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DEWEY
Massachusetts
Institute of
Technology
Department of Econonnics
Working Paper Series
INTERNATIONAL CREDIT AND WELFARE
Some Paradoxical
Results with Implications for the Organization of
International
Lending
Kaushik Basu
Hodaka Morita
Working Paper 02-18
April 2002
Room E52-251
50 Memorial Drive
Cambridge, MA 02142
This paper can be downloaded without charge from the
Social Science Research Network Paper Collection at
http://papers.ssrn. com/abstractJd=xxxxx
10^
Massachusetts Institute ot Technology
Departnnent of Economics
Working Paper Series
INTERNATIONAL CREDIT AND WELFARE
Some
Paradoxical Results with Implications for the Organization of
International
Lending
Kaushik Basu
Hodaka Morita
Working Paper 02-18
April 2002
Room
E52- 251
50 Memorial Drive
Cambridge, MA 02142
This paper can be downloaded without charge from the
Social Science Research Network Paper Collection at
http://papers.ssrn. com/abstractJd=xxxxx
"
MASSACHUSETtS INSTITUTE
OF TECHNOLOGY
MAY
8 2002
LIBRARIES
April 29, 2002
INTERNATIONAL CREDIT AND WELFARE
Some Paradoxical
Results with Implications for the
Organization of International Lending
Kaushik Basu
Department of Economics
Hodaka Morita
School of Economics
Cornell University
The University of New South Wales
Sydney 2052, Australia
Ithaca,
NY
14853,
USA
and
Department of Economics
E-mail: H.Morita(a)unsw.edu.au
M.I.T.
Cambridge,
MA 02142, USA
E-mail: Kbasu@mit.edu
Abstract
This paper models a developing nation that faces a foreign exchange shortage and
hence
its
demand
for foreign
goods
is
limited both by
its
income and
its
foreign exchange
balance. Availability of international credit relaxes the second constraint.
that in this setting the availability
of intemational credit
the borrowing nation worse off than if
This 'paradox of benevolence'
to intemational lending
exchange
it
had
to
It is
shown
concessionary rates can leave
borrow money
at
higher market
rates.
then used to motivate a discussion of policies pertaining
and the Southern government's method of rationing out foreign
to the importers.
Keywords: Intemational
JEL
is
at
classification
credit, foreign
exchange, foreign
aid.
numbers: F30, LIO, D60.
Acknowledgements:
We are grateful to Abhijit Banerjee, Raquel Femandez, Arvind
Wan and the participants of a conference
where the paper was presented.
Panagariya, Priya Ranjan, Debraj Ray, Henry
the University of California, Irvine,
at
1.
There
is
Introduction
a small literature that argues that the benefits of international credit do
not accrue to the recipient developing country, ending up, instead, benefiting the donors
or in the coffers of large corporations that sell goods to the developing country.'
of this paper
while there
is to
is
subject this claim to careful theoretical scrutiny.
no reason
to believe that this
hypothesis
there do exist parametric configurations under
enough because of its paradoxical nature. At
credit (or,
more
which
first
is
it
sight
What we
The aim
find
is that,
always or even generally
is valid.
it
seems
This
is
true,
interesting
of
that the availability
generally, availability of credit at better terms) cannot
make
the recipient
nation worse off because the recipient has the option not to take the credit or to pay a
higher interest than what the donors
However, such simple
demand
(by, for instance, burning money).
logic runs into difficulty in the
domain of strategic
international
finance.
We construct a formal model
and show
that
when
a nation buys goods from large
corporations with monopolistic power, the availability of cheaper international credit
actually leave the recipient
currently borrowing
institution
worse
money from
may become worse
off.
In particular, a poor developing country that
may
is
a profit-maximizing international bank or financial
off if some 'benevolent' organization steps
in,
in place of
the profit-maximizing bank, and begins to lend hard currency at a zero or subsidized
interest rate.
Since public foreign lending
is
usually motivated by altruism and to
fill
in
For works that either defend this proposition or debate it, see Winkler (1929), Hyson and Strout (1968),
Bhagwati ( 1 970), Gwyne (1983), Taylor ( 1 985), Darity and Horn ( 1 988), Basu ( 1 99 ), and Deshpande
'
1
(1999).
for market failures (Eaton, 1989, p. 1308)
situations
where the
it is
indeed surprising to find that there are
recipient nation does better
when
it
gets
its
foreign capital from
private sources.
The
reason, roughly speaking,
is
that the
lowered interest rate for borrowing
foreign exchange changes the strategic environment in which the developing country
buys goods from large corporations
and more, flow out of the country.
interest rate,
While the model we construct
some of the
such a manner that the benefits of the lower
in
finer details of reality,
it
is
is
theoretical and, perforce, abstracts
motivated by real-world experience and the hope
of influencing policy. One country lending money
on enhancing
its
own
exports
is
away from
not unusual
at all.
to another or giving aid
Many
with an eye
industrialized countries give
loans to developing countries with the explicit requirement that the latter then use these to
buy goods from
Commodity
expand
who
the
main beneficiary
is,
multilateral organizations, such as the
that give subsidized credit.
there are situations
some more) from
longer the best
this paper,
or
the loan-recipient or the exporter,
as a consequence (Eaton, 1986, 1989; Fleisig
Our model has important implications
by
Bank
Credit Corporation often give loans directly to the foreign importers and
not always clear
sales
the former. Organizations such as U.S.'s Export-Import
The model
and
whose
for the organization of international lending
World Bank and, more
pertinently, the
IMF,
in this paper alerts such lending agencies that
where the benefits of cheap money may flow out
to give relief to nations facing foreign
by making
is
Hill, 1984).
entirely (and then
the recipient nation. In such environments a lowered interest
way
it
international lending organizations
is
no
exchange shortages. Hence,
aware of this
risk
of an adverse
them
effect of international credit, urges
international lending
The model
to
be extra careful
programs and selecting the
interest rate.
also highlights the crucial role of the
limited foreign exchange
is
in designing their
mechanism through which
released to the importers in the borrower country
by
the
the
borrower government (or the Central Bank). The allocation rules followed by the
government can make
a crucial difference in determining
or aid has on the well-being of the recipient nation.
what
Hence
effect international credit
the model, despite
its
use of a
rather stylized framework, depicts theoretically the general idea explored empirically
Bumside and Dollar (2000) on how
critically
by
the nature of governance in the borrowing nation can
determine whether aid (or subsidized international lending) will work to
its
advantage or not.
