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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
Revised: January 26, 2005
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January 26, 2005
INTERNATIONAL CREDIT AND WELFARE:
A Paradoxical Theorem and its Policy Implications
Hodaka Morita
Kaushik Basu
Department of Economics
School of Economics
Cornell University
The University of New South Wales
Ithaca,
NY
14853,
USA
Sydney,
E-mail: kb40@comell.edu
NSW 2052, Australia
E-mail; H.Morita(a),unsw.edu.au
Abstract
This paper considers 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. We
develop a simple model of strategic interaction between lending institutions and finns,
and show that the availability of international credit at concessionary rates can leave the
borrowing nation worse off than if it had to borrow money at higher market rates. This
'paradox of benevolence' is then used to motivate a discussion of policies pertaining to
international lending and the Southern government's method of rationing out foreign
exchange to the importers.
Keywords: Bank-firm
JEL
classification
interaction, foreign aid, international credit, welfare comparison.
numbers: LIO, F30, OlO.
Acknowledgements:
We are
grateful to Abhijit Banerjee, Jonathan Eaton,
Fernandez, Arvind Panagariya, Priya Ranjan, Debraj Ray, Henry
participants of a conference at
presented.
Wan
Raquel
and the
the University of California, Irvine, where the paper was
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
The aim
or in the coffers of large corporations that sell goods to the developing country.'
of this paper
is
claim to
to subject this
carefiil theoretical scrutiny.
while this hypothesis need not always be
under which
sight
it
it is
seems
valid.
This
is
true, there
interesting because of
that the availability of credit (or,
better terms) caimot
make
do
more
the recipient, whether
it
What we
(by, for instance, burning
is that,
exist parametric configurations
its
paradoxical nature. At
first
generally, availability of credit at
be an individual or a nation, worse off
because the recipient has the option not to take the credit or to pay a higher
what the donor demands
find
interest than
money). However, such simple logic
runs into difficulty, especially 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 credit
leave the recipient worse
may
In particular, a poor developing country that is currently
off.
borrowing money from a profit-maximizing international bank or financial
may become worse
off if
some 'benevolent' organization
maximizing bank, and begins
Since public foreign lending
market
actually
to lend
is
institution
steps in, in place of the profit-
hard currency at zero or a subsidized interest
usually motivated by altruism and the need to
failures (Eaton, 1989, p. 1308)
it
seems quite surprising
fill
rate.
in for
to find that there are
For works that either defend this proposition or debate it, see Winkler (1929), Hyson and Strout (1968),
Bhagwati (1970), Gwyne (1983), Taylor (1985), Darity and Horn (1988), Basu (1991), and Deshpande
'
(1999).
where the recipient nation does better when
situations
it
gets
its
foreign capital from
private sources.
To
see the logic, note that if a poor country has to
maximizing lender
at
an interest
(assuming the exchange
i
and pay a price p
rate is 1) the effective price
to a
and the manufacturer controlling
sets the interest rate equal to zero,
p.
Now
which reduces the
raising
this price rise results in a welfare loss, since a part
its
own
foreign exchange.
On
is (1
manner with
+
i)p.
Here the
the lender controlling
suppose that a 'benevolent' lender steps
The manufacturer takes advantage of this by
by
profit-
manufacturer for the good, then
on the margin
lender and the manufacturer compete in an interesting
i
borrow money from a
effective price
its
from
price from p to p'.
(1
+
is
and
i)p to p.
On one
of the country's purchase
in
hand,
financed
the other hand, for the other part of the purchase that
financed by the lender, the country
is still
the effective price p' turns out to be
still
is
benefited from the benevolent lending because
lower than
former disadvantage of the benevolent lending
is
(1
+
i)p.
We
demonsfrate that the
greater than the latter advantage of it
under a range of parameterization conditions.
In brief, this paper proposes a
sti^ategic interaction
between lending
possibility of paradoxical reactions
process
it
draws attention
to
paying particular attention
new
game-theoretic framework for analyzing the
institutions
(which
we
call the
how we may want
to the
market
and producers, and demonsfrates the
'paradox of benevolence'). In the
to reorganize international lending,
stiTJcture that the recipient
as to ensure that the benefits reach their intended target.
country confronts, so
2.
In this section
theoretical
framework
though the
latter is
One
own
we
is
present a
is
number of real- world contexts
to
which our
applicable, and explore the policy implications of our analysis,
picked up once again in Section
country lending
exports
The Factual Context
money
not unusual at
all.
to
6.
another or giving aid with an eye on enhancing
Many
industrialized countries give loans to developing
countries with the explicit requirement that the latter then use these to
former (Eaton, 1989; Fleisig and
Hill, 1984). Virtually all
provisions for providing export credit. This
for those nations to
buy goods from
is
This
is
buy goods from the
OECD countries have special
money given
to other nations specifically
the donor nation. Moreover, importantly, a lot of this
credit is given at concessionary rates, and, in particular, at
rates.
its
lower than market interest
done, ostensibly, to help the recipient nations. Sweden, for instance, has the
Swedish Export Credit Corporation or
AB
Svensk Exportkredit (SEK).
Tlris
was
established in 1962 "for the purpose of financing exports of Swedish capital goods and
services on commercial terms"
(OECD, 2001 Sweden
,
p. 3).
Up
to
1978
SEK used to
grant credit on strictly commercial terms. Since then there has been a program of
subsidized lending. Subsidies are funded from Sweden's Development Aid Budget.
