This paper presents a simple general equilibrium model of financial intermediation, entrepreneurship and economic growth. In this model, the role of financial intermediation is to pool savings and to lend the pooled funds to an entrepreneur, who in turn invests the funds in a new production technology. The adoption of the new production technology improves individual real income. Thus financial intermediation promotes economic growth through affecting individuals’ saving behaviour and enabling the adoption of a new production technology.financial intermediation, entrepreneurship, economic growth

Wenli Cheng

English

Research Papers in Economics

 
 
DEPARTMENT OF ECONOMICS 
ISSN 1441-5429 
DISCUSSION PAPER 18/07 
FINANCIAL INTERMEDIATION, ENTREPRENEURSHIP AND ECONOMIC GROWTH   
 
 
Wenli Cheng
*† 
 
 
Abstract:  This paper presents a simple general equilibrium model of financial 
intermediation, entrepreneurship and economic growth.  In this model, the role of financial 
intermediation is to pool savings and to lend the pooled funds to an entrepreneur, who in turn 
invests the funds in a new production technology.  The adoption of the new production 
technology improves individual real income.  Thus financial intermediation promotes 
economic growth through affecting individuals’ saving behaviour and enabling the adoption 
of a new production technology. 
 
Key words: financial intermediation, entrepreneurship, economic growth 
 
JEL classification: G21, D90, O40 
 
                                                 
* The author is grateful to Professors Yew-Kwang Ng and Xiangkang Yin for their helpful comments. 
† Department of Economics, Monash University, June 2007 
 
© 2007 Wenli Cheng 
All rights reserved. No part of this paper may be reproduced in any form, or stored in a retrieval system, without 
the prior written permission of the author. 
   1
FINANCIAL INTERMEDIATION, ENTREPRENEURSHIP AND ECONOMIC GROWTH 
 
1. Introduction 
There is a growing theoretical and empirical literature suggesting that financial development 
plays a positive role in economic growth (see, for example, Greenwood and Jovanovic, 1990, 
Bencivenga and Smith, 1991, King and Levine 1993a, 1993b, Greenwood and Smith, 1997, 
Levine, 1997, Levine and Zervos, 1998, McCaig and Stengos, 2005).  But how does financial 
development enhance growth?  This paper develops a simple general equilibrium model in 
which financial intermediation enhances income growth by influencing the rate of capital 
formation and technological innovation (Levine 1997).  In particular, the function of financial 
intermediation in our model is to pool savings to fund an entrepreneur’s investment in a new 
production technology.  The new technology is assumed to be available but its 
implementation requires a sum of capital that is larger than personal savings achievable by an 
entrepreneur.  Thus financial intermediation enables a technological innovation rather than an 
invention.   
 
Our model formalises two often-neglected insights.  First, by pooling funds, financial 
intermediaries play an important role in permitting the implementation of new technologies, 
as pointed out by Bagehot (1873, p10) 
  “We have entirely lost the idea that any undertaking likely to pay, and seen to 
be likely, can perish for want of money;…A citizen of London in Queen 
Elizabeth’s time … would have thought that it was no use inventing railways 
(if he could have understood what a railway meant), for you would have not 
been able to collect the capital with which to make them.” 
Second, capital rather than technological advance per se is often the binding constraint on 
economic growth.  Indeed, most of the products that were first manufactured during the early 
periods of the Industrial Revolution had been invented much earlier; and what caused the 
delay in the implementation of many of the existing inventions were the large capital 
requirements (Hicks, 1969). 
 
In our model, the availability of financial intermediation is a determinant of 
technological choice, and the entrepreneur is the “initiator” of the implementation of 
new technology.  In this sense our model is related to the literature that links   2
technological choice to the cost of trading in financial markets (Bencivenga et al., 
1995), and also related to the literature that emphasises the entrepreneur’s innovative 
activities in the presence of financial intermediation (King and Levine, 1993b).  Our 
model however has two distinctive technical features.  
 
First, it is “methodologically individualistic” as it treats all individuals as consumer-
producers and explicitly and simultaneously models individual consumption, production, and 
saving decisions for all agents in the economy.  Secondly, financial intermediation is 
endogenised in the sense that only under certain conditions (namely that the new technology 
is sufficiently more productive relative to the old technology; capital goods associated with 
the new technology can be easily converted from savings; and that time preference is 
sufficiently weak), will financial intermediation occur in general equilibrium.  If these 
conditions do not hold, the equilibrium involves financial autarky.  
 
We present our model in section 2 below and offer some concluding remarks in section 3.  
 
2. A Model of Intermediation, Entrepreneurship and Growth 
2.1. The economic environment 
Consider an economy with m individuals who live for 2 periods (t = 1, 2).  All individuals 
derive utility from consumption of a single good X and have the same utility function: 
12 Uc c θ =+  
where ci (i = 1,2) is quantity of good X consumed at time i; θ<1 is the individual’s time 
preference parameter; large θ indicates weak time preference.  
 