In constructing our
in order to
model we
try to steer a
keep the algebra tractable and building
make our model
relevant to at least
some
show
model
this for the
'paradox of benevolence'.
possible
is
to
phenomenon
tries to establish is the
See also Collier
(
1
that certain
is in reality,
need
in
enough features of reality so
we
should warn that the purpose of a
phenomena
are possible. In this paper
To determine how
we need
for empirical
as to
particular realities.
Before proceeding to build the model
theoretical
path between using strong assumptions
we show
plausible this theoretically
empirical work. In that sense what this paper
work
997) and Hansen and Tarp (200 1 ).
in a certain direction.
The Model
1.
Consider a two-period model
South, and an industrialized country
ovra currencies but for
is
This
is
in
is
as fixed at
it
it
to
buy more foreign goods
some
we treat the exchange rate
1
.
That
is,
at the
in that period.
rigidity in the
first
period.
going exchange rate
The
fact
exchange
of a country
rate.
For
as fixed and, without loss of generality,
one unit of the hard currency changes for one unit of the
soft currency. This is not as strong an
many
We shall refer to the South's
buy more hard currency
facing a shortage of hard currency suggests
treat
- henceforth
countries have their
our model, has a shortage of 'hard currency' in the
would do so and use
we
a developing country
- henceforth North. The two
the 'hard' currency.
so in the sense that if it could
reasons of simplicity
is
currency.
'soft'
The South,
which there
inter-country trade and exchange the only acceptable currency
the North's currency. This
currency as the
it
all
in
assumption as appears
at first sight.
The
fact that
Third World nations do face a shortage of hard currency, suggests that exchange
rates are at least partially rigid in reality.
structure of international
why, even
exchange
after
economic
relations
suspect that there are irmate factors in the
which cause
developing country governments go for a
rate to
this.
How else can one explain
firee float
and allow the
be market driven, shortages of hard currency persist?
The stronger assumption
country government.
which
in this
paper concerns the modeling of the developing
We treat the government not as a strategic agent, nimbly
maximizing some payoff, but as
rigid rules, to
We
it
a
somewhat mechanical bureaucracy which has some
adheres. In particular,
we assume
that there are
m (>2) licensed
importers in the South, to which the government (or the Central Bank) allocates
limited foreign exchange balance in period
abroad and
them
sell
in the South.
strategic agent is for simplicity; the
also believe that this description
One
1
;
and they are given the
reason
why we
model has a
surfeit
is fairly realistic in
treat the
right to
its
buy goods
government as not a
of strategic agents. However,
we
the case of many developing and
transition economies.
We shall in this paper focus on one good, which the South likes to consume but
does not produce. The good
the
good (may be
in the
is
in fact
North but also)
Northern firm produces the good
chooses the price p
at
produced by a firm based
which
it
at a
in the
in the
it
North, which sells
South through the licensed importers. The
constant marginal cost
sells to the South.
Though
c,
in
faces no fixed cost, and
our formal model
we work
with one such firm, our qualitative results would be unchanged under n oligopolistic
firms.
Let us begin by modeling the South, in particular, the South's demand in period
1.
We assume, without loss of generality, that the South has one consumer, who is a price
taker and has to decide
periods
1
and
2.
The consumer's
u = u(x,
where x and y
is
the total
period
2.
on how much of the domestic and foreign goods
are the
function
is
(in soft currency) spent
summing up of amount
meant
to
in
given by:
amount of foreign and domestic goods consumed
in
period
1
and yj
on foreign and domestic goods
in
spent on foreign and domestic goods in period 2
done here for algebraic convenience, but
period
is
consume
y, y2),
amount of money
This
utility
to
it
is
not unrealistic either. In this model each
be a long stretch of time (say, a few years). Hence,
in
planning over
is
two periods, most of us would think of the
details
domestic and foreign goods to consume) and on
consumption
in
period
and y2
2,
to put
away
how much money
exactly that variable.
is
consumption where the consumer chooses
much money
of today's consumption (how much of
as savings
Let the Southern consumer's
is
how much
to put aside for total
The standard model of
an exact analogue of this.
total
amount of wealth be Y. This includes
and hard currency endowment. Let the price of the domestic good be
the foreign
constraint
good be
is
Since
p.
we
how
of each good to buy today and
shall take the
exchange
rate to
1
its
soft
and the price of
be fixed
at 1, the
budget
given by
px + y + y2 = Y.
In solving the utility maximization
of one more constraint.
we are
now
that
that, in
to,
order to
however, take account
buy foreign goods,
consumer
is
assuming here) or (more
currency from importers
who have
it
R is the hard currency endowment of the
We later show that, from a modeling point of view,
difference whether the Southern
currency (as
problem the consumer has
This arises from the fact
needs hard currency. Assume for
Southern consumer.
(1)
assumed
to
it
makes no
have direct access to hard
realistically)
buys foreign goods using
soft
access to hard currency.
We shall soon be considering the South's demand for international credit. Now,
clearly the South will
want
to
borrow hard currency
in period
1
only
current shortage of foreign exchange to be less acute in the future.
make
this
assumption
is
to
if it
expects
The simplest way
So
its
future
to
suppose that in period 2 the South expects no foreign
exchange shortage. In other words, the South's currency becomes convertible
future.
its
demand
is
not expected to be constrained by
its
in the
foreign exchange
reserves.
We shall here make such an assumption.
keep the algebra
essential but helps us
tractable.
This extreme assumption
The Southern consumer can then devote
foreign exchange reserve to buying foreign goods in period
all its
cannot borrow any hard currency in period
1
,
not
is
1
.
