Journal of Financial Risk Management
2013. Vol.2, No.1, 1-9
Published Online March 2013 in SciRes (http://www.scirp.org/journal/jfrm) DOI:10.4236/jfrm.2013.21001
Foreign Entry and Multi-Period Bank Competition
Based on Collateral View
Xudong Chen*, Yong Zeng
School of Management and Economics, University of Electronic Science and Technology of China,
Chengdu, China
Email: *chenxudong198401@163.com
Received January 16th, 2013; revised February 15th, 2013; accepted February 22nd, 2013
This paper constructs the multi-period model of spatial bank competition between the local bank and the
foreign bank with financing cost (efficiency) advantage, the results show that: 1) when the amount of the
high risk borrowers in the marker reaches a threshold, both banks will use collateral as screening device
to distinguish different risk borrowers, only low risk borrowers will borrow money from the bank; 2) the
space distance (production differentiation) can help local bank confront the foreign bank’s cost (efficiency)
advantage. Further comparative static analysis shows: the bank’s profit decreases with its financing cost,
and the bank will require higher loan rate and less collateral with its financing cost increasing; Decreasing
transaction cost and better legal environment will facilitate the bank to require more collateral and lower
loan rate.
Keywords: Multi-Period Bank Competition; Collateral; Screening
Introduction
In the last few decades, the active liberalization of global
banking markets has led to a sharp increase in the foreign
banks’ entry into many countries. Claessense et al. (2008) indi-
cates that from 1995 to 2006, the number of foreign banks and
their market shares of Latin America, Eastern Europe and some
regions in low and middle-income countries of central Asia
increase rapidly. Moreover, the foreign banks’ market share in
some countries of Eastern Europe accounts for more than 80%.
In China, banking system has been reformed fast and deeply
recently, the introduction of foreign strategic investors is cen-
tral to Chinese bank reform (Zhu et al., 2008). In 2001 China
joined the WTO, we promised to open our financial market
completely to the foreign investor in five years later. In 2006,
all the non-prudential restrictions on foreign banks’ entry into
China were cancelled, consequently foreign banks are develop-
ing quickly in China. By the end of 2011, 37 banks from 14
countries and regions have established locally incorporated
foreign banks, the gross assets of foreign banks in China in-
creased by 23.6% year-on-year. It is worthy to analyze how the
foreign banks’ entry impact domestic banks.
Lending is core business of commercial bank, the traditional
financial intermediation theory shows that information asym-
metry is key point in bank lending. On the one hand, bank and
borrower have asymmetric information about the ability of
borrower to repay loans, on the other hand, different banks have
asymmetric information about the ability of borrower to repay
loans because of their different lending relationship. Dell Aric-
cia (2001) constructs the framework of multi-period model of
spatial bank competition, which shows that the information
asymmetries are important determinates of the bank compete-
tion. Li (2010) considers multi-period credit competition and
steady state between the local bank with information advan-
tages and the foreign bank with the financing cost advantage,
and the conclusion shows that the local bank’s information
advantage can not hinder the foreign bank’ entry. Deng (2010)
studies the strategic cooperation decision of the foreign bank
and domestic bank through real option method, results show
that besides the high growth and scale of the local credit mar-
kets, the chance of foreign bank acquiring local bank in the
future will be a significant reason for foreign bank’s entry into
China. Hauswald & Marquez (2003, 2006) analyzes how in-
formation asymmetry affects the structure of the bank competi-
tion and the interest rate, through different screening ability
reflecting information asymmetry between both banks. Further
more, Lehner (2008, 2009) analyzes how the size of market and
screening ability affect entry mode choice. Gormley (2007)
considering the favorable and adverse impact exerted by for-
eign bank’s entry on local market in pure strategy framework.
Another researches analyzing information asymmetry in
bank competition find that collateral can be used as a screening
device to deal with information asymmetry, famous for such
works as Bester (1985), Bensanko & Thakor (1987a, 1987b),
