepreneurship an Growth 2.1. The economic environment Consier an economy with m iniviuals who live for 2 perios (t = 1, 2). All iniviuals erive utility from consumption of a single goo X an have the same utility function: U = c + θc where c i (i = 1,2) is quantity of goo X consume at time i; θ<1 is the iniviual s time preference parameter; large θ inicates weak time preference. Each iniviual is enowe with 1 unit of labor in each perio an labor cannot be transferre inter-temporally. Goo X can be prouce at home using only labor (l): X h = al Or it can be prouce in a factory with employe labor (E), capital (K), an an entrepreneurial input (l E ) 2

4 X f α β AK E ( α + β < 1, K > Ra) if le = 1 = 0 if le < 1 The entrepreneurial input captures the time an energy evote by the entrepreneur to utilising capital funs, hiring workers an organising prouction. It is assume that to run a factory successfully, the entrepreneur nees to evote all his labour enowment to it, that is, factory prouction can take place only if l E = 1. Capital is accumulate from savings at the en of the perio 1 after goo X is prouce. Each unit of goo X save can be converte into R unit of capital. It is assume that the minimum amount of capital require for factory prouction is greater than the maximum saving a single iniviual can make at t = 1, i.e., K Ra. Thus, to aopt the factory prouction technology, it is necessary to pool savings of multiple iniviuals, an len them to the entrepreneur. This task is carrie out by a financial intermeiary (the banker), an requires the time an energy of the banker, enote by the banker s input, l B. It is also assume that to run a bank successfully, the banker has to evote all his labor enowment to it, i.e., l B = The case without financial intermeiation In the absence of a financial intermeiary, only home prouction technology can be use, an the economy is characterise by autarky. An iniviual s ecision problem is: max U = c + θc ( θ < 1) c1, c2 st.. x = al x l = al 2 2 = l = 1 c + c = x + x c x where x i (i = 1,2) is goo X prouce in perio i; l i (i = 1,2) is labor enowment in perio i. We assume that iniviuals can store goos for later consumption without incurring storage costs. Solving this problem we obtain: c1* = c2* = a 3

5 Since technology is the same in both perios, an labor is not transferable across time, time preference ictates that iniviuals will not save in perio t = 1. The iniviual utility (real income) level over the two perios is U * = (1 + θ ) a. A 2.3. The case with financial intermeiation an entrepreneurship In the presence of financial intermeiation an entrepreneurship, savings may be poole by the banker, an the funs borrowe an investe in factory prouction by the entrepreneur. Since savings are not mae until the en of perio 1, all iniviuals use the home prouction technology to prouce goo X in perio 1. In perio 2, however, iniviuals may engage in ifferent activities. We group the iniviuals into four ifferent categories accoring to their perio 2 activities: (1) Consumer-home proucers ( home proucers ), who employ the home prouction technology to prouce X for self consumption, an fun aitional consumption from savings plus interests. (2) Consumer-factory workers ( factory workers ), who work in a factory in exchange for a wage, an receive aitional funs from their savings plus interests. (3) Consumer-banker ( the banker ), who collects eposits from home proucers an factory workers, lens the funs (incluing his own savings) to the entrepreneur, an retains the ifference between the payment to epositors an repayment from the entrepreneur. (4) Consumer-entrepreneur ( the entrepreneur ), who invests in factory prouction technology using funs borrowe from the banker an his own savings, an hires factory workers to prouce goo X. He obtains the resiual prouction after making wage payments to factory workers an loan repayment to the banker. We assume that entry into banking an factory prouction is free so that neither the banker nor the entrepreneur behaves monopolistically. The interrelationships between four categories of iniviuals are illustrate in Figure 1. The ecision problems for the four types of iniviuals an the solutions are presente in table 1. There are two possible equilibria. If r * (1 θ ) / θ, the equilibrium is the same as that of the moel without financial intermeiation. If r * > (1 θ ) / θ, the equilibrium involves 4