OECD (2001,
Sweden
exports", though this
p. 10) notes,
is
"Concessionary credits are mainly tied to Swedish
not necessarily
In U.S.A., the Trade and
As
so.
Development Agency (TDA), formerly known
Trade and Development Program (TDP), has two objectives
—
as the
to give subsidized credit to
help developing and middle-income countries and to promote the export of goods and
services to those countries. In the
US
tied aid has legal authorization
because the Trade
and Development Act, 1983,
the
Eximbank and USAID
to
in particular,
its
sections 644 and 645, explicitly authorize
provide tied aid and credit to other nations.
These are just two among many examples found
to believe that the subsidized international credit sector,
and help the recipient country
is
substantial.
As
Fleisig
in
OECD (2001).
which aims
and
to
There
is
reason
promote export
Hill (1984, pp. 322-3) noted,
"Outstanding direct subsidized and export credits of the major lending countries (Canada,
Italy,
Japan, the United
Kingdom and
the United States)
amounted
end of 1978. These lenders offered substantial subsidies, charging
7
and 8%,
at the
Under
same time
that private lenders
$55 billion
interest rates
charged between 5 and
1
at the
between
5%."
the requirement that the export credit should be used to import goods
the donor nation, the loan-recipient countiies
limited
to
number of potential
sellers.
That
requirement could end up creating or
is,
forced to choose a seller from a
the provision of export credit with such a
at least bolstering the sellers'
paradoxical result of our model suggests that
been better off if they were exposed
may be
from
some of these
to the private credit
market power. The
recipient countries
market with
its
may have
non-
concessionary lending.
There are accounts galore of countries that have received subsidized international
credit but
have adamantly remained basket cases. There are a number of reasons for
The money may have been
may have been
dissipated in consumption and not invested diligently; there
coiTuption and leakage at the level of the government. But, in addition,
our model suggests that there
beneficiaries
this.
may
may be
another previously- unexplored reason
not have done well. This
is
to
why
the
do with an unholy alliance between
subsidized credit and the market structure of firms and banks that confront die borrowing
country.
One
The money may have leaked out
implication of our model
concessionary
rate, it
is that,
to international
when an
producers with market power.
export credit
is
offered to a country at a
should be ensured that the recipient country uses the credit to
import goods from competitive markets.
Our model
also yields important implications for the organization of international
lending by multilateral organizations, such as the World
Bank and
subsidized credit. The IMF, for instance, provides financing to
under different types of credit anangements
at
("facilities").
its
the
IMF,
member
that give
countries
These include regular
facilities
market-related interest rates, and a concessionary facility for low-income countries
(The Poverty Reduction and Growth Facility (PRGF)).
three-year period, with repayments over 5.5
See
IMF
-
PRGF
arrangements cover a
10 years at an interest rate of 0.5 percent.^
(2001a) for further details on types of fiind arrangements offered by the IMF.
A number of IMF-supported programs (in particular, practically all concessionary
financing arrangements) have included a variety of structural conditionalities.
Concerning trade-related conditionality, the
measured by the trade restrictiveness index
IMF
that
often requires trade liberalization
combines the average
protection as well as the coverage of non-tariff barriers (IMF, 2001b).
indicates that the
IMF
level of tariff
Our model
should also keep an eye on the structure of the markets from which
the borrower countries import goods. In particular, if a borrower country imports goods
from industries with substantial market power,
^
PRGF was
Facility
established in 1999.
(SAF) and the Enhanced
it
The predecessors of the
Structural
may be
better off by having to
PRGF had been
Adjustment Facility (ESAF).
borrow
the Structural Adjustment
from a non-concessionary
investigation
is
facility rather
than a concessionary
facility,
needed regarding the type of lending arrangement
The model
also highlights the crucial role of the
limited foreign exchange
is
that
and so careful
is
suitable.
mechanism through which the
released to the importers in the borrower country
borrower government (or Cenfral Bank). The paper suggests
the
that the rules for allocating
by the government can make
the limited foreign reserves followed
by
a crucial difference in
determining what effect international credit or aid has on the well-being of the recipient
Hence
nation.
the model, despite
its
use of a rather stylized framework, depicts
theoretically the general idea explored empirically
by Bumside and Dollar (2000) on how
the nature of governance in the borrowing nation can critically determine whether aid (or
subsidized international lending) will
As
a final point,
we
work
to
its
advantage or
not.'*
discuss an application of our theoretical framework to infra-
countiy rural credit markets. In rural regions of developing countries, peasants often face
short-term
money
shortage in the pre-harvest season. Hence, borrowing
is
widespread
in
such times with repayment occurring after the harvest when the peasant regains
liquidity.
According
Bardhan,
to a large-scale survey
of confractual relationships
1984, Chapter 9, for details), landlords often lend
where
There
the loans can be for
is
openness
now
a lot of evidence
in general leads to the
many
different purposes
to their
own
—consumption
share tenants,
to tide
over the lean
from cross-country studies on how trade liberahzation and greater
growth of income
1995; Frankel and Romer, 1999).
more competitive
money
in rural India (see
What we show
trade environment as one
concessionary facility offered by the IMF.
may
(see, for instance,
is that, if
Ben-David, 1993; Sachs and Warner,
the trade liberalization and openness leads to a
expect, then this
may
also increase the efficacy of the
season or production purpose loans. Interestingly, Bardhan reports that these loans can
often be without interest. If such a peasant faces a monopolistic product market from
which he buys
the
goods that he needs, then our theoretical framework suggests
paradoxical result can occur.^ That
exposed
to a profit-maximizing
it
is
often
such a peasant could be better off if he were
money
government subsidized
In this context,
that
is,
made
credit to
industrialized country
poor peasants
may
not be the panacea
The Model
a developing country
- henceforth North. These
- henceforth South, and an
countries have their
for all inter-country trade and exchange the only acceptable currency
currency. This
is
lender.