which show that: low risk borrowers are more willing to pro-
vide collateral to the bank than high risk borrowers so as to
show that themselves are low risk. The reason is that the higher
failure probability of high risk borrowers’ investment leads
high risk borrowers more reluctant to provide collateral to the
bank. Based on the above conclusion it shows that collateral
can help bank exactly distinguish different risk borrowers so as
to reduce the bank to suffer from the loss caused by the adverse
selection. However, Barro (1976) also shows that collateral is
costly to be used as screening device in distinguishing different
risk borrowers, because when the borrowers investment fails
and borrowers are not able to repay the loans, the bank will take
possession of and liquidating the collateral, which incurs a loss
between the bank and the borrowers. Consequently, the collat-
eral value for the bank is lower than that for the borrowers.
*Corresponding author.
Copyright © 2013 SciRes. 1
X. D. CHEN, Y. ZENG
Hainz (2008) analyzing the loans of 70 countries shows that:
when the bank competition is weak, the bank may require the
borrowers to provide collateral. Further researches as Sengupta
(2007, 2009) study bank competition between informed in-
cumbent bank and uninformed foreign bank, which indicates
that: both ex ante better information and ex-post stronger legal
protection facilitate foreign bank’s entry.
However previous research about collateral research are con-
structed as single period, while the bank competition between
local bank and foreign bank is dynamic, the bank will make
optimal decisions based on its future expected return. In this
sense only can multi-period and dynamic bank competition
describe real competition between the two banks. Besides, to
the best of my knowledge, there are few papers that consider
bank competition where interest rate and collateral are the stra-
tegic variables of competition.
In this paper bank competition is constructed as interaction
between asymmetrically informed banks: local bank is more
familiar with the local credit market, while foreign has finance-
ing cost (efficiency) advantage, and both banks use collateral as
a screening device to distinguish different risk borrowers. At
the base of Dell Ariccia (2001) and Sengupta (2007), we ex-
tend to discuss each bank’s optimal credit strategy in the
multi-period and dynamic bank competition, the study shows
that: when the ratio of high risk borrowers in the markets ex-
ceed a certain critical value, both banks require borrowers to
provide collateral and pay loan rate, so only low risk borrowers
would like to borrow money from bank, high-risk borrowers
give up borrowing money from any bank; multi-period and
dynamic bank competition will eventually achieve steady state,
in the steady state the situation in every period is the same, the
space distance (production differentiation) can help local bank
confront foreign bank’s cost advantage. Further comparative
static analysis shows: the local bank’s profit becomes smaller
with bigger financing cost, and bank will require higher rate
and less collateral with its financing costs increasing, increasing
transaction cost will facilitate the bank to require higher interest
rate and lower collateral. Better legal environment facilitates
the bank to require more collateral and lower interest rate.
The rest of is arranged as following: Section 2 lays out the
basic hypothesis of bank credit competition; Section 3 estab-
lishes the bank competition, Section 4 is the comparative static
analysis. Section 5 provides the results. All proofs are listed in
the Appendix.
Basic Assumption
Similarly as Sengupta (2007), there are two banks in the
credit market: bank I, the local bank which exists a long time in
the market; bank E, the foreign bank who entered the market
right now, two banks locates two endpoints of a line of measure
1, all borrowers uniformly distribute along the line.
Local bank and foreign bank’s financing costs are respec-
tively
I
and
E
. Foreign bank has financing cost (effi-
ciency) advantage, namely
E
I
. Borrowers will borrow 1
from the bank and invest a project which generates gains
X
with probability 1
and 0 with probability
. Banks face
two kinds of different risk borrowers: fraction of high risk
borrowers whose probability of successful project is 1
v
H
and fraction of low risk borrowers whose probability of
successful project is 1
1v
L
, where LH
01
 . We as-
sume that the low risk borrowers (good borrowers) are worthy
to lending (i.e.,
10,
j
L,
X
jIE