Each individual is endowed with 1 unit of labor in each period and labor cannot be 
transferred inter-temporally.  Good X can be produced at home using only labor (l): 
h X al =  
Or it can be produced in a factory with employed labor (E), capital (K), and an 
entrepreneurial input (lE) 
   3
(1 , ) 1
01
E
f
E
AK E K Ra if l
X
if l
αβ αβ ⎧ +< > =
= ⎨
< ⎩
 
The entrepreneurial input captures the time and energy devoted by the entrepreneur to 
utilising capital funds, hiring workers and organising production.  It is assumed that to run a 
factory successfully, the entrepreneur needs to devote all his labour endowment to it, that is, 
factory production can take place only if  1 E l = .  
 
Capital is accumulated from savings at the end of the period 1 after good X is produced.  
Each unit of good X saved can be converted into R unit of capital.  It is assumed that the 
minimum amount of capital required for factory production is greater than the maximum 
saving a single individual can make at t  = 1, i.e., KR a ≥ .  Thus, to adopt the factory 
production technology, it is necessary to pool savings of multiple individuals, and lend them 
to the entrepreneur.  This task is carried out by a financial intermediary (the banker), and 
requires the time and energy of the banker, denoted by the banker’s input, lB.  It is also 
assumed that to run a bank successfully, the banker has to devote all his labor endowment to 
it, i.e.,  1 B l = . 
 
2.2  The case without financial intermediation 
In the absence of a financial intermediary, only home production technology can be used, and 
the economy is characterised by autarky.  An individual’s decision problem is: 
12
12 ,
11
22
12
12 12
11
max ( 1)
..
1
cc Uc c
st x al
xa l
ll
cc xx
cx
θ θ =+ <
=
=
==
+=+
≤
 
where xi (i = 1,2) is good X produced in period i; li (i = 1,2) is labor endowment in period i.  
We assume that individuals can store goods for later consumption without incurring storage 
costs.  Solving this problem we obtain:  12 ** cca = =  
   4
Since technology is the same in both periods, and labor is not transferable across time, time 
preference dictates that individuals will not save in period t = 1. The individual utility (real 
income) level over the two periods is  * (1 ) A Ua θ = + . 
 
2.3. The case with financial intermediation and entrepreneurship 
In the presence of financial intermediation and entrepreneurship, savings may be pooled by 
the banker, and the funds borrowed and invested in factory production by the entrepreneur.  
Since savings are not made until the end of period 1, all individuals use the home production 
technology to produce good X in period 1.  In period 2, however, individuals may engage in 
different activities.  We group the individuals into four different categories according to their 
period 2 activities:  
(1)  Consumer-home producers (“home producers”), who employ the home production 
technology to produce X for self consumption, and fund additional consumption from savings 
plus interests.   
(2)  Consumer-factory workers (“factory workers”), who work in a factory in exchange 
for a wage, and receive additional funds from their savings plus interests.   
(3)  Consumer-banker (“the banker”), who collects deposits from home producers and 
factory workers, lends the funds (including his own savings) to the entrepreneur, and retains 
the difference between the payment to depositors and repayment from the entrepreneur.   
(4)  Consumer-entrepreneur (“the entrepreneur”), who invests in factory production 
technology using funds borrowed from the banker and his own savings, and hires factory 
workers to produce good X.  He obtains the residual production after making wage payments 
to factory workers and loan repayment to the banker.  
 
We assume that entry into banking and factory production is free so that neither the banker 
nor the entrepreneur behaves monopolistically.   The interrelationships between four 
categories of individuals are illustrated in Figure 1.  
 
The decision problems for the four types of individuals and the solutions are presented in 
table 1. 
 
There are two possible equilibria.  If  * (1 )/ d r θ θ ≤ − , the equilibrium is the same as that of 
the model without financial intermediation.  If  * (1 )/ d r θ θ >− , the equilibrium involves   5
financial intermediation.  Since financial intermediation only occurs in equilibrium within the 
parameter set defined by  * (1 )/ d r θ θ >− , financial intermediation is endogenously 
determined.  For example, starting from an initial set of parameters that satisfies 
*( 1 ) / d r θ θ ≤− , changes in parameters may lead to  * (1 )/ d r θ θ >− .  This will cause the 
equilibrium to shift from one without financial intermediation to one with finance 
intermediation.  In other words, financial intermediation can endogenously emerge. 
 