Hence,
if the
South
x must be such that
px<R.
The Southern consumer's problem
Let us
now assume
is
(2)
then to maximize u(x, y, y2) subject to (1) and
(2).
further that the utility fimction takes the following quasi-linear
form:
u(x, y, yi)
where
(j)
is
—
= ax
+
(|)(y)
+
y2,
an increasing and concave function. Substituting (1) into
this function,
we can
write the consumer's problem simply as follows;
Max
+
ax
subject to
To
From
solve
this, let
a
In other words, if
Y - px - y
px < R.
us
(2)
first
we
ignore the constraint and choose x to maximize
we have
the first-order condition
for foreign
+
(|)(y)
2
(jt.y)
- bx =
the following:
(3)
p.
could ignore the foreign exchange constraint, the South's demand
goods would be a linear function of the price of the foreign good.
referred to as the unconstrained
straight line aF.
utility.
Note
that (3)
demand curve, and
this is depicted in
can be written, alternatively,
x=^^.
Figure
(3) will be
1
by the
as:
(4)
.
.
Now to solve the
(2).
it
If the value
full
curve of the South
then the South's
is
demand
is
us take account of the constraint,
satisfies (2),
then x
=
(a
- p)/b.
If
x = R/p. Hence, the actual demand
given by:
. =
is
let
of x that solves the above equation (4)
fails to satisfy (2),
This
maximization problem,
rmn\^-J^A\
(5)
demonstrated by the thick line in Figure
[Figure
1
somewhere
1
here]
Let us assume that a Northern monopoly produces the good that the South
demands. The firm produces the good
and choose the price p
work with one such
oligopolistic firms
To
fix
at
which
sells to the South.
firm, our qualitative results
produced
some
it
at a constant
this
good
marginal cost
Though
is, if
.
a+c
monopoly
,
and X* =
.
analysis
a~c
.
2
This point
is illustrated
by point E*
2^7
in
we assumed
demand
that
n
for the North's
were no foreign exchange shortage
shows
and quantity sold by the Northern firm would be given by:
p* =
if
we
in the North.
there
constraining the South), then standard
faces no fixed cost
our formal model
would be unchanged
useful notation, check that // the South's
product were given by (3) (that
in
c,
Figure
1
in period
that the price charged
1
In order to focus on the interesting case,
we
shall
South's foreign exchange reserve R, though positive,
attained in period
Assumption
1
1
.
In other words,
are
making
that the
insufficient for this point
E*
to
be
the following assumption.
a'-c'
0<R<
:
we
is
from here on assume
4b
That
the
is,
the shortage of hard currency
monopoly
is
such that the Northern firm carmot fully capture
rent associated with the unconstrained
demand
curve.
We now incorporate international lending into our model, where we will consider
the following
Case
Case
I:
two
cases:
There
is
to the
South
II:
There
a non-profit 'international organization' that lends hard-currency credit
is
at a
subsidized interest
rate.
a profit-maximizing international
bank (based
in the
North) that gives
hard-currency credit to the South.
Before continuing with the formal analysis,
let
us explain our assumption
concerning the use of the limited foreign exchange by the South in period
onwards,
we
will
of hard currency
the
govenmient
assume
that the
in period
sets a
1.
1
From here
.
Southern government has a reserve currency of R units
How does the
quota for each of the
government use
m
(
this?
We will assume that
> 2) importers. That
is,
each importer
is
given the right to acquire foreign exchange up to this quota limit by giving up an
equivalent amount of soft currency. With this foreign exchange the importers buy goods
from the North which they then
sell to the
Southern consumers in period
1
.
While
a slew
of different methods for rationing out limited foreign exchange have been used by
different developing countries
and transition economies, the structure
that
we
are using
is
not unrealistic, and, in the case of, for instance, Pakistan and India, especially through the
seventies and eighties,
fits reality
We shall, for simplicity, assume that all
quite well.''
importers are treated identically, and so each importer has access to
currency.
p,
will
It
be assumed
and the interest
rate,
i,
R/m units of the
that the importers take the international price
hard
of the product,
as given and constitute a Bertrand oligopoly in the domestic
market.
It
will
be shown
later (in Section 4) that, for the
model works the same way as a model
in
purpose of our analysis, such a
which the Southern government gives
consumers direct access to a fixed amount of foreign exchange
is unrealistic, its
mathematical equivalence to the above more
demonstrated formally later in Section 4) implies that
assuming
that the
Southern government gives
amount of foreign exchange
the Southern
in order to
consumer under
this
Hence,
we
are
with the government
addition,
we
is
this
develop our model by
exactly what
1
.
The behavior of
we worked
out above and
available to the Southern
shall consider the possibility that the
The Southern consumer can
return
at
exchange balance of R units
consumer
in period
1
,
and, in
consumer can borrow additional hard
the interest rate,
i,
chosen by the
borrowed hard currency with
interest (if
any) in the second period, because the South's currency becomes convertible in period
Writing in the very early nineties on Pakistan, Baysan (1992,
bans and
restrictions,
be
realistic specification (to
in period
that this entire foreign
currency from the Northern lending institution
institution.
Though
.
(5).
now assuming
made
is
1
citizens direct access to a certain
its
buy foreign goods
assumption
which gave us the demand fimction,
we can
in period
p.
468) observed, "Distinct from import
value limits on individual licenses against cash for imports of machinery and
2.
.
11
We
shall,
throughout, assume, without loss of generality, that the market interest
rate for hard currency credit is zero
have direct access
the Northern
to the
Northern credit market, but the international organization and
bank have access
cost of lending
money
to the
borrowing country never
in reality
and there
is
The Southern consumer and government do not
.
to
So
it.
South
defaults.
is
to these latter agents the opportunity (interest)
zero.
Though
As described above, we assume
that the
default (or the threat of default)
is
important
a substantial literature that investigates this (for surveys see Sachs,
1984; Kletzer, 1988; and Eaton and Fernandez, 1995), to introduce default would be a
distraction, given the focus
The
of this paper.
analysis of Case
I is
straightforward. Let us suppose that the international
organization lends to the South at the opportunity cost interest, that
zero.