) and the high risk
borrowers (bad borrowers) are unworthy to lending (i.e.,
1
j
H0,,
X
jIE

 ), bank and borrower have asym-
metric information about the risk type of borrowers, namely
before the bank loans to the borrowers, all borrowers know
their risk types, while the bank does not know their risk types.
Following Sengupta (2007), bank provides a loan contract
,
R
C to the borrower, which specifies that borrower need
provide an amount of collateral to the bank and pay inter-
est rate
C
R
. In detail, if the project successes, borrower pays
interest rate
R
to the bank and collateral will be paid to
the bank if the project fails. According to the Barro (1976), the
disparity in collateral valuation between the borrower and the
bank by noting as
C
, namely the value of the collateral
which the borrower provides becomes
C
C
for the bank,
Where 01
. The size of the discount rate
reflects the
legal environment of the host country. Poor legal environment
means smaller discount rate. When the bank provide the loan
contract
,
R
C to borrowers, the bank’s expected profit func-
tion is given by
π,1RCR C
 
 , the expected
revenue of borrowers is given by
,1uRCX RC
 , so the above loan contract
,RC will yield a surplus

1

1
X
C


. The
surplus is the total profit of the investment, part of which will
be assigned to the bank and the other part will be assigned to
the borrower. Meanwhile, we find that the use of the collateral
will lead a loss of society surplus
1C
, which is just the
price of the use of collateral. As Sengupta (2007) shows, col-
lateral can be used as a perfect screening device to help bank
exactly distinguish the borrowers’ risk type, namely low risk
borrower would like to provide more collateral and pay lower
rate
R
, while high risk borrower would like to pay higher rate
R
and provide less collateral, the loss of society surplus
1C
can be thought as the cost of screening. Bank
j
provides the loan contract
,
j
j
kk
R
C to the borrower . For
simplicity, borrowers are assumed to have unconstrained access
to collateral. The borrowers’ reservation utility is 0, all borrow-
ers are live for two periods, both banks face only new borrow-
ers in the first period. In each period later, there are new and
old borrowers in the market for both banks, the new borrowers
derive from the credit market growth (or recession), and the old
borrowers come from the new borrowers in the previous period,
and the old borrowers disappear in the end of this period; obvi-
ously, all the new borrowers will disappear in the two period
later. Among the new borrowers the ratio of high risk and low
risk is
k
:1vv
. In each period the amount of new borrowers
is
times that of old borrowers, namely the ratio of new
borrowers to old borrowers in each period is :1
.
Borrowers still need to pay transaction cost
I
wx besides
interest rate and collateral,
x
is the distance between bor-
rower and bank ,
I
I
w
I
E
is the unit transaction cost for borrower
lending form bank . According to Dell Ariccia (2001), trans-
action costs can be viewed as a measure of degree of product
differentiation. For example the distances between the borrower
and bank , bank are respectively I
x
and 1
x
, the
transaction costs of the borrower lending from bank and
bank are respectively
I
E
,1
IE
wxwx. Because local bank
has enough understanding about the local economic and
cultural environment, together with wide local customer re-
sources, and mostly set up a relatively stable lending relation-
ship. So local bank is more familiar to borrowers, while foreign
bank is not familiar with borrowers for its new entry. In other
I
Copyright © 2013 SciRes.
2
X. D. CHEN, Y. ZENG
words compared with foreign bank, the local bank has the in-
formation advantage. The transaction costs of two banks reflect
the information asymmetry between two banks, local bank is
more familiar to the market so its transaction cost is smaller
than that of foreign bank. When bank provides loan con-
tract
I
,
I
I
kk
R
C to the borrower whose risk type is , the ex- k
pected profit of borrower is
,
II
kk I
uRC wx
k
. Similarly when
bank provide loan contract E
,k
E
E
k
R
C to the borrower, the
expected profit of borrower is
E
,
k
EE
C1x
kk
uR w. A bor-
rower located at a distance
x
from bank is indifferent
between lending from bank and lending from bank
I
I
E
if
,,
k
II E
kkkI kkE
C wxuRCw 
x1
E
uR (1)
Bank Competition of the Basic Model
Single Period Competition
In a single period bank competition, both banks face only
new borrowers, borrowers know their risk type, but both banks
cannot distinguish different risk borrowers. Neither bank has
old borrowers (old borrowers are those borrowers who have
lending relationship with the bank), bank need seek optimal
strategies to maximize their expected profits according to the
current situation. The competition process is as follows: first
each bank decides its loan rate
R
and requires borrowers to
provide collateral , then each borrower maximizes its ex-
pected profit by choosing which bank to borrow money from.
Higher rate
C
R
and more collateral can increase the ex-
pected profit from per borrower, but more borrowers will apply
loan to its rival bank, so both bank will make an appropriate
loan rate
C
R
and collateral to maximize the bank’s ex-
pected profit.
C
Similarly as Sengupta (2007), we analyze the condition that
both banks will use collateral as screening device. We can get
the Proposition 1 whose proof can be seen in the Appendix A.
Proposition 1: if 11
jj
HL
H
L
uu

, when ratio of the high risk
borrowers in the new borrowers satisfies ,
where
1
vv

12
11
1
LL
H
LL
 
v
 


, both banks will use collateral
as screening device, bank
j
will provide two loan contracts