.
3.
is
money
lender rather than to a 'benevolent'
out to be.
In this model there
that the
the 'hard' cuiTency.
We
own
is
currencies but
the North's
shall refer to the South's currency as the 'soft'
currency.
The South,
that if
it
to
it
in
our model, has a shortage of 'hard currency'. This
could buy more hard currency
buy more foreign goods. The
suggests
some
rigidity in the
without loss of generality,
assumption
"
is to
See also Collier
It is
(1
(
1
make
the
fact
exchange
we
treat
model
it
going exchange rate
at the
it
so in the sense
is
would do
so and use
of a country facing a shortage of hard currency
rate.
We treat the exchange rate as
as fixed at
tractable,
we
1
.
fixed and,
Although one reason for making
also feel that this
is
this
not as strong an
997) and Hansen and Tarp (2001 ).
plausible that poor peasants often buy goods from sellers with substantial market power. Bardhan
984) argues that highly personalized
ties
between transacting agents
that are typically
observed in
isolated rural villages often result in monopolistic power. See Bhaduri (1983) for a similar
regarding 'personalized rural market'.
argument
assumption as
may
appear
The
at first sight.
fact that
many
Third World nations do face
a shortage of hard cuiTency, suggests that exchange rates are at least partially rigid in
reality.
We
relations
suspect that there are innate factors in the structure of international economic
which cause
governments go for a
this.
How
free float
else
can one explain why, even
and allow the exchange
rate to
after
developing country
be market driven,
shortages of hard currency persist?
Another assumption
in this
paper concerns the modeling of the developing
We treat the government not as a
country government.
strategic agent,
nimbly
maximizing some payoff, but as a somewhat mechanical bureaucracy which has some
rigid rules, to
to
which
it
adheres. In particular,
which the government
(or the Central
balance; and they are given the right to
One reason why we
model has a
surfeit
treat the
licensed importers in the South,
its
limited foreign exchange
buy goods abroad and
government as not a
sell
strategic agent
we
them
is
in the South.
for tractability; the
also believe that this description
is
of many developing and transition economies. For instance,
the case of Pakistan and India,
it fits
reality quite well especially
in
through the seventies
eighties.*
We
shall in this
paper focus on one good, which the South likes to consume but
does not produce. The good
the
Bank) allocates
of strategic agents. However,
fairly realistic in the case
and
we model
good (may be
in the
is
in fact
produced by a firm based
North but also)
in the
in the
it
North, which sells
South through the licensed importers. The
Writing in the very early nineties on Pakistan, Baysan (1992,
p.
468) observed, "Distinct from import
bans and restrictions, value limits on individual licenses against cash for imports of machinery and
mill work 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."
...
Northern firm produces the good
chooses the price p
at
which
it
constant marginal cost
at a
Though
sells to the South.
c,
faces
no fixed
cost,
our formal model
in
and
we work
with one such firm, our qualitative results would be unchanged under n oligopolistic
firms.
On
:
who
consumer,
hard currency
demand
demand
the
is
side
we assume,
without loss of generality, that the South has one
a price taker. Imagine
at the
going exchange
fiinction for the
first that
rate. In
good sold by
consumer has
the
such a case
let
fi:ee
access to the
the consumer's inverse
the North be given by:
p = a-bx,
where
will
a
>
c,
b>
0,
and p
is
(1)
the price of the product and x the
amount demanded. This
be called the unconstrained demand cun>e. Without a shortage
in the absence
of licensed importers
(that
is,
assuming
that the
in hard
cunency and
consumers buy
directly
from the Northern producers), standard monopoly analysis shows the equilibrium price
and quantity
to be:
a+c
.
p =
,
;
.
and x
Figure
1
by
-c
a
.
2b
2
Tliis point is illustrated in
=
the point E*.
Note
currency needed to buy the equilibrium amount of the good
that the total
is
amount of hard
given hy p*x''
a' -c'
Ah
We
shall
from here on consider the case
reserve R, though positive,
we
are
making
Assumption
1:
is
in
which the South 's foreign exchange
insufficient for this point
the following assumpfion.
Q<R<
a
2
—c
Ab
2-'
E*
to
be attained. In other words,
10
That
the
the shortage
is,
monopoly
It is
of hard currency
is
such that the Northern firm cannot fully capture
demand
rent associated with the unconstrained
being assumed here
that,
what the South suffers from
insolvency but illiquidity. In other words,
exchange in the
The simplest way
future.
its
not a problem of
is
expects to have adequate access to foreign
it
make
to
South's currency becomes convertible in the
constrained by
curve.
this
So
fixture.
foreign exchange reserves.
formal
We will
is
to
suppose that the
in the future its
assume
demand
that our
model
the
m (> 2) importers.
exchange up
this foreign
to this
We will
That
is,
a reserve
assume
of R units of hard currency.
that the
each importer
is
government
sets a
as given
It
sell to
will be
the Southern consumers.
assumed
and constitute
It
will
model works
a
be shown
the
does
quota for each of
quota limit by giving up an equivalent amount of soft currency. With
We
to
buy goods from
shall, for simplicity,
importers are treated identically, and so each importer has access to
currency.