6 financial intermeiation. Since financial intermeiation only occurs in equilibrium within the parameter set efine by r * > (1 θ ) / θ, financial intermeiation is enogenously etermine. For example, starting from an initial set of parameters that satisfies r * (1 θ )/ θ, changes in parameters may lea to r * > (1 θ ) / θ. This will cause the equilibrium to shift from one without financial intermeiation to one with finance intermeiation. In other wors, financial intermeiation can enogenously emerge. The equilibrium with financial intermeiation is characterise as follows. First, all iniviuals utility levels are maximise, an the market for goo an the market for loans s clear. From the loan market clearing conition, = K* = Rma =, we obtain the equilibrium rate of loan interest: α+ β β α 1 1 β 1 β 1 β 1 β r * ( ) = Rm A αβ a. Clearly r * is negatively relate to capital availability (as inicate by R, m, a) an positively relate to capital prouctivity (as inicate by A, α, β). Assuming that the number of workers employe by the entrepreneur is less than the total number of iniviuals available to work in a factory, the equilibrium utility level of home proucers an that of factory workers are equalise ue to labor mobility between home an factory. From this conition we obtain the equilibrium wage rate, w* = a. In aition, the equilibrium utility of the banker an that of the entrepreneur are equalise ue to free entry to both activities. This conition gives us the equilibrium rate of eposit interest, r * = [1/( m 2) a][( m 2) ar * π * a], where * AK ( *) α χ π ( E*) (1 + r*) K* w* E* w* is the equilibrium level of profit of the entrepreneur. The profit will be riven own to zero if all iniviuals can potentially become the entrepreneur. Otherwise if only talente people (i.e., the banker an the entrepreneur in our moel) can become the entrepreneur, then the profit can be positive even in equilibrium until, for example, still newer technology is aopte, in which case creative estruction will isplace the ol equilibrium an eliminate the profit associate with the factory prouction technology. Our moel however oes not capture that ynamic. It is easy to see that the ifference between loan an eposit interest rates covers the entrepreneurial profit an the banker s labor input value at the equilibrium wage rate. 5

7 It is straightforwar to show that provie r * > (1 θ ) / θ the equilibrium with financial intermeiation an entrepreneurship prouces higher utility for all iniviuals compare to the equilibrium without financial intermeiation. In the case with zero entrepreneurial profit the equilibrium conition becomes α+ β β α 1 1 β 1 β 1 β 1 β ( Rm) A αβ a (1/( m 2) > (1 θ) / θ which is more likely to hol if: (1) prouctivity associate with the factory prouction technology is high (A, α, β are large) an the prouctivity associate with home prouction technology is low (a is small); (2) savings can be efficiently converte to capital goos (R is large); an (3) iniviual time preference is low (θ is large). This implies that financial intermeiation an entrepreneurship will more likely promote economic growth the more efficient the new technology is relative to ol technology, the more easily savings can be converte to capital goos, an the more willing iniviuals are to sacrifice current consumption for future consumption. In the case of zero entrepreneurial profit, the utility level of the banker an the entrepreneur is θ a(2 + r *), where α+ β β α 1 1 β 1 β 1 β 1 β r * ( ) = Rm A αβ a ; an the utility level of the home proucer an the factory workers is θ a(2 + r *), where r * = [1/( m 2) a][( m 2) ar * a]. 3. Concluing remarks This paper presents a simple general equilibrium moel of financial intermeiation, entrepreneurship an economic growth. In this moel, the role of financial intermeiation is to pool savings an to len the poole funs to an entrepreneur, who in turn invests the funs in a new prouction technology. The aoption of the new prouction technology improves iniviual real income. Thus financial intermeiation enhances income growth through affecting iniviuals saving behaviour an enabling the aoption of a new prouction technology. It may be argue that financial intermeiation is not require for the aoption of a new prouction technology because the entrepreneur may borrow irectly from iniviuals. Our moel rules out this possibility as the entrepreneur is resource constraine so that he cannot engage in both the activity of pooling funs an organising prouction. The separation of pooling funs an organising prouction may also be justifie if part of the banker s role is to monitor the entrepreneur on the behalf of all epositors (Diamon, 1984). 6