Once
is,
an interest rate of
the South has access to such credit, the foreign exchange constraint of
becomes immaterial. South's demand
for the product
is
R
given by equation (1) and the
equilibrium price and quantity are given by p* and x*, which are represented by point
in Figure
E*
1
Case
II is
Southern country
the interesting case, and
may be better off in
this case
depict the equilibrium that will arise in
Case
interaction
II
can be formalized
in
what
Case
two
we go on
to
show,
than under Case
later, is that
But
I.
the
we need to
first
II.
different ways. First,
between the bank and the firm occur
at the
we
same time
could assume that the
in period
and the firm, confronting the Southern demand as captured by equation
1
.
The bank
(5),
millwork have been (and still are being) maintained .... These ceilings
function as nontariff barriers
and serve as a nonprice rationing mechanism for the allocation of foreign exchange."
.
.
.
12
simultaneously announce, respectively, an interest rate and a price. In this sub-case the
relevant equilibrium notion
is
naturally the
Nash
equilibrium.
We characterize such a
Nash equilibrium below.
Secondly, and this
assuming
that the
may seem more
natural to some,
Northern bank has a first-mover advantage.
sub-case by assuming that period
bank announces the
1
and then
1
price.
These two stages could be thought of as two
1
.
This
is
formalize Case
by
II
We shall formalize this
can be thought of as broken up into two stages. In
Stage
the
we may
interest rate
in Stage 2 the firm
instants,
announces the
with Stage 2 following Stage
simply a construction to capture the realistic possibility that the
Bank has
a
first
mover advantage.
The
natural equilibrium notion in this sub-case
equilibrium.
is
that
of a sub-game perfect
We shall here fully describe such an equilibrium. An interesting finding is
that the paradoxical result
(whereby the South does better under lending from a
maximizing firm than from an international organization giving subsidized
remains valid in both these sub-cases. In other words,
we show below
that
profit-
credit)
our result
is
robust to the sequence of moves.
Since the central issue in the analysis of Case
between the firm and the bank
useful to begin
in period
1
II is
the strategic interaction
(either simultaneously or in sequence),
by deriving the main ingredients of our
it
is
analysis, namely, the reaction
functions (more precisely, as explained below, 'implicit reaction functions') of the firm
and the bank. Let us
start
with the firm. Consider
whatever the South buys from the North
has no foreign exchange endowment.
it
first
the case
where
R = 0,
that
is,
has to borrow money from the bank, since
for
it
13
[Figure 2
In Figure 2, aF
is
somewhere
the South 's unconstrained
Suppose the bank charges an
(1)).
the effective price to the Southern
curve
is
here]
interest rate
consumer
given by the line a'F where
implies that the firm's best response
Oa =
is
to
of i. Then
is (1
+
(1
+
i,
and plotting the mid-point
choose a price
it
is
the firm's 'implicit reaction function.''*
0, the firm's implicit reaction function
horizontal axis.
By
the effective
monopoly
demand
analysis
that is represented
by the
considering different interest
that represents the firm's best response for each
obtain the firm's best response curve. This
call
Hence
i)p.
firm charges a price of p,
if the
i)Oa'. Standard
midpoint of line segment a'H', shown by point E'.
rates,
demand curve (given by equation
The reason why we
we
We
represented by the broken line E*E'C.
The reader should
would be
call this
i,
also
a vertical line from
check
that, if c
E* down
an 'implicit' reaction function
is
were
to the
because,
unlike in a conventional reaction Sanction where the two variables chosen by the two
players are represented on the two axes, here the interest rate
represented on any axis, but
is
implicit in the effective
[Figure 3
Now
let
The mathematical
(1995).
is
demand
chosen by the bank,
is
not
curve.
somewhere here]
us bring in the fact that
charged by the bank
i,
R>
0, as
shown
in
Figure
such that the effective demand curve
is
3.
If the interest rate,
i,
a'F, then the actual
properties of the implicit reaction function are spelled out in Anant,
Basu and Mukherji
14
demand curve
(the
one which takes into account the
does not need to borrow hard currency)
and D. The firm's impHcit reaction
E*E'C curve
value of i, starting from
=
by point E'
i=0, and
rises E'
moves
The
0.
jump
occurs.
To
passes through point
is
jump
K in Figure 3.
the total cost
indifferent
To
i
is
point B,
is
B
South
where
E*K
is
a
is
represented by point E*
when
positive but sufficiently small. Then, as
to point B. Let us denote
Clearly, the firm
B
see this, gradually increase the
see that this will happen, suppose that
price that corresponds to point
same and
in Figure 2.
when
R units, the
to
southwest direction. But before E' reaches point
in the
the firm's best response point will
the
E*K' and
firm's best response
(see Figure 2)
up
given by the thick Hne, going through points
fiinction is
truncated segment of the
i
is
fact that
i
K (in Figure 3),
by K' the point where
such that the
is
i
line, a'F,
better off by choosing the
is strictly
rather than point K; since at both prices revenue
is
the
smaller at point B. Hence, there exists point K', where the firm
between choosing point K' and point B.