How
given the right to acquire foreign
exchange the importers use the hard currency
which they then
this
it is
studies.
So the Southern government has
the government use this?
not
that this foreign-exchange
constrained position lasts for one period (which can of course be very long) and
one period
is
R/m
the North
assume
that all
units of the hard
that the importers take the international price of the product
Bertrand oligopoly in the domestic market.
later in Section 5 that, for the
same way
as an alternative
gives consumers direct access to a fixed
mathematical equivalence,
in
model
in
puipose of our analysis, such a
which the Southern government
amount of foreign exchange. Given
this
what follows we proceed our analysis by supposing
Southern government announces that the consumer can acquire up to
R units
that the
of hard
11
currency. In other words, the
amount of foreign good,
x, that the
consumer buys must
satisfy
x<R/p
Keeping
in
constraint)
demand
This
is
mind
is
that (1) implies that the
given by x
=
(a-p)/b,
function of the South
is
demand
and combining
function (with no foreign exchange
this
with (2)
we
see that the actual
given by:
demonstrated by the thick
line in
[Figure
We now
(2)
1
Figure l/
somewhere here]
incorporate international lending into our model;
we
will consider the
following two cases:
Case
Case
I:
There
is
to the
South
II:
There
a non-profit 'international organization' that lends hard currency credit
is
subsidized interest
at a
rate.
a profit-maximizing international
bank (based
in the
North) that gives
hard-currency credit to the South.
We
shall,
throughout, assume, without loss of generality, that the interest rate
prevailing in the North
If
we were
have
consumer
is
zero.
The Southern consumer and government do not have
thinking of this as an mtra-country, credit market problem,
demand curve
maybe because
a 'true'
liquid cash,
is
(that is, in the
we
could think of consumers
absence of any liquidity problems) given by
(1
)
this is the pre-harvest, lean season. If the liquid cash available
given by R, then his effective
demand
function for the good in questions
is
but have
with the
given by
who
little
(3).
12
direct access to the Northern credit market, but the international organization
Northern bank have access
of lending money
to the
to
So
it.
South
is
to these latter agents the opportunity (interest) cost
Given our focus on
zero.
insolvency) problems faced by the South,
The
analysis of Case
I is
we assume
illiquidity (rather than
that the
South never defaults.
straightforward. Let us suppose that the international
organization lends to the South at the oppoitunity cost interest, that
zero.
Once South has access
to
and the
such
credit, the foreign
becomes immaterial. South's demand
for the
product
an
is,
interest rate
of
exchange constraint of R
is
given by equation (1) and the
equilibrium price and quantity are given by p* and x*, which are represented by point
in Figure
1
Case
II is
Southern country
the interesting case, and
may be better
what we go on
to
show,
off in this case than under Case
depict the equilibrium that will arise in Case
I.
later, is that the
But
first
we need
II is
the strategic interaction
between the firm and the bank, we derive the reaction functions (more precisely
reaction functions') of the firm and the
us start with the firm. Consider
buys from the North
it
has to
first
first
is
where
R = 0,
that
is,
for
'implicit
equilibria.
Let
whatever the South
borrow money from the bank.
[Figure 2
In Figure 2, aF
bank and then characterize Nash
the case
to
II.
Since the central issue in the analysis of Case
(1)).
E*
somewhere
the South's unconstrained
Suppose the bank charges an
interest rate
here]
demand cun'e
of i. Then
if the
(given by equation
firm charges a price of p,
13
the effective price to the Southern
curve
is
consumer
Oa =
given by the Hne a'F where
implies that the firm's best response
to
is
+
(1
it
By
E'.
demand
the effective
Standard monopoly analysis
choose a price that
is
represented by the
considering different interest
and plotting the mid-point that represents the firm's best response for each
i,
obtain the firm's best response curve. This
call
Hence
i)p.
i)Oa'.
midpoint of line segment a'H', shown by point
rates,
+
is (1
is
the firm's 'implicit reaction function.'^
0, the firm's implicit reaction
horizontal axis.
function
The reason why we
represented by the broken line E*E'C.
The reader should
would be a
vertical line
also check that, if c
from E* down
an 'implicit' reaction function
call this
i,
is
we
We
were
to the
because,
unlike in a conventional reaction function where the two variables chosen by the tvvo
players are represented on the two axis, here the interest rate
represented on any axis, but
is
implicit in the effective
somewhere
[Figure 3
Now
let
charged by the bank
demand curve
(the
does not need
to
The fmn's
is
one which takes
borrow money)
'
is
into
i
=
The mathematical
0.
is
To
The firm's best response
is
not
curve.
shown
in Figure 3. If the interest rate,
is
line,
i,
a'F, then the actual
account the fact that up
E*K' and
in Figure 2.
chosen by the bank,
here]
given by the thick
implicit reaction function
from
0, as
demand
such that the effective demand curve
segment of the E*E'C curve
starting
R>
us bring in the fact that
i,
to
R units,
the South
going through points
point B, where
E*K
is
B and
D.
a truncated
see this, gradually increase the value of i,
is
represented by point
properties of this function are spelled out in Anant,
E* when
i=0,
Basu and Mukherji (1995).
and by
•
14
.
point E' (see Figure 2)
in the
i
positive but sufficiently small. Then, as
is
southwest direction. But before E' reaches point
response point will
To
when
jump
to point B.