The equilibrium with financial intermediation is characterised as follows.  First, all 
individuals’ utility levels are maximised, and the market for good and the market for loans 
clear.  From the loan market clearing condition, *
ds LKR m a L = == , we obtain the 
equilibrium rate of loan interest: 
11 1
111 1 *( ) L rR m A a
αβ β α
β ββ β αβ
+ −−
− −− − = .  Clearly  * L r  is negatively 
related to capital availability (as indicated by R,  m, a) and positively related to capital 
productivity (as indicated by A, α, β). 
 
Assuming that the number of workers employed by the entrepreneur is less than the total 
number of individuals available to work in a factory, the equilibrium utility level of home 
producers and that of factory workers are equalised due to labor mobility between home and 
factory.  From this condition we obtain the equilibrium wage rate, * wa = .  In addition, the 
equilibrium utility of the banker and that of the entrepreneur are equalised due to free entry to 
both activities.  This condition gives us the equilibrium rate of deposit interest, 
* [1/( 2) ][( 2) * * ] dL rm a m a r a π =− − − − ,  
where  *( * ) ( * )( 1* ) ** ** L AK E r K w E w
αχ π ≡− + − −  is the equilibrium level of profit of the 
entrepreneur.  The profit will be driven down to zero if all individuals can potentially become 
the entrepreneur.  Otherwise if only “talented” people (i.e., the banker and the entrepreneur in 
our model) can become the entrepreneur, then the profit can be positive even in equilibrium 
until, for example, still newer technology is adopted, in which case “creative destruction” will 
displace the old equilibrium and eliminate the profit associated with the factory production 
technology.  Our model however does not capture that dynamic.  It is easy to see that the 
difference between loan and deposit interest rates covers the entrepreneurial profit and the 
banker’s labor input valued at the equilibrium wage rate.  
   6
It is straightforward to show that provided  * (1 )/ d r θ θ >−   the equilibrium with financial 
intermediation and entrepreneurship produces higher utility for all individuals compared to 
the equilibrium without financial intermediation.  In the case with zero entrepreneurial profit 
the equilibrium condition becomes 
11 1
111 1 ( ) (1/( 2) (1 ) / Rm A a m
αβ β α
βββ β αβθ θ
+− −
−−− − −− > − which 
is more likely to hold if: (1) productivity associated with the factory production technology is 
high (A, α, β are large) and the productivity associated with home production technology is 
low (a is small); (2) savings can be efficiently converted to capital goods (R is large); and (3) 
individual time preference is low (θ is large).  This implies that financial intermediation and 
entrepreneurship will more likely promote economic growth the more efficient the new 
technology is relative to old technology, the more easily savings can be converted to capital 
goods, and the more willing individuals are to sacrifice current consumption for future 
consumption.  In the case of zero entrepreneurial profit, the utility level of the banker and the 
entrepreneur is  (2 *) L ar θ + , where 
11 1
111 1 *( ) L rR m A a
αβ β α
β ββ β αβ
+ −−
− −− − = ; and the utility level of the 
home producer and the factory workers is  (2 *) d ar θ + , where 
* [1/( 2) ][( 2) * ] dL rm a m a r a =− − − . 
 
3. Concluding remarks 
This paper presents a simple general equilibrium model of financial intermediation, 
entrepreneurship and economic growth.  In this model, the role of financial intermediation is 
to pool savings and to lend the pooled funds to an entrepreneur, who in turn invests the funds 
in a new production technology.  The adoption of the new production technology improves 
individual real income.  Thus financial intermediation enhances income growth through 
affecting individuals’ saving behaviour and enabling the adoption of a new production 
technology. 
 
It may be argued that financial intermediation is not required for the adoption of a new 
production technology because the entrepreneur may borrow directly from individuals.  Our 
model rules out this possibility as the entrepreneur is resource constrained so that he cannot 
engage in both the activity of pooling funds and organising production.   The separation of 
pooling funds and organising production may also be justified if part of the banker’s role is to 
monitor the entrepreneur on the behalf of all depositors (Diamond, 1984).   7
 
In this model, the banker is a pure financial intermediary, and there is no money multiplier 
effect. Future research may extend the model to investigate the implications of fractional-
reserve banking on investment and growth.  
 
References:   
 
Bagehot, Walter (1873), Lombard Street, reprinted by BiblioBazaar, 2006. 
 
Bencivenga, Valerie, Smith, Bruce and Starr, Ross (1995), “Transaction costs, technological 
choice, and endogenous growth”, Journal of Economic Theory, 67, 153-177. 
 
Diamond, Douglas (1984), “Financial intermediation and delegated monitoring”, Review of 
Economic Studies, 51(3), 393-414. 
 
Greenwood, Jeremy and Jovanovic, Boyan (1990), “Financial development, growth and the 
distribution of income”, Journal of Political Economy, 98(5), 1076-1107. 
 
Greenwood, Jeremy and Smith, Bruce (1997), “Financial markets in development and the 
development of financial markets”, Journal of Economic Dynamic and Control, 21, 145-181. 
 