,,
jj
HH
RC R,
jj
LL
C to the borrowers, where

11
,,
,0
1
j
j
jj HL H
jj
HL LH
LL
HL HLHL
j
jj
H
HH
H
uu
uu
RX C
u
RX C

 

 

 
L

(2)
As banks and borrowers have ex ante information asymmetry,
namely bank cannot distinguish the risk type of the borrowers,
if bank do not use collateral as a screening device, bank has to
require all borrowers the same interest rate
R
, and the bank
will suffer from the loss caused by adverse selection. If bank
use collateral as a screening device, the screening cost is
1C
. so each bank faces a trade-off between loss caused
by adverse selection and the screening cost, if the amount of
high risk borrowers is bigger, namely there are much more bad
borrowers in the market, the loss caused by adverse selection
will the be more than the screening cost caused by using collat-
eral, then the bank prefers to use collateral as a screening de-
vice. If the amount of high risk borrowers is smaller, bank pre-
fers the same interest rate for all borrowers, in this case there
are enough good borrowers, bank would not like to require
borrowers to provide collateral.
As contract theory shows that: “to any Bayesian Nash equi-
librium of a game of incomplete information, there exists a
payoff-equivalent revelation mechanism that has an equilibrium
where the players truthfully report their types” (revelation prin-
ciple). Bank can provide two loan contracts, one contract is
higher loan rate and lower collateral and another contract is
higher collateral and lower loan rate. The high risk borrowers
are willing to choose the first contract and the low risk borrow-
ers are willing to choose the second contract. By the mecha-
nism offered by the bank, borrowers will not hide their risk
type.
For simplicity, in the subsequent study we assume 1,
namely the amount of the high risk borrowers in the market is
large, both banks are willing to use collateral as a screening
device. So banks can accurately distinguish the different risk of
two kinds of borrowers. Because high risk borrowers are un-
worthy to lend, the bank only lend money to low risk borrowers.
We can get the Proposition 2 whose proofs can be seen in the
Appendix B.
vv
Proposition 2: when the bank j provides loan contract
,
j
j
L
L
R
C to all the borrowers so that the low risk expected
revenue is no less than
j
L
u, only low risk borrowers lend from
bank
j
, high-risk borrowers will not lend from any bank. The
expected profits of bank j is give
by
π11 1
j
jj
LLL
vXMu
 
,
where
11
LH
HL
M



. The interest rate and collateral
are respectively:

1
,
j
j
H
L
jj
HL
LL
HL HL
u
u
RX C

 
(3)
From (3) we can get the relationship between the loan rate and
collateral
1
jj
H
LL
H
R
CX
(4)
The screening cost can be shown as follows

11 1
LH
jjj
L
L
HL
LL
M
uu
 



C
(5)
According to Proposition 2, both banks offer only one con-
tract
,
j
j
L
L
R
C, only low risk borrowers will borrow from the
bank. No matter high risk borrowers lend or do not lend, their
expected profits are 0. So high risk borrowers do not lend from
any bank, this is the revelation principle. Meanwhile we can
find the screening cost is
j
L
M
u, bigger
j
L
u means bigger
screening cost, then the expected profit of the bank become less.
By (4) we know bank will decrease interest rate together with
more collateral. By (5) we find that more collateral required by
the bank, the expected profit for the borrowers is more, but the
screening cost is big, the bank’s profit is less. So bank will
Copyright © 2013 SciRes. 3
X. D. CHEN, Y. ZENG
choose the least collateral so long as high risk borrowers are not
willing to apply loan to the bank. In addition through the
Proposition 2 we can know that the optimal loan contract
provided by the banks is one-to-one correspondence
with the expected revenue of the borrowers
,RC
j
L
u, that is to say,
every loan contract offered by the bank can lead one
and only one
,RC
j
L
u. In the other hand, for each
j
L
u there exists
unique optimal loan contract . The bank selects
,RC
R
,
as its decision variables in the previous researches, based on the
Proposition 2, bank can choose
C
j
L
u rather than its decision
variable
R
, , which can simplify our analysis. C
Consequently, we obtain the equilibrium of the single period
bank competition as Proposition 3, proofs can be seen in the
Appendix C.
Proposition 3: If
12 12
EI
E
IIE
M
wwMww