3
Clearly, the firm
.
B
corresponds to point
the total cost
indifferent
is
is strictly
i
is
such that the
line, a'F,
jump
passes through point
rather than point K; since at both prices revenue
is
the
same and
smaller at point B. Hence, there exists point K', where the firm
is
between choosing point K' and point B.
a price, p, such that
—>
suppose that the firm has fixed
holds. In this case, the South does not
currency because the consumer's
is
First
borrow hard
b
P
feasible without
demand given by
the unconstrained
demand curve
borrowing any hard currency. Then, any value of i
bank's best response, because the bank cannot make any profits fiom lending
South, for
occurs.
better off by choosing the price that
Now we turn to the bank's reaction function.
p = a-bx)
3), the firm's best
Let us denote by K' the point where the
see that this will happen, suppose that
K in Figure
K (in Figure
moves
rises E'
i
all
i
>
is
the
to the
0.
Next suppose
that the firm has fixed a price, p, such that
—<
p
—
holds. This
b
condition means
that,
demand curve
not feasible without borrowing hard currency because the Southern
is
(i.e.,
government has only
under the price, the consumer's demand given by the unconstrained
R
(> 0) units of hard currency. Graphically, the price
between the prices represented by point
B
and
can make a profit from lending hard currency
D
in Figure 3.
to the South,
Given such
which
is
is stiictly
price, the
given by
bank
15
somewhere
[Figure 4
Graphically, the bank's profit
has fixed a price
at
is
represented by area
p=p' and the bank has chosen
bank chooses
i
so that the area
QRST is
bank chooses
i
such that point
T in
given
p', the
here]
bank's best response
i
QRST
in
Figure 4, where the firm
represented by a'F. Given
p', the
maximized. The maximization implies that the
Figure 4 becomes the midpoint of QZ. Then, for any
is
choose
to
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.
We call
it
are
now
somewhere
price
is
given by
a'F. Tliis
is
here]
ready to identify Nash equilibria. Superimpose the firm's implicit
reaction function (E*K' in Figure 3) here.
intersection of the
obtain
the bank's 'implicit reaction fiinction.'
[Figure 5
We
we
A
Nash equilibrium
is
depicted by the point of
two reaction functions, shown here by point N, where the equilibrium
p and
the interest rate
is
the one implicit in the effective
an equilibrium in which a positive amount
is
borrowed.
demand curve
We call
this the
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
chooses a very high interest
rate.
This
is
an equilibrium
in
B
and the bank
which no lending occurs.
16
4.
The Paradox
of Benevolence
We now demonstrate that the paradox of benevolence
The aggregate welfare earned by
equilibrium.
Figure 6 as the area
call this, in brief,
W"
,
b
is
when
Our claim
for benevolence.
We will say that the
borrow from
a
this
shown
is
in
is
ti
a reminder that this
we need
good
it is
is
is
the welfare of the
a profit-maximizer. Let us denote South's aggregate
is
benevolent (and charges no
is that
interest)
there are parameters of the
to first depict
benevolent lender (Case
examining Figure 6
N-
here]
'paradox of benevolence' occurs
price of the Northern
Now, we
is
the Northern lender
To prove
the South in the N-equilibrium
somewhere
where the
South when the lender of credit
welfare
in the
STQpa.
[Figure 6
Let us
can happen
I,
W
.
clear that a priori
where
if this inequality is true.
Recall that
Hence W''
we cannot
,
model where
when
the South can freely
above) equilibrium occurs
given by p*.
by W''
is
at point
the area of aE*p*.
say which
is
E* and the
By
larger W'' or
W
"
are able to state the central result of the paper.
Proposition (The Paradox of Benevolence): For any parameter values that satisfy
Assumption
fixed, the
1
,
there exists a value c (>0) such that, holding all parameter values except c
model exhibits the following property
for all c
e
[0,
c
]:
17
The N-equilibrium
exists
and the paradox of benevolence occurs
in that equilibrium.
[Proof] See Appendix.
To understand
profit
the logic behind the result,
maximizing behavior
firm's marginal revenue
Case
in
when
Case
it
and Case
I
sells
let
us compare the Northern firm's
Let MR(p, x) denote the Northern
II.
x units of the good
to the
South
at the price
the international organization lends to the South at the interest rate
I,
Northern firm
sells
becomes equal
x* units of the good
to the
marginal cost,
at the price
maximizing international bank charges
>
i
0,
and the
of p* so that the marginal revenue
MR(p*, x*) =
i.e,
=
i
of p. In
In
c.
Case
II,
the profit-
Given the shortage of hard currency
0.
in the
South, the positive interest rate reduces the South's willingness of pay, which in turn
reduces the Northern producer's marginal revenue. In order to
the Northern producer can
[1/(1
+ i)]MR(p*,
now
charge only
MR([I/(1 +
i)]p*,
X*)
=
[1/(1
Northern firm's optimal quantity
rate
where MR([1/(1 +
i)]p*,
x*) =
its
c is zero.
Then, in Case
marginal revenue MR(p*, x*)
I,
is
under
zero. In
although the positive interest rate reduces the South's willingness to pay, the
Northern firm's marginal revenue when
is,
ij]p*,
where the marginal cost
the Northern firm's optimal choice (p*, x*)
II,
+
x* units to the South,
x*).