Now we turn to the bank's reaction function (which we will need for the Nash
equilibrium analysis, though not for the subgame perfect equilibrium sub-case). First
suppose that the firm has fixed a price,
p,
such that
—>
P
—
holds. In this case, the
b
South does not borrow hard currency because the consumer's demand given by the
unconstrained demand curve
(i.e.,
currency. Then, any value of i
is
p - a-bx)
feasible without
borrowing any hard
the bank's best response, because the
any profits from lending to the South for
Next suppose
is
that the firm
all i>0.
has fixed a price,
p,
such that
—<
p
condition means
that,
bank carmot make
—
holds. This
b
under the price, the consumer's demand given by the unconstrained
15
demand curve
is
not feasible without borrowing hard currency because the Southern
government has only
strictly
the
1
,
R
(> 0) units of hard currency in period
between the prices represented by point
bank can make a
which
is
B
and
in
Graphically, the price
Figure
3.
from lending hard currency
profit in period 2
Given such
to the
is
price,
South in period
given by
7!^b(0
[Figure 4
has fixed a price
at
=
somewhere
Graphically, the bank's profit
is
HP
^a-pil + i)'
represented by area
p=p' and the bank has chosen
i
so that the area
QRST is maximized.
bank chooses
i
such that point
R
in Figure
bank's best response
is
to
QRST in Figure 4, where the
represented by a'F. Given
i
p', the
R
here]
bank chooses
given
D
1.
p', the
The maximization implies
[Figure 5
We call
somewhere
it
that the
4 becomes the midpoint of QZ. Then, for any
choose
i
such that corresponding a'F line goes
through the midpoint of QZ. Plotting such midpoints for different values of p',
the broken line in Figure 5.
firm
we
obtain
the bank's 'implicit reaction function.'
here]
We are now ready to characterize the case where the bank and the firm move
simultaneously and to identify the Nash equilibria. Superimpose the firm's implicit
reaction function
(E*K'
in
Figure 3) here.
A Nash equilibrium is then depicted by the
point of intersection of the two reaction functions,
shown here by
point N, where the
16
equilibrium price
is
demand curve aF
call this the
.
given by
This
is
p
and the interest rate
is
the one implicit in the effective
an equilibrium in which a positive amount
is
borrowed.
We
N-equilibrium. Note that the N-equilibrium does not always exist because
the broken line does not necessarily intersect with E*K'.
Note also
that there exists
another Nash equilibrium, where the firm chooses the price that corresponds to point
and the bank chooses a very high
This
interest rate.
is
an equilibrium
in
B
which no lending
occurs.
The Paradox of Benevolence
2.
We now demonstrate that the paradox of benevolence can happen in the Nequilibrium.
The aggregate surplus earned by
Figure 6 as the area
call this, in brief,
the South
when
W'' where b
,
W"
,
somewhere
where the
the lender of credit
aggregate surplus
is
when the Northern
is for
is
shown
in
STQpa.
[Figure 6
Let us
the South in the N-equilibrium
tt
here]
is
a reminder that this represents the welfare of
a profit-maximizer. Let us denote South's
lender
benevolence. Our claim
is
benevolent (and charges no interest) by
is that
where
W''
> W".
there are parameters of the
model
17
Note
that,
the South's overall aggregate welfare
is
lower
say that the 'paradox of benevolence' occurs
To prove
this
we need
price of the Northern
examining Figure 6
good
it
is
is
in
Case
I
than in Case
inequality
if this
to first depict W''. Recall that
borrow from a benevolent lender (Case
Now, we
W^ > W"
under our specification of the South's consumer's utihty,
I,
Hence W**
clear that a priori
we
is
Hence,
we
will
is true.
when
the South can freely
above) equilibrium occurs
given by p*.
II.
implies that
By
the area of aE*p*.
cannot say which
is
E* and the
at point
larger W'' or
W
.
are able to state the central result of the paper.
Proposition
1:
For any parameter values that
satisfy
Assumption
c (>0) such that the model exhibits the following property for
The N-equilibrium
e
all c
and the paradox of benevolence occurs
exists
1,
there exists a value
[0,
c
]:
in that equilibrium.
[Proof] See Appendix.
To understand
producing the good,
c, is zero.
As we have
implicit reaction function is a vertical line
is
vertically
below E*
W
demand
(>0). If the vertical
already seen,
from E'
.
when
this
happens, the firm's
Hence, the N-equilibrium point, N,
(see Figure 5). In that case the area depicting
inside the area depicting
Continuity of the
where the marginal cost of
the result graphically, consider the case
,
which implies
that
we have
function implies that W''
<
W''
W
sits
< W" when
W^ holds
c=0.
for all small
segment of the reaction function of the firm
is
properly
enough
c
not long enough, an
N-
18
equilibrium will not exist.
reasoning and explains
To show
why
happen
that this will not
the formal proof
is
entails
some
long.
Just as the proposition establishes the kinds of value of the cost
is
likely to give rise to the
levels of foreign
paradox of benevolence,
instance,
it
is
so large that the point
R were equal
E*
horizontal axis represents
have computed the
The
when R =
c
e
[0,
value of c, denoted
must hold
c"""".
10, 20, or 40, respectively.
a
=
10,
is
easy to
very large (for
c"""",
0.4,
made
is
for the case
where a
1.
we have
c"''"'=
2.23, 6.06, or 3.00,
Namely, the Paradox of Benevolence occurs
b = 0.4 and
R = 20.
Note
for the Northern firm to sell a positive
we
such that the paradox occurs for
The computation
b=
space in which the
For each value of R
c.
0.4 or 0.5 and the results are displayed in Table
when
it
It is
likely to arise for countries with
axis represents
table tells that, for instance, with
6.06]
to zero or
in the (R, c)-space, in particular, a
non-negative values of c less than
= 10 and b =
paradox.
what
We conducted numerical simulations to
R and the vertical
maximum
interesting to inquire into
rise to the
may be more
'intermediate' foreign exchange reserves.
compute the zones of paradox
is
of production that
achievable with the existing foreign exchange
is
balance). This suggests that the paradox
all
it
exchange reserves are likely to give
verify that the paradox cannot arise if
intricate
that c
<
a (= 10 in these
amount of goods
for all
examples)
to the South.
The
numerical examples therefore seem to indicate that the Paradox of Benevolence occurs in
non-trivial ranges of parameter values.
19
Table
1.