 , in the
single bank competition, there is a point
s
L
x
, the lower risk
borrowers located in the
s
L
x
left lend from bank I, lower risk
borrowers located in the
s
L
x
right lend from bank E, the ex-
pected profits of two banks are:
 
Mw
 
new
sI
 2
E
w
1
12
I
Mw

 

91
E I

IE
v
w(6)
 
Mw
 
new
sE
 2
I
w


1
12
E
Mw
 
91
I E

IE
v
w
(7)
where
 
21
w
I
1
IE
ww31
L
x
M
sE


I
E
w
M
The conclusion shows that space distance (or production dif-
ferentiation) can confront against foreign bank’s cost (effi-
ciency) advantage.
Multi-Period and Dynamic Compet ition
In brief, the main difference between multi-period and dy-
namic competition and single period bank competition is that
bank will determine the optimal decision according to their
future expected profit. The competition process is indicated as
follows: first, both banks decide interest rate
R
and collateral
, and the new low risk borrowers decide which bank to bor-
row money to maximize the expected profit. For the old bor-
rowers of each bank itself, the bank must offer at least the profit
that its rival bank can offer in order to avoid their old borrowers
to borrow money from its rival bank as a new borrower. So for
its old borrowers, each bank will make different decision from
new borrowers. For the old borrowers, since lending relation-
ship has been set up with the original bank and the profit given
by the original bank is the same as the profit given by the rival
bank, the old borrowers will choose to loan from the original
bank. Therefore, for each bank, their old borrowers’ interest
rate and collateral is no longer bank’s decision variable, the
competition between two banks is only embodied in the new
borrowers’ competition.
C
Due to 1, banks face new borrowers market and old
customers who are identified as high risk borrowers by the
competitors, intuitively there are too many bad new borrowers
in the market. So both banks require all borrowers to provide
collateral to distinguish two kinds of customers.
vv
In the process of competition period, we construct dynamic
competitive framework of bank competition where borrowers
are alive for two periods, the total profit of the bank derives
from the following four categories borrowers:
a) The initial old borrowers (no old borrowers in the first pe-
riod, there are old borrowers in the every period later);
b) The new borrowers of the first period (including the new
borrowers of the market and the initial high risk old borrowers
who are screened as high risk borrowers by the rival bank in the
earlier period);
c) The old borrowers of the second period (initial old bor-
rowers in the first period disappear in the second period, the old
borrowers derive from the new borrowers of the first period);
d) The new borrowers of the second period (including new
borrowers in the market and the old borrowers derive from the
new borrowers of the second period).
Because both banks require borrowers to provide collateral
and pay interest rate, only low risk borrowers will borrow
money, so no matter local bank or foreign bank, their profits are
from low risk borrowers. We note the discount rate as
, and
01
, we can get the Proposition 4 that is proved in the
Appendix D.
Proposition 4: If

 
1211
121
EI
IE
EI
ww M
ww M

 

 

,
in multi-period and dynamic bank competition, there is a point
m
L
x
, low risk of borrowers located in the m
L
x
left loan from
bank , low risk of borrowers located in the Im
L
x
right loan
from bank
E
, and both banks only provide only a contract,
only low risk borrowers are willing to borrow money, the ex-
pected profits of the two bank are respectively
 
 




new 2
2
112 11
2
31 1
111
mI
IE
EI IE
v
ww M
Mww
 

 

 


 
2


(8)
 
 




new 2
2
112 11
2
31 1
111
mE
IE
IE EI
v
ww M
Mww
 

 

 


 
2


(9)
where
 


 

1
31
112
m
L
IE
EI IE
xMw w
wwM
 
 
 

1
The above propositions tell us that both banks use collateral
as screening device. Further more, the interest rate and the col-
lateral are different for two banks. As collateral required by the
bank, the high risk borrowers will not apply loan from any bank,
only low risk borrowers will loan from the bank, so collateral is
an accurate screening device, this is the revelation principle.
Comparative Static Analysis
This section are comparative static analysis, analyzing how
the financing cost, the transaction cost and legal environment
Copyright © 2013 SciRes.
4
X. D. CHEN, Y. ZENG
influence the profit, interest rate and collateral.
Financing Cost
Through the Proposition 4 we can get the financing cost’s
effect on the banks’ profit, interest rate and collateral. Proof can
be seen in the Appendix D.
Corollary 1:
new 0, 0,0
mjjjjjj j
jjjjjjj
RRuCCu
uu
 

 