First consider the case
Case
[1/(1
sell
charged
in
Case
II
it
sells
+ i)]MR(p*,
is
x*
in
x* units
x*)
Case
II
=
0, if
is
unaffected and
MR(p*, x*) =
as well as in
Case
I.
still
Hence, the
0).
That
is,
does not result in any additional quantity distortion.
hand, the Northern firm must reduce
its
price from p* to [1/(1
+
i)]p* to sell
And, given the positive amount of the South's foreign reserve (R >
0), the
zero (that
the interest
On
the other
x*
units.
South gets
18
benefit from the lower price charged
some
South
is strictly
Now
let
Case
better off in
II (i.e.
by
the Northern firm.
under the Northern firm's optimal choice (p*, x*)
stricdy
now
below
the marginal cost c (that
is
[1/(1
+ i)]MR(p*, X*) <
Case
in
the marginal cost c
is
II
and hence the South
what the Proposition
The
result
is strictly
(denoted x)
is
more than
Case
better off in
N-equilibrium point, N,
Northern firm's optimal quantity
capture area aE*p* (which
Case
South also captures area
is
x*
in
the South's
is
Case
TQ^ p*
as
its
represented by area E*p*a.
Case
II,
the N-equilibrium point, N,
is
II
consumer
suiplus in Case
is
when
holds
it
sells
is,
the
x*
than x*.
strictly less
small. Then,
is
offset
by the benefit of the lower
when
c is small
II
is
let c
=
a vertical line
now
vertically
as well as in
enough. This
in
Then, as
0.
is
below E*. Since the
I,
Case
I)
represented by area
is
not vertically
The
suiplus.
E*TQ p
a, is
Now let c >
0.
we have
from E*. Hence, as
Case
the South can
as a part of
by
its
the firm, the
result is that the South's
greater than
its
Then, as shown
below E* anymore, and
x where x < x*. This additional quantity distortion
,
0.
=
In addition, due to the lower price charged
II.
in
quantity
=
the South's lower
II,
i)]p*, x*)
now
consumer surplus
consumer surplus
I,
is
can also be understood graphically. First
in
In Case
I.
>
c
c
states.
in Figure 7, the
consumer surplus
Case
MR([1/(1 +
is,
already seen, the firm's implicit reaction function
shown
in
small, the degree of this distortion
negative impact on the South's welfare
price,
when
This results in an additional quantity distortion; that
c).
Northern firm's optimal quantity
this
MR(p*, x*) =
implies that the Northern firm's marginal revenue
units
However, when
result is that the
the paradox of benevolence occurs)
the marginal cost c be strictly positive, so that
willingness to pay
The
in
consumer
in
Figure
the firm's optimal
Case
II
reduces the
6,
19
South's consumer surplus. However,
area
RQ p p*,
which implies
if c is relatively small,
South
that the
Case
axis represents
c'"^^,
c.
For each value of R
made
is
displayed in Table
1.
The
6.06, or 3.00,
when R =
occurs for
c
all
which
g
[0,
for the case
we have computed
where
a
all
=
the
I.
10 and b
10, 20. or 40, respectively.
6.06]
when
a
=
10,
b = 0.4 and
Benevolence occurs
therefore
in non-trivial
seem
maximum
=
b =
b = 0.4
b = 0.5
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
4.35
3.31
3.63
2.57
3.00
1.91
2.44
1.23
1.91
-
1.37
-
0.73
-
-
-
value of c,
c"^^''.
0.4.
we have c™^=
2.23,
Namely, the Paradox of Benevolence
R = 20.
Note
that c
<
a (= 10 in
amount of goods
to indicate that the
ranges of parameter values.
5
and the vertical
0.4 or 0.5 and the results are
Numerical examples for the Paradox of Benevolence
(The value of c™" when a = 10).
R=
R
non-negative values of c less than
table tells that, for instance, with
The numerical examples
1.
than in Case
.
these examples) must hold for the Northern firm to sell a positive
Table
smaller than
here.]
the horizontal axis represents
such that the paradox occurs for
The computation
South.
II
is
conducted numerical simulations to compute the zones of paradox in the (R,
c)-space, in particular, a space in
denoted
better off in
somewhere
[Figure 7
We
is still
SE*RT
area
Paradox of
to the
20
interesting to note the table exhibits an "inverted-U" shape in the (R, c)-
It is
space. That
when
is,
holding other parameter values fixed, the value of c'"^"
the value of R
relatively large.
property in
all
Although
of them,
we have worked
we have been
5.
In Section 3
and
relatively small,
is
number of examples and
unable to prove that this
Competition
we began
out a
with the
Among Licensed
realistic
bank
in order to import
goods
for
domestic
is
identified this
the general property.
that, in the
South, the
to acquire hard currency
sale.
from the
We then pointed out that, if
these importers took the international price, p, of the good and the interest rate,
i,
given, and chose the domestic sale price (that
we
is,
they played a Bertrand game),
ignore these importers for the purpose of our analysis. Given
we
this,
to the designated importers. In this section
indeed ignore the importers in order to derive out
As
before, the Southern
demand
for the
as
could
derived our result
under the assumption that government allocated foreign exchange directly
consumers rather than
R
Importers
assumption
government gives some designated importers the right
central
increasing in
R when the value of R is
decreasing in
it is
is
to the
we show
that
we can
results.
Northern good
is
given by:
a-r
where
r is
the price that the consumers have to pay. Tliere are
They can buy
producer
the
good (subject
at a price, p,
to
m identical importers.
having the requisite foreign exchange) fi^om a Northern
chosen by the Northern producer.