Hicks, John (1969), A theory of economic history, Oxford: Clarendon Press.  
 
King, Robert and Levine, Ross (1993a), “Finance and growth: Schumpeter might be right”, 
Quarterly Journal of Economics, 108(3), 717-737. 
 
King, Robert and Levine, Ross (1993b), “Finance, entrepreneurship, and growth: theory and 
evidence”, Journal of Monetary Economics, 32, 513-542. 
 
Levine, Ross (1997), “Financial development and economic growth: view and agenda”, 
Journal of Economic Literature, 35(2), 688-726. 
 
Levine, Ross and Zervos, Sara (1998), “Stock markets, banks, and economic growth”,   
American Economic Review 88, 537–558. 
 
McCaig, Brain and Stengos, Thanasis (2005), “Financial intermediation and growth: some 
robustness results”, Economics Letters, 88, 306-312. 
   8
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Home producers 
X=al 
Deposits  Principal+ 
deposit interests 
Wage
Entrepreneur  Banker 
Factory workers 
Deposits 
Principal+ 
deposit interests 
labor
Principal+ 
loan interests 
Loan 
X=AK
αE
β
Figure 1.  An economy with financial intermediation and entrepreneurship 
Good X 
Good X 
Good X 
Payment 
Payment 
Payment   9
Table 1.  Individual decision problems and solutions 
 Decision  problems  Solutions 
Home 
producers 
12
12 ,
11
11 1
12 2
12
11
max
..
(1 )
1
cc
d
Uc c
st x al
xcs
sr x c
ll
cx
θ =+
=
=+
++=
==
≤
 
where s1 is savings in t = 1, rd is deposit 
interest rate. The price of good X is 
normalised to be 1 
If   (1 )/ d r θ θ >−  
12 *0 ,*2 ,
*( 2 )
d
HP d
cc a r
Ua r θ
= =+
=+
 
If (1 )/ d r θ θ ≤ −  
12 *, *,
*( 1) HP
ca ca
Ua θ
= =
=+
 
Factory 
workers 
12
12 ,
11
11 1
12 2
12
11
max
..
(1 )
1
cc
d
Uc c
st x al
xcs
sr w l c
ll
cx
θ =+
=
=+
++ =
==
≤
 
where w is the wage rate. 
If   (1 )/ d r θ θ >−  
12 *0 ,* ( 1 ) ,
*[ ( 1)]
d
FW d
cc a r w
Ua r w θ
= =++
=+ +
 
If (1 )/ d r θ θ ≤ −  
12 *, *,
*( 1) FW
ca ca
Ua θ
= =
=+
 
Banker 
12
12 ,
11
11 1
11 1
11 2
12
11
max
..
(1 ) (1 )
1
cc
Ld
Uc c
st x al
xcs
DsL
rL rD c
ll
cx
θ =+
=
=+
+=
+− + =
==
≤
 
where  D1 is deposits collected, L1 is 
loans made.  rd and rL are the deposit and 
loan interest rates, respectively.  We 
assume that  rL> rd if l2 = 1, and rL= 0 if 
l2 ≤ 1 
If   (1 )/ L r θ θ >−  
1
21
1
*0 ,
*( ) ( 1 )
*[ ( ) ( 1) ]
Ld L
BL d L
c
cr r D r a
Ur r D r a θ
=
=− + +
=−+ +
 
If (1 )/ L r θ θ ≤ −  
12 *, *,
*( 1) B
ca ca
Ua θ
= =
=+
   10
Entrepreneur 
12
12 ,
11
11 1
11
2
2
2
21 2
12
11
max
..
()
(1 )1
01
(1 )
1
cc
L
Uc c
st x al
xcs
KR Ls R a
AK E if l
x
if l
xr L w E c
ll
cx
αβ
θ
αβ
=+
=
=+
=+ >
⎧ + <=
= ⎨
< ⎩
−+ − =
==
≤
If   (1 )/ L r θ θ >−  
1
2
11
11 1
11
11 1
*0 ,
** * ( 1 ) ( * )*
*[** ( 1) ( * ) * ]
*( ) ( ) ( 1 )
*( ) ( ) ( 1 )
L
EL
L
L
c
cA K E r K a w E
UA K E r K a w E
where
KA r R a
w
EA r
w
αβ
αβ
ββ
αβ αβ αβ
αα
αβ αβ αβ
θ
β
α
α
β
α
α
−
−− −− −−
−
−− −− −−
=
=− + − −
=− + − −
=+ >
=+
If (1 )/ L r θ θ ≤ −  
12 *, *,
*( 1) E
ca ca
Ua θ
= =
=+
 
 

FINANCIAL INTERMEDIATION, ENTREPRENEURSHIP AND ECONOMIC GROWTH

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