Numerical examples for the Paradox of Benevolence
(The value of
when
c"''"
b = 0.4
R=
5
0.94
1.22
R=10
R=15
2.23
3.22
7.00
6.29
R = 20
R = 25
R = 30
R = 35
R = 40
R = 45
R = 50
R = 55
R = 60
R = 65
6.06
5.16
5.16
4.16
space. That
3.31
3.63
2.57
3.00
1.91
2.44
1.23
1.91
-
1.37
-
0.73
-
holding other parameter values fixed, the value of c™'*"
is,
when the value of R
relatively large.
property in
4.35
interesting to note the table exhibits an "inverted-U" shape in the (R, c)-
It is
all
Let us
moves
= 10).
b = 0.5
a
relatively small,
is
Although
of them,
now
after that
and
we have worked
it
and chooses
p.
where
From
R
out a number of examples and identified this
we have been unable
turn to the case
increasing in
R when the value of R is
decreasing in
is
is
the
to
prove that
bank moves
this is the general property.
first
and chooses
i;
and the firm
the firm's reaction function, described above and
derived mathematically in the appendix,
we know how p
will
depend on
i.
This
is
described by the fiinction p(i) in equation (A7) in the appendix.
Hence, using n(/)
to
denote the bank's profit-function in this two-stage game,
can see (by suitably modifying (A9)
n(/) =
Max
in the
appendix) that this will be as follows:
a-p{i){\ + i)
i\p{i)
-i?
,0
we
,
20
The sub-game
perfect equilibrium
is
now
easy to characterize: (i^ p^)
perfect equilibrium (henceforth simply 'an S-equilibrium
for all
i,
and p^ =
What
of this game
a
subgame
n(/') > n(/)
if
p(i^).
interesting is that the
is
")
is
paradox of benevolence occurs even
in this
two-
period game.
Proposition 2: Consider a two-stage
and the Northern firm next chooses
Assumption
Much
we
p.
Then
what we
=
0.
chooses
i
for any parameter values that satisfy
It starts
up
to
As
in the
fi-om
where
it
E*
in,
for instance Figure 3,
and
is
=
0, in Figiire 3,
=
easy to see using (A7). If c =
to touch the rectangular hyperbola,
E*K' would be
depicted in Figure
=
a/2,
3,
first
a vertical straight line
would
and
x = R/p, then
i
is
set
p
at the
low enough
n>n^,
and
p(i)
which
must be a
is
In addition, of
height of point B.
for the
=
demand curve
.
2(1
i)
consider
R/p. In other words,
K (which would now be vertically below E*).
course, for sufficiently high interest rate, the firm
implies p(i)(l +
1,
Hence,
represented by a vertical
touches the rectangular hyperbola, x
and K' would coincide with
is
proof of Proposition
1.
Graphically, the firm's reaction function p(i) takes the following
are claiming is that, if c
This
first
of the proof follows the same route as the proof of Proposition
the case where c
straight line
which the Northern Bank
paradox of benevolence occurs in that equilibrium.
give simply a sketch of the proof here.
simple form.
in
there exists a value c (> 0) such that for all c e [0, c] an S-equilibrium
1,
exists and the
game
But
this
+
a constant. Hence, the firm's reaction function as
vertical line:
For
all
i,
p(i) will
be such that the consumer
21
price p(i)(l
Assumption
+
i) is
1
the same.
impHes
It is
easy to verify that
i^
—t^-I and
=
p^
= 4bR
(note:
—t=-\ >0).
l4hR
Now since the firm's reaction function is line going down vertically from E*, the
S-equilibrium point
is
vertically
below E*.
It
follows, for the
analysis immediately after the statement of Proposition
the aggregate welfare of the South
lender,
who
is
when
also the first-mover.
argument extends
to values
4.
1,
same reason
that W''
< W'^^ where
W^ is
faced with a profit-maximizing international
The proof is concluded by showing
of c in the neighborhood of c =
Competition
as in the
Among Licensed
that this
0.
Importers
In Section 2, concerning the use of the limited foreign
exchange
the realistic assumption that, in the South, the government gives
we began with
some designated
importers the right to acquire hard currency from the central bank in order to import
goods
for domestic sale.
We then pointed out that, if these importers took the
international price, p, of the
sale price (that
is,
good and the
interest rate,
they played a Bertrand game),
purpose of our analysis. Given
this,
we
government allocated foreign exchange
designated importers. In this section
order to derive out results.
we
i,
as given, and chose the domestic
could ignore these importers for the
derived our result under the assumption that
directly to the
consumers rather than
we show that we can
to the
indeed ignore the importers in
22
As
before, the Southern
demand
for the Northern
x=
where
r is
good (subject
the
at a price, p,
to
have to borrow
wants
buy x
to
chosen by the Northern producer.
from a Northern bank
at
If they
now
given by:
m identical importers.
It is
is
assumed
that the
given access to
it
Southern
R/m
units of
want more foreign exchange they
an interest rate of i. Hence,
good from the North
units of this
is
having the requisite foreign exchange) from a Northern
by the Southern government.
this
1
.
importers take this price as given. Each of these importers
foreign exchange
in period
a-r
the price that the consumers have to pay. There are
They can buy
producer
good
has to incur a
if
total cost,
an importer
TC(x), given
by:
px,ifpx<—.
'"
TC{x) =
—+
i?
m
^,
{l
..
/?
,
+ i)p{x
mp
m
m importers have to choose a price at which
Now, each of these
the product to the Southern consumers. If
we may
(6)
R
),ifpx> —
.^
.
denote the strategy n-tuple of the
r^
it
offers to sell
denotes the price offered by importer
i,
then
m importers by
(ri,....,rm)
The
profit
earned by importer
Our aim
is
.
.,
r*)
>
then be denoted by
7:i(r*,
7t,(ri,
.
.
.,
rm).
Nash equilibrium (Bertrand equilibrium
in this
We will in particular be interested in the symmetric Nash
equilibrium. In other words,
.
may
to characterize the
case) of this game.
7:i(r*,
i
.
.
.,
n,
.
.
.,
we
define
r*),
r
for all
to
rj.
be an "equilibrium"
if,
for all
i
=
1
,
.
.
.