8 In this moel, the banker is a pure financial intermeiary, an there is no money multiplier effect. Future research may exten the moel to investigate the implications of fractionalreserve banking on investment an growth. References: Bagehot, Walter (1873), ombar Street, reprinte by BiblioBazaar, Bencivenga, Valerie, Smith, Bruce an Starr, Ross (1995), Transaction costs, technological choice, an enogenous growth, Journal of Economic Theory, 67, Diamon, Douglas (1984), Financial intermeiation an elegate monitoring, Review of Economic Stuies, 51(3), Greenwoo, Jeremy an Jovanovic, Boyan (1990), Financial evelopment, growth an the istribution of income, Journal of Political Economy, 98(5), Greenwoo, Jeremy an Smith, Bruce (1997), Financial markets in evelopment an the evelopment of financial markets, Journal of Economic Dynamic an Control, 21, Hicks, John (1969), A theory of economic history, Oxfor: Clarenon Press. King, Robert an evine, Ross (1993a), Finance an growth: Schumpeter might be right, Quarterly Journal of Economics, 108(3), King, Robert an evine, Ross (1993b), Finance, entrepreneurship, an growth: theory an evience, Journal of Monetary Economics, 32, evine, Ross (1997), Financial evelopment an economic growth: view an agena, Journal of Economic iterature, 35(2), evine, Ross an Zervos, Sara (1998), Stock markets, banks, an economic growth, American Economic Review 88, McCaig, Brain an Stengos, Thanasis (2005), Financial intermeiation an growth: some robustness results, Economics etters, 88,

9 Payment Deposits Home proucers X=al Banker Principal+ eposit interests oan Goo X Deposits Principal+ loan interests labor Principal+ eposit interests Payment Goo X Factory workers Payment Goo X Wage Entrepreneur X=AK α E β Figure 1. An economy with financial intermeiation an entrepreneurship 8

10 Table 1. Iniviual ecision problems an solutions Decision problems Home proucers Factory workers Banker max c1, c2 U = c +θc st.. x = al x = c + s 1 s (1 + r ) + x = c l = l = 1 c x where s 1 is savings in t = 1, r is eposit interest rate. The price of goo X is normalise to be 1 max c1, c2 U = c +θc st.. x = al x = c + s 1 s (1 + r ) + wl = c l = l = 1 c x where w is the wage rate. max c1, c2 U = c +θc st.. x = al x = c + s 1 D + s = 1 (1 + r ) (1 + r ) D = c l = l = 1 c x 1 where D 1 is eposits collecte, 1 is loans mae. r an r are the eposit an loan interest rates, respectively. We assume that r > r if l 2 = 1, an r = 0 if l 2 1 Solutions If r > (1 θ ) / θ c * = 0, c * = 2 a+ r, U * = θ (2 a+ r ) HP If r (1 θ ) / θ c * = a, c * = a, U * (1 ) HP = a + θ If r > (1 θ ) / θ c * = 0, c * = a(1 + r ) + w, U * = θ[ a(1 + r ) + w] FW If r (1 θ ) / θ c * = a, c * = a, U * (1 ) FW = a + θ If r > (1 θ ) / θ 1 c * = 0, c * = ( r r ) D + (1 + r ) a 2 1 U * = θ[( r r ) D + (1 + r ) a] B 1 If r (1 θ ) / θ c * = a, c * = a, U * (1 ) B = a + θ 9

11 Entrepreneur max c1, c2 U = c + θc st.. x = al x = c + s 1 K = R( + s ) > Ra α β AK E ( α + β < 1) if l2 = 1 x2 = 0 if l2 < 1 x (1 + r ) we = c l 2 = l = 1 c x If r > (1 θ ) / θ 1 2 c * = 0, α β c * = AK* E* (1 + r )( K* a) we* α β U * = θ[ AK* E* (1 + r )( K* a) we*] E where 1 β β 1 1 α β β 1 α β 1 α β K* = ( α A) ( ) (1 + r ) > Ra α w α α 1 α β β 1 α β 1 α β E* = ( α A) ( ) (1 + r ) α w If r (1 θ ) / θ c * = a, c * = a, U * (1 ) E = a + θ 10