The above conclusions show that, the local banks’ profit de-
creases with its financing costs increasing, however, while for-
eign bank’s profits and market share increase. In fact, the local
bank financing cost increases, its efficiency become bad and its
competitiveness become weak, which leads smaller market
share and less profit. Meanwhile, bank will require higher rate
and less collateral with its financing costs increasing. In the
other words, the decreasing efficiency of the bank reduces its
desire to use collateral, consequently reduces the profit of the
borrowers.
Transaction Cost
Through the Proposition 4 we can get transaction cost’s ef-
fect on the banks’ profit, interest rate and collateral. Proof can
be seen in the Appendix D.
Corollary 2:
if
11212
EI EI
Mw w
 


0
,
new 0
mI
I
w

;
if
11212
EI EI
Mw w
 


0
,
new 0
mI
I
w

Corollary 3:
0, 0
jjjj jj
jj
jjj j
RRu CCu
wuw wuw
 

 
Corollary 2 shows that when the transaction cost is small,
both banks compete intensely for borrowers, increasing trans-
action cost means the weak competitiveness of the bank, so the
profit of the bank is less. When the transaction cost is big, the
bank competition becomes weak, both banks prefer monopo-
lizing their borrowers rather than competing with its rival. In-
tuitively speaking, the increasing transaction cost means that
the borrowers have to spend more to borrow money from any
bank. That is to say, the borrowers who are captured by the
local bank are more reluctant to borrow from foreign bank. In
other words, the borrowers are more captive by the local bank.
then both banks begins to exploit its borrowers just as parts of
markets are monopolized by the local bank and parts of market
are monopolized by the foreign bank, so the profit bank of both
banks increase. Consequently, the profit of the borrowers
should be less.
Corollary 3 shows that increasing transaction cost will facili-
tate the bank to require higher interest rate and lower collateral.
Increasing transaction cost implies that the bank competition is
less intense, as described before, the screening cost by using
collateral as a screening device is

1C
, so the bank pre-
fers as few collateral as possible so long as high risk borrowers
are not willing to loan from the bank, then the bank will ask
borrowers provide less collateral and higher rate. Under the
circumstances, bank will obtain more profit but profits of bor-
rowers are less.
Legal Environment
Through the Proposition 4 we can get legal environment’s
effect on the interest rate and collateral. Proof can be seen in
the Appendix D.
Corollary 4:
0, 0
jjjj jj
jj
RRu CCu
uu
 
 
 

Better legal environment means bank use collateral as the
screening device less costly, namely the screening is more effi-
cient, which makes the bank be willing to require more collat-
eral and lower interest rate.
Conclusion
This paper considers the multi-period model of spatial bank
competition between the local bank and the foreign bank with
cost (efficiency) advantage and explores the effect of foreign
entry and bank competition on firms’ access to credit, the re-
sults show that: when the amount of the high risk borrowers in
the marker is more enough, both banks prefer to use collateral
as screening device to distinguish different risk borrowers
rather than suffering the loss caused by adverse selection, only
the low risk borrowers will apply loan from the bank; the space
distance (production differentiation) can help local bank con-
front against foreign bank’s cost advantage.
Further comparative static analysis shows: the local bank’s
profit decreases with its financing cost, and the bank will re-
quire higher rate and less collateral with its financing costs
increasing. Increasing transaction cost will facilitate the bank to
require higher interest rate and lower collateral. Better legal
environment facilitates the bank to require more collateral and
lower interest rate.
Combined with the reality situation in China, the non-pru-
dential foreign banks’ entry restrictions are removed in 2006,
foreign banks can establish locally-incorporated foreign bank in
China. Compared with domestic banks, foreign banks enjoy
super national treatment on the tax. Moreover, foreign banks
have much better ability of converting deposits to loans. So
compared with domestic banks, foreign banks have cost (effi-
ciency) advantage. However domestic banks also have their
competitive advantage: domestic banks are more familiar with
local national circumstances and have wide borrowers re-
sources. Further more domestic banks have established a rela-
tively stable and long-term lending relationship with many local
firms. Under the same conditions firms are apt to borrow
money from domestic banks. In short, domestic banks are more
familiar with the local market, the domestic banks’ transaction
cost is less than foreign banks’ transaction cost, and foreign
banks have cost (efficiency) advantage, according to the Propo-
sition 4 shows that some of good borrowers (low risk borrowers)
accept loan from domestic bank, other good borrowers accept
loan from foreign bank, all bad borrowers (high risk borrowers)
can not accept any loan from either bank. For borrowers, better
Copyright © 2013 SciRes. 5
X. D. CHEN, Y. ZENG
Copyright © 2013 SciRes.
6
legal environment and higher efficiency of the bank will require
borrowers to pay lower loan rate and provide more collateral so
that the borrowers’ circumstances are improved.
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X. D. CHEN, Y. ZENG
Appendix A: The Proof of Proposition 1
We consider the following two loan contracts
,,,
jj jj
HH LL
RCRC offered by the bank, so that the revenues
of low risk and high risk borrowers are respectively are no less
than ,
j
j
L
H
uu.
Then we maximize the bank’s profit by choosing appropriate
loan rate and collateral:

 
πmax 1
11
jjj
HH HH
jj
LL LL
vRC
vRC






 
j
j
(A1)
s.t
,,
j
jjjjj
H
HHH LL
uRCuRC (A2)
,,
j
jjjjj
LLLLHH
uRC uRC (A3)

,
j
jj j
H
HH H
uRCu (A4)
,
j
jj j
L
LL L
uRC u (A5)
Similar as Sengupta (2007), we solve the above maximiza-
tion step by step.
First
H, intuitively high-risk borrowers hope to pay
higher interest rate and provide less collateral. Second, (A2) is
tight. Third, (A5) is tight, namely
0
j
C

,
j
jj j
L
LL L
So the above optimization problem can be expressed as:
uRC u.

 
πmax 1
11
jjj
HH
jj
LL LL
vR
vRC






 

j
(A5)
s.t
1
j
j
Hj
H
L
H
L
R
R

C (A6)
1
j
j
Lj
H
L
L
L
R
R

C (A7)
1
j
jH
H
H
u
RX

(A8)
11
j
jj
L
LLL
L
L
u
RCX


(A9)
The above problem is a linear programming problem with
three variables, as 11
j
HL
j
H
L
uu

, we get, if , the bank
1
vv
will use collateral to distinguish two different types of borrow-
ers, and the rate and collateral are respectively

,0,
1
11
jj
jjj
HHL
HHL ,
j
LH
H
HL HL
jj
HL LH
j
L
HL
uu
RXC RX
uu
C

u



 


(A10)
Appendix B: Proposition 2’s Proof
If 1
vv, both banks choose to use collateral to distinguish
different risk borrowers, as high risk borrowers are unworthy to
lend, obviously the bank is not willing to loan to high-risk bor-
rowers, thus high risk borrower’s revenue is 0, assuming that
the revenue of low risk borrowers loaning to bank
j
is
j
L
u,
we calculate the bank’s profits:
πmax11)
j
jj
LLLL
vRC
j
L
 
 
(B1)
s.t
,
jjj
HLL
uRC0 (B2)
,
j
jj j
L
LL L
uRC u (B3)
Similar as Proposition 1, we can get
 
π111
j
j
LL
vXMu
j
L
 
(B4)
where
11 1
,,
L
L
HL
LH
jjjj
HH
LL
HL HL
RX uC
 
 



u
M
(B5)
Appendix C: Proposition 3’s Proof
First consider single period bank competition, the borrower
located at a distance
x
from bank is indifferent between
lending from bank and lending from bank if
I
I E
1
IE
LIL E
uwxuw x
  (C1)
so
I
E
E
LL
IE
wuu
xww

(C2)
The lower risk borrowers located in the
x
left loan to the
local bank, other borrowers will loan to the foreign banks, both
banks use
I
L
u,
E
L
u as their decision variables.
Local banks’ profit is
 
new 111
I
E
sII I
E
L
IE
ww

L
LL
wuu
vXMu
 

  

(C3)
Foreign banks’ profit is

new 11 1
E
I
sEE E
I
L
IE
ww

L
LL
wu u
vXMu
 

  

(C4)
Both banks choose appropriate
I
L
u,
E
L
u to maximize their
own profit:
new new
ππ
0
sI sE
IE
LL
uu

 (C5)
Then we get



12 2
,
3
3
131
12 2
131
31 3
IE
I
L
EI
L
EI
E
L
I
L
EI IE
E
S
L
IE
ww
uX
MM
w
uX
MM
ww
wM
xww




 


 