,
m,
23
Fortunately, to characterize such an equiHbrium
every importer charges the same price
If all importers, excepting importer
consumers respond as follows.
rj
>
to
i.
r,
all
who
fail
to
These are
fairly
If
buy from
consumers go
not need to fully
We will here make the following reasonable assumptions.
characterize the Ki function.
consumers
we do
i,
ri
i,
r,
then each importer faces a
charges
<
r,
r
and importer
importer
direct their
i
faces a
demand
to the importers other than
i.
i
If
demand of (a-r)/bm.
charges
ri
{^
demand equal
at price r to the
r),
then the
to (a-ri)/b. All
other importers. If
Only those with unmet demand turn
normal assumptions and one can find a formal statement of these in
Basu(1993).
Let us
now suppose
that the firm has fixed a price, p, such that
—<
—
Also suppose
that the
bank has fixed an
interest rate,
i,
such that
—<
that, if
—
holds.
b
P
This condition means
holds.
b
P
government allocated foreign exchange directly
to the
consumers, then the consumers' demand given by the unconstrained demand curve
feasible without
not
borrowing hard currency and so they borrow a positive amount of hard
currency from the bank. Under such p and
marginal cost functions (derived from (6))
=
+
to
show
r
then no one can do better by deviating.
that in this case r
(l+i)p, the profit earned
price, an importer
(l+i)p,
is
(1
i)p is
no one will buy
frorri
the horizontal
the thick line
is
summation of all importers'
shown
an equilibrium. That
To
by each importer
can only do worse.
i,
If,
is
is, if
see this note that
in
Figure
7.
It is
easy
each importer charges
when everybody charges
given by iR/mp. Clearly by undercutting
on the other hand, an importer charges
him. Hence, his profit will drop to zero.
r,
>
this
24
The
analysis in the previous paragraph indicates that, for any p and
the conditions described above, the profits of the firm and the
bank are
i
that satisfy
identical with or
without the designated importers. Also, consumers face the same marginal price and
demand
shown
the
same amount of the good
of p and
for other combinations
the strategic interaction
two
in the
i.
Since
A
cases.
we
similar equivalence can be
focus on the welfare consequences of
between the firm and the bank,
this
equivalence allows us to
ignore the importers in our analysis.
[Figure 7
5.
The model and
implications. First,
it
somewhere
here]
Policy Implications
the results described in this paper have important policy
cautions aid donor agencies not to presume that subsidized credit,
given to a Third World nation, necessarily benefits the recipient relative to the case in
which
credit is
first sight it
made
seems
available
by
a profit-maximizing
we have shown
market, the advantages of subsidized credit
sell
financial institution.
At
of subsidized credit cannot make the recipient
that the availability
nation worse off. However,
bank or
that,
may
depending on the structure of the import
flow into the hands of corporations that
goods to the recipient nations. In such a situation the donor agency has to think of
ways, other than subsidized
on aid-tying used
to
credit, for
reaching benefit to nations. The classical literature
be concerned with
this question.
What we have shown
in this paper.
25
however,
is
flow-back of benefit
that the
to the
North can occur even when aid
is
not tied,
but depending on the market structure of imports and the strategic position of the donor.
In trying to reach out to poor nations, most international organizations use the
method of lowering
interest rates.
indebted and poor nations, while
The IMF uses
at the
method
this
same time combining
for the
most highly
the generous loan terms
with 'conditionalities', which pertain to macroeconomic policies such as the need to keep
the fiscal deficit under control
us to
is
and money supply growth
the fact that such policies
may not be enough
benefits of cheap credit get frittered away.
main route through which
to plug the holes
The 'market
the immiserization occurs,
What our paper
in check.
structure'
by causing
through which the
of trade
all
alerts
may be
the
the benefits to flow
out to the international firms that export goods to the South. Hence, before lending at
concessional rates,
it
is
worth examining and advising recipient governments on the
channels and structure of trade and methods of releasing limited foreign exchange
reserves.
And, counter-intuitive though
developing country
is
this
of a certain kind and
may
this
sound,
if
the market structure facing a
cannot be changed, there
reconsidering the policy of lending to the country
at
may be
a case
concessional rates. This brings us to
the subject of policy from the Southern point of view.
The model suggests (though we have not
really
gone into
this) that there
may be
advantages to the South of giving the import rights to a single agent. This would
empower
the importers vis-a-vis the Northern manufacturer and
the Southern consumer. Secondly, the Southern government
more pro-active
in the foreign
quotas to different agents
may
may end up
may
benefiting
stand to gain by being
exchange market. Releasing the foreign exchange as
not be a good idea.
26
Let us take up the
first
point
In our
first.
because they compete against one another both
international credit market. If they could
power. However, collusive behavior
model the Southern importers do poorly
in the
product market and the
behave collusively, they could exercise market
is difficult to
sustain
on
its
own - a point made
persuasively in the context of international borrowing by governments by Fernandez and
Glazer (1990). However, in our model since the borrowers are agencies within a nation,
the government can enable
them
to exercise
market power. The system of 'canalized'
imports used by some nations, for instance, India, could have potentially played this role.
In practice, canalized imports have
been
inefficient
and bureaucratically cumbersome.
Its
potential has not been understood, let alone realized.
Let us
now
turn to the second subject of how to ration the limited foreign
exchange reserve. The method analyzed
in this paper
exchange
-
is
rationed out to the importers
is
- namely, one where
not the only one.
The government could
(and they often do) place quantity restrictions on the amount each importer
The
analysis of this
is
the foreign
may
import.
not trivial since, while each importer will of course take the
quantity ration as given, the government should be modeled as choosing that quantity
ration,
given which the
government has
(or
total
import value equals the amount of foreign exchange the
wants to
rationing, for instance
one
in
release).
There can be other more sophisticated kinds of
which the amount of foreign exchange released
to
an
importer could depend on the terms of trade. Each such ration will change the market
outcome and the
total benefit
benevolence. In the
fiiture
it
generated to the South and
will
may even
avert the paradox of
be worth examining formally the welfare
effects
of
27
different systems
to
of releasing limited foreign exchange and for the Southern government
choose a system consciously to maximize the welfare of its consumers.