It is
importers take this price as given. Each of these importers
foreign exchange by the
now
Southem government.
If they
is
assumed
that the Southern
given access to
R/m
units of
want more foreign exchange they
21
have
to
wants
from a Northern bank
borrow
this
buy x
units
to
by:
at
an
interest rate
of this good from the North
it
of i. Hence,
has to incur a
if
total cost,
an importer
TC(x), given
.
px, if px<—.
TC{x)
R
—
+
,,
jv
.
+ i)p{x
{l
m
mp
Now, each of these
in
m importers have to choose a price at which
the product to the Southern consumers. If
we may
(4)
R
),ifpx> —
.^
,
it
offers to sell
denotes the price offered by importer
rj
i,
then
m importers by
denote the strategy n-tuple of the
(ri, ....,rm)
The
profit earned
Our aim
by importer
is
case) of this game.
may
then be denoted by
to characterize the
We will
equilibrium. In other words,
7ti(r*,
i
define
be interested
to
r
in the
ti,
function.
We
will here
every importer charges the same price
If all importers, excepting importer
consumers respond as follows.
consumers who
i.
r,
.
.
,
rm).
in this
symmetric Nash
if,
for all
=
i
1,
.
.
.,
m,
...,r')>7i,(r', ...,ri, ...,r*), for all n.
characterize the
>
.
be an 'equilibrium'
Fortunately, to characterize such an equilibrium
ti
,
Nash equilibrium (Bertrand equilibrium
in particular
we
7i,(ri
all
fail to
buy from
consumers go
These are
If
i,
ri
i,
r,
make
r,
r
direct their
and importer
i
faces a
demand
i.
fiilly
the following reasonable assumptions. If
importer
to importers other than
fairly usual
not need to
then each importer faces a
charges
<
we do
i
demand of (a-r)/bm.
charges
rj
{^
demand equal
r),
then the
to (a-ri)/b.
All
at price r to the other importers.
Only those with unmet demand turn
If
to
assumptions; a formal statement of these occur in Basu (1993).
22
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
—<
holds.
b
P
This condition means that,
if
holds.
b
P
government allocated foreign exchange
directly to the
consumers, then the consumers' demand given by the unconstrained demand curve
feasible without
marginal cost functions (derived from (4))
=
+
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
no one
The
not
borrowing hard currency and so they borrow a positive amount of hard
cuiTency from the bank. Under such p and
(l+i)p,
is
(1
will
the horizontal
the thick line
is
summation of all importers'
shown
an equilibrium. That
i)p is
To
by each importer
can only do worse.
i,
If,
is
is,
see this note that
if
in Figure 8.
It is
each importer charges
when everybody charges
given by iR/mp. Clearly by undercutting this
on the other hand, an importer charges
buy from him. Hence,
easy
ri
>
his profit will drop to zero.
analysis in the previous paragraph indicates that, for any p and
the conditions described above, the profits of the finn and the
bank
i
that satisfy
are identical with or
without the designated importers. Also, consumers face the same marginal price and
demand
shown
the
same amount of the good
for other
in the
combinations of p and
the strategic interaction
i.
two
Since
cases.
we
A
focus on the welfare consequences of
between the firm and the bank,
this
ignore the importers in our analysis.
[Figure 8
somewhere
similar equivalence can be
here]
equivalence allows us to
23
^.
The model and
implications. First,
6.
.
Policy Implications
the results described in this paper
have important policy
cautions aid donor agencies not to presume that subsidized credit,
it
given to a Third World nation, necessarily benefits the recipient relative to the case in
vifhich credit is
sight
first
it
made
seems
we have shown
market, the advantages of subsidized credit
goods
to the recipient nations.
ways, other than subsidized
on aid-tying used
however,
is
financial institution.
that the availability of subsidized credit cannot
nation worse off However,
sell
bank or
available by a profit-maximizing
to
may
the recipient
depending on the structure of the import
flow into the hands of corporations that
donor agency has
In such a situation the
to think
of
reaching benefit to nations. The classical literature
credit, for
be concerned with
that the flow -back
that,
make
At
this question.
What we have shown
of benefit to the North can occur even
when
in this paper,
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,
method of lowering
nations, while
to
interest rates.
The IMF uses
this for the
combining the generous loan terms with
macroeconomic
policies such as the need to
money supply growth
may
most international organizations use the
in check.
most indebted and poor
'conditionalities',
keep the
fiscal deficit
Wliat this paper alerts us to
is
which pertain
under control and
the fact that such policies
not be enough to plug the holes through which the benefits of cheap credit get
frittered
away. The 'market structure' of trade
may be
the
main route through which the
immiserization occurs. 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.
24
The model suggests (though we have not
really
gone
may be
into this) that there
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
more pro-active
in the foreign
quotas to different agents
may
Let us take up the
first
may end up
government may stand
benefiting
by being
to gain
exchange market. Releasing the foreign exchange as
not be a good idea.
point
first.
In our
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. Tlie 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.
potential has not been understood, let alone realized.