E
w
(C6)
Loan contract offered by the local bank is as follows
Copyright © 2013 SciRes. 7
X. D. CHEN, Y. ZENG
Copyright © 2013 SciRes.
8


12 2
,
131 3
11 22
131 3
IE
IHL E
L
HL
IE
IHLEI
L
HL
ww
RX X
MM
ww
CX
MM


 









 



I
(C7)
  
2112
91
new
sEI EEI
IE
vMww
Mw w


 


(C10)
Appendix D: Proposition 4’s Proof and the Proof
of Corollary in Comparative Static Analysis
Loan contract offered by the foreign bank is as follows


12 2
131 3
11 22
131 3
EI
EHL I
L
HL
EI
EHL IE
L
HL
ww
RX X
MM
ww
CX
MM


 


 



 





E
(C8)
The new borrower located at a distance
x
from bank is
indifferent between lending from bank and lending from
bank
I
I
E
if
 

,,1 ,
,1
11
mItmE tmE t
LILEL E
mI t
LI
uwxEu wxuwx
E
uw

 

x
(D1)
Both banks’ profits are respectively
  
new
2112
91
sIE IIE
IE
vMw w
Mw w


 


(C9)
Then
 
, ,,1,1
,
1
mI tmEtmEtmIt
mt ELL LL
L
IE IE
wuu EuEu
xww ww


 


(D2)
Local Banks in the new customer market profits for

,,,,,1 ,1 ,1,1 ,1 ,
new newnewold
max π,π,π,
mItmItItmtmIt ItmtmIt Itmt
LLLL LL
uxEuxEu x


 
(D3)
where

  
, ,,1,1
,,, ,
new
π,11 11
mI tmE tmEtmI t
mI tmI tmtmI tIELL LL
LLL L
IE IE
wuu EuEu
uxvX Muww ww

 

 

 


(D4)

 

 

 
 
,
,1,1 ,,1
old 0
,,,1 ,
,1
,,
π,1 11d
11 11
11
2
mt
L
x
mI tmItmtmEtI
LLLLIE E
mI tmE tmE tmI t
mE tIELL LL
LLE
IE IE
mI tmE t
ELL
IE
IE
uxvXMuww w
wuu EuEu
vXMuw
ww ww
wuu
Mw www
 







1
 

 


 
 
2
,1 ,1
1
mE tmI t
LL
IE
Eu Eu
ww








(D5)
The both banks choose appropriate , to maximize their profits
,mI t
L
u,mEt
L
u
,,
new new
,,
0
mI tmE t
mI tmEt
LL
uu
 
 (D6)
When the market achieves steady state, the banks’ profits and borrowers’ revenue change no longer, and the loan contracts offered
by each bank every period are the same. According to the Proposition 2 that the two banks' profit means that customer benefits un-
changed, so the steady-state condition is:
,,1,
,
mI tmItmEtmEt
LLL L
uEuuEu
,1
 (D7)
So we can get

 


 



 


 

2
,
2
,
21 1
21
1
131 31
21 1
21
1
131 31
1112
31
IE EI
mI tL
L
EI IE
mE tL
L
mEI
LIE
IE
ww
uX
MM
ww
uX
MM
xw
Mw w






 


 



 



 1wM
(D8)
The loan the contract offered by local bank is

 




 



2
,
2
,
211
21
1,
131 31
211
21
11
131 31
IE EI
mI tHL
L
HL
IE EI
mI tHL
L
HL
ww
RX X
MM
ww
CX
MM











 






 


(D9)
X. D. CHEN, Y. ZENG
The loan the contract offered by foreign bank is

 



 



2
,
2
,
21 1
21
1,
131 31
21 1
21
11
131 31
EI IE
mE tHL
L
HL
EI IE
mE tHL
L
HL
ww
RX X
MM
ww
CX
MM







 


 
 






 


(D10)
Two banks’ profits are as follows:

 



new
2
2
112 11
21112
31 1
mI EI IE
IE
v
Mww
wwM
 
 


 


 

 (D11)

 



new
2
2
112 11
2111
31 1
mE IE EI
IE
v
Mww
wwM
 
 

2


 

 (D12)
We analyze how the cost affects the banks’ profit by (D16), (D17)





new
sgn11120
mI
EI IE
IMww
 



 


(D13)
We analyze how the transaction cost affects the banks’ profit by (D16), (D17)


 
new
sgn sgn
mI


11 21
EI EI
I
Mw w
w
 

 


(D14)
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