As
import
a final point, if the Southern
tariffs as a tool for
government behaves
maximizing welfare,
strategically,
as, for instance, in the
it
could use
model of Brander
and Spencer, 1984 (Anant, Basu and Mukherji, 1995, consider similar interventions by
govenmient, though in the context of an indigenous industry). The nature of the Northern
lending institution (for-profit or not-for-profit) would affect the strategic environment for
the Southern government,
which
in turn
would
alter the
optimal tariff policy and
its
welfare consequences. The analysis of such strategic use of tariff in our framework will
entail
expanding the model
to a three-player
current focus of the paper. But this
game and
will take us to issues
would be an exercise worth pursuing
beyond
the
in the ftjture.
28
Appendix
Proof of Proposition
1:
We first analyze the firm's best response given
First consider
i
i
(>0) chosen by the bank.
that satisfies (Al).
,,^!z4^.
(Al)
4bR
Under (Al),
the South does not
Northern firm. To see
this,
borrow any hard currency for any p chosen by the
note that (Al)
is
equivalent to
'
/?
>
—
— holds
for
b
all p.'
Given such
i,
the firm chooses
p such
currency to purchase the good; namely
Any
p=
(p, i)
=p
such that p=p'^ and
R units of hard
chooses p such that p[(a-p)A)]=R holds. Hence,
.
>
/
South spends
by (A2).
the firm's best response is given
(A2)
it
that the
a
is
Nash equihbrium.
Graphically, in this
4bR
Nash equilibrium
the
bank chooses high enough
twice. In this equilibrium
firm's profit
(A3)
is
(we
i
call
it
B-equilibrium), the bank's profit
given by (A3).
ip'-c)(a-p'')^^s
Next consider
i<
i
that satisfies (A4).
a^-4bR
.
4bR
in Figure 3
and
so that a'F does not intersect the rectangular hyperbola
b
/A^^
(A4)
B
the firm chooses the price that corresponds to point
.
is
zero and the
29
Consider the monopolist
the price given
who
faces the
by (A5) and the quantity demanded
a+
(1
+ i)c
2(1
x=
<3
+
- (1 + i)c
is
p=(a-bx)/(l+i).
It
charges
given by (A6).
=p
(A5)
(A6)
demand curve given by
_
=x
2b
Note
that the Northern firm can earn
chosen by the bank. Then, given
Hence
i,
n by choosing p=p^ regardless the value of i
the firm chooses
the Northern firm's reaction function
a+
(A7)
P(i)
=
{\
2(1
+ i)c
^
-p
if
is
p
if
and only
if ?r
= ( ^ -c) jc
>7r^
given by (A7).
^
B
n>n
+
a-v4a^ -4bR
=p
other-wise
Next we analyze the bank's best response given
that the firm
chooses p that
satisfies (A8).
(A8)
p[(a-p)/b]>R
Given such
p=a-bx)
is
demand given by
that,
demand schedule (which
The bank chooses
a-p{\ + i)
that
given (A8), the bank can choose i>0 such that n(i)>0. The standard
i{p)
=
pa-p^-bR
2p'
is
is
maximizes
R
maximization exercise then implies that the bank's best response
(A 10)
i
by (A9).
n{i)^i\p
(A9)
the unconstrained
not feasible unless the bank sets i=0.
profit given
Note
price, the
given by (A 10).
its
30
Now we characterize a Nash
positive
amount of hard currency
to the South. Insert
(A 10)
into (A5),
and we obtain
f(p)=2p^-cp^-(2bR+ac)p+bcR=0.
(All)
Note
equilibrium in which the bank lends a strictly
that
root that
f(0)=bcR>0 and f(c)=c^(c-a)-bcR<0. This means
is strictly
greater than
c.
that
We denote the root by p*.
(All) has exactly one
If there exists a
Nash
equilibrium in which the bank lends a strictly positive amount of hard currency to the
South, such equilibrium
is
characterized by (p,
game
if
and only
equilibrium of the
if (p, i)
=
=
i)
Nash
(p*, i(p*)). This constitutes a
(p*, i(p*)) satisfies
n >Tt^ and
(A8); or
equivalently if (AI2) and (AI3) hold.
[fl-(l
(A12)
+ /(p*))cf
4^7(1
(A 13)
Note
^^ c{a-4a'-^hR)
+ /(p*))
Ih
p*[(a-p*)^]>R
that
p*
is
continuous in
c,
which implies
Let c=0. Then f(p)=2p^-2bRp, and so
find that,
when
Note
Assumption
that
continuous in
hold for
all
c=0, (A12)
c.
is
that i(p*) is also continuous in c.
^*=4hR and
equivalent to di>l-4hR and (A13)
implies a>2v^i? holds
I
i{p*)
when
is
= "^^^
.
We
equivalent to a>2-slbR
c=0, and that both p* and i(p*) are
This implies that there exists c* (>0) such that both (A 12) and (A 1 3)
cs[0,c*].
Next,
we assume
ce[0, c*], and
Nash equilibrium represented by
let
W" denote South's aggregate welfare
(p*, i(p*)).
As
STQ pa in
Figure
6,
in the
stated in the text, the social welfare
A
represented by the area
(A14)
^^^
which
W''=(l/2)[a-(l+i(p*))p*]x*+i(p*)R,
is
given by (A 14).
is
.
31
where x*s
^
(\
+ iip*))p*
when
c=0,
we have (A 15).
b
2b
Sb
where
strict
X* are
all
inequality holds because
continuous in
c.
Sb
a>2^bR by Assumption
1
.
Note
that p*, i(p*)
and
This implies that there exists c**>0 such that W^>W'' holds
for all ce[0, c**]. Finally, let c
=Min
[c*, c**],
and
we
obtain the desired result.
D
32
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34
Figure
1
Figure 2
35
P^
i.
X=
a
r/p
a'
gVs
Figure 3
\
E*
^^^=i^^^
c
H'"^
^
Figure 4
36
Figure 5
Figure 6
37
Figure 7
(l+i)p.
2003
Date Due
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