Let us
now
turn to the second subject of /;ovv to ration the limited foreign
exchange reserve. The method analyzed
in this
exchange
-
is
rationed out to the importers
is
paper - namely, one where the foreign
not the only one. The government could
(and they often do) place quantity restrictions on the amount each importer
The
analysis of this
is
not
trivial since,
given which the
total
import.
while each importer will of course take the
quantity ration as given, the government should be
ration,
may
modeled as choosing
that quantity
import value equals the amount of foreign exchange
tlie
Its
25
government has
(or
wants
to release).
rationing, for instance one in
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 future
it
generated to the South and
will
choose a system consciously
to
avert the paradox of
be worth examining formally the welfare
different systems of releasing limited foreign
to
may even
maximize
effects
of
exchange and for the Southern govermnent
the welfare of its consumers.
26
Appendix
Proof of the Proposition:
We
analyze the firm's best response given
first
First consider
/>
(Al)
i
i
(>0) chosen by the bank.
that satisfies (Al).
a^-AbR
.
-
4bR
Under (Al),
the South does not
Northern firm. To see
this,
borrow any hard currency
note that (Al)
is
equivalent to
for
'
i?
any p chosen by the
>
—
^^
^^
holds for
b
all p.'
Given such
i,
the firm chooses p such that the South spends
currency to purchase the good; namely
the finn's best response
.,^,
(A2)
Any
p=
(p,
i)
a + ^a^
-AbR
twice. In this equilibrium
(A3)
is
= ps
.
>
i
is
(we
i
call
it
(y-c)(a-p') ^^s_
Next consider
a^
<
i
that satisfies (A4).
-AbR
AbR
equilibrium. Graphically, in this
conesponds
to point
B-equilibrium), the bank's profit
given by (A3).
i
Nash
B
in Figure 3
and
so that a'F does not intersect the rectangular hyperbola
b
(A4)
a
the firm chooses the price that
bank chooses high enough
fimi's profit
chooses p such that p[(a-p)/b]=R holds. Hence,
given by (A2).
such that p=p^ and
Nash equilibrium
the
is
it
R units of hard
is
zero and the
27
who
Consider the monopolist
the price given
by (A5) and
(A5)
p=
a+
2(1
X=
(A6)
(3
demand curve given by
the quantity
+ i)c
(1
faces the
+
demanded
is
p=(a-bx)/(l+i).
It
charges
given by (A6).
_
=p
- (1 + i)c
— = X~
^
lb
Note
that the
Northern firm can earn n by choosing p=p
chosen by the bank. Then, given
Hence
i,
the firm chooses
the Northern firm's reaction fiinction
a + (1 + /)c
2(1
(A7)
_
.
-
is
p
if
regardless the value of i
and only
\f
n = {p
-c)x
>7i
.
given by (A7).
_
o
+
Pij)
a + yla~ ~4bR
= p^
otherwise
Next we analyze the bank's best response given
that the firni
chooses p that
safisfies (A8).
(A8)
p[(a-p)/b]>R
Given such
p=a-bx)
is
demand given by
that,
a-pil + i)
The bank chooses
i
that
R
pa- p' -bR
Kp)
2p'
that the
bank's best response
is
is
maximizes
given (A8), the bank can choose i>0 such that n(i)>0. The standard
maximization exercise then implies
(A 10)
demand schedule (which
by (A9).
nil) ^ tip
(A9)
the unconstrained
not feasible unless the bank sets i=0.
profit given
Note
price, the
given by (A 10).
its
Now we
positive
Nash equihbrium
amount of hard currency
in
which the bank lends a
to the South. Insert
(A 10)
into (A5),
and
strictly
we
obtain
f(p)E^2p^-cp'-(2bR+ac)p+bcR=0.
(All)
Note
characterize a
that
root that
f(0)=bcR>0 and f(c)=c^(c-a)-bcR<0. This means
is strictly
greater than
c.
We denote
the root
by
that
(All) has exactly one
p*. 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
equivalent^
if
Note
(p*, i(p*)) satisfies
7f>n^ and (A8); or
^^ c(a-Va^-4M)
+ /(;^*))cr
4b{l
(A13)
=
i)
Nash
(p*, i(p*)). This constitutes a
(A12) and (A13) hold.
[fl-(l
.^12)
if (p,
=
i)
+ iip*))
2b
p*[(a-p*)/b]>R
that
p*
is
continuous in
c,
which impHes
that i(p*) is also continuous in
Letc=0. Thenf(p)=2p^-2bRp,andsop*=VM and i(p*) =
"^^^
c.
"^^
.
We
2bR
find that,
when
Note
Assumption
that
continuous in
hold for
all
c=0, (A12)
c.
is
equivalent to
implies
1
a>2^bR
a>2^bR and (A13)
holds
when
is
equivalent to &>2-JbR
c=0, and that both p* and i(p*) are
This implies that there exists c* (>0) such that both (A 12) and (A 13)
ce[0,c*].
Next,
we assume
ce[0, c*], and
Nash equilibrium represented by
let
W"
(p*, i(p*)).
denote South's aggregate welfare in the
As
stated in the text, the social welfare is
A
represented by the area
(A14)
STQpa in Figure
6,
which
W"=(l/2)[a-(l+i(p*))p*]x*+i(p*)R,
is
given by (A14).
.
29
where x* =
'^
^^ ^^^
.
w'^=^^
(A15)
When
we have (Al 5).
^^''-^^K jv'=^,
2b
Sb
where
strict
X* are
all
for
ce[0, c**]. Finally,
all
c=0,
&b
inequahty holds because a.>l^bR by Assumption
continuous in
c.
1.
Note
that p*, i(p*)
This implies that there exists c**>0 such that
let
c
sMin
[c*, c**],
and
we
and
W">W'' holds
obtain the desired result.
D
30
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World Peace
32
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