International Review of Economics and Finance 15 (2006) 346–363

www.elsevier.com/locate/iref

Local content requirement on foreign direct investment under

exchange rate volatility

Sajal Lahiria,*, Fernando Mesab

aDepartment of Economics, Southern Illinois University, Carbondale, IL 62901-4515, USAbSubdirector Estudios Macroeconomicos, Direccion de Estudios Economicos, Departamento Nacional de Planeacion,

Calle 26 No 13-19, Piso 18, Bogota, Colombia

Received 4 November 2003; accepted 19 May 2004

Available online 11 September 2004

Abstract

This paper analyzes the effects of exchange rate volatility of both the host country and the parent country on

host-government policy related to local content requirement (LCR) on export-oriented foreign direct investment

(FDI) in the context of an oligopolistic market in a third country. We, inter alia, find that an increase in the

volatility foreign exchange rate decreases optimal LCR both under free entry and exit of foreign firms and when

the number of foreign firms is fixed. We also find that the government uses a less strict LCR policy when the

number of foreign firms is endogenous than when it is exogenous.

D 2004 Elsevier Inc. All rights reserved.

JEL classification: F23; F31

Keywords: Multinational firms; Foreign exchange uncertainty; Foreign direct investment; Local contents

1. Introduction

Over the last two decades, the world economy has witnessed a dramatic increase in direct investments

by transnational corporations (TNCs), and also a radical change in the conception about the benefits of

foreign direct investment (FDI). In fact, FDI has grown significantly faster than trade flows, particularly

1059-0560/$ -

doi:10.1016/j.i

* Correspond

E-mail add

see front matter D 2004 Elsevier Inc. All rights reserved.

ref.2004.05.001

ing author. Fax: +1 44 618 453 2717.

resses: lahiri@siu.edu (S. Lahiri)8 fmesa@dnp.gov.co (F. Mesa).

S. Lahiri, F. Mesa / International Review of Economics and Finance 15 (2006) 346–363 347

among the world’s most developed economies, and according to UNCTAD (2000) the combined inward

and outward FDI stocks made 31.7% of global GDP, and FDI’s export accounted for 46% of global

exports of goods and non-factor services in 1999.

The new generalized view about FDI has moved governments to dismantle many barriers in order to

attract foreign investment. However, some recurrent practices of intervention and a number of important

qualifications proposed by trade researchers have led over recent years to an abundance of theoretical

and empirical research which examines this issue, using a diverse range of analytical approaches.

Different economic models have been constructed to analyze the effects of a wide range of policies on

TNC behavior and on host country welfare. These models point out the interrelationships between

different economic variables and issues such as labor demand, income distribution, market-share rivalry,

technology spillover effects, environment degradation, etc. However, the study of FDI behavior under

conditions of uncertainty has not had the same degree of attention. This paper attempts to contribute to

the theoretical literature in this direction.

The main objective of this paper is to examine the behavior of TNCs and a host government when the

latter applies local content (or sourcing) requirements (LCR) on foreign firms under conditions of

uncertainty about exchange rates.

LCR becomes an issue when a firm establishes operations abroad but buys most of inputs from the

firm’s dhomeT base, thus failing to build interdependent or complementary linkages in the host country.

Under such situations, LCR may have desirable domestic welfare effects, since this policy could help to

raise employment level and economic growth in the host country.1 Two points need to be noted here.

First, a stricter LCR policy may drive some TNCs out of the country and thus reduce employment and

growth. Second, in the presence of competing domestic firms, a host government may use LCR as a

strategic instrument as these requirements are limited to foreign owned firms producing in the host

country and thereby give local firms a competitive advantage.

Our model which is based on an imperfectly competitive market for a final good, analyzes the impact

of LCR on employment level. A number of foreign firms compete with domestic firms for the

oligopolistic market of a homogeneous good in a third consuming country. Thus, FDI in this paper is

purely export-oriented. Furthermore, in making its policy decision, the host government takes into

consideration the effect of uncertainty of exchange rate variations on the variables of the model.

The relevant literature can be divided into two categories. The first category considers the relationship

between FDI and LCR. An early analytical contribution is Grossman (1981) who, under a partial

equilibrium framework with a competitive firm, finds that LCR raises the price of the domestic input,

thus benefiting input suppliers but harming the final-good producer.2 Later, Richarson (1993) showed

that, under a general equilibrium framework, LCR may induce foreign firms to invest in the input-

producing sector, and therefore the price-raising effect of LCR could be mitigated to some extent.

The second group of studies is about the relationship between FDI and exchange rate uncertainty. The

effects of exchange rate uncertainty on FDI have been examined, among others, by Cushman (1985),

Goldberg and Kolstad (1995) and Hongmo and Lapan (2000). The scope of the papers is restricted to the

analysis of the effects of uncertainty on TNC decisions such as where to buy inputs, where to produce

1Structural unemployment has become a major concern in many countries, specially in less developed economies, and if we are to understand

government policy related to FDI, it ought to be included in any analysis of FDI. According to Davidson et al. (1985), although LCR reduces

world and home outputs, legislators consider it as a policy target because of its effect on local employment.2Other papers that followed Grossman (1981) are Davidson, Matusz, and Kreinin (1985), Krishna and Itoh (1988), Hollander (1987),

Vousden (1987), Belderbos and Sleuwaegen (1997), and Qiu and Tao (1998), among others.

S. Lahiri, F. Mesa / International Review of Economics and Finance 15 (2006) 346–363348

and where to sell output, and where to finance capital acquisitions from. Kenneth (1990) examines how a

TNC can potentially contribute to the explanation of excessive exchange rate volatility, through their

ability to move capital.3 However, none of these papers analyze the issue of LCR.

The model most directly relevant for the present one is that in Lahiri and Ono (1998, 2004).4 They

develop a partial equilibrium model where the number of domestic firms is fixed but the number of

foreign firms that locate themselves in the host country is endogenous. The two sets of firms compete in

the oligopolistic market for a non-tradeable homogeneous good in the host country. The host

government uses LCR and profit taxation to maximize welfare which is affected by both employment

and the price of the good. Optimal LCR is low when foreign firms are significantly more efficient than

domestic firms, and when the domestic industry is highly oligopolistic. Here the effect of lower prices

dominates the effect on employment. Optimal LCR is higher when foreign firms are inefficient relative

to domestic firms, and when the domestic industry is highly competitive. In this case, the employment

effect is dominant. Finally, when the LCR is zero (i.e., no employment effect), optimal policy is to

subsidize FDI if the domestic industry is highly oligopolistic, to obtain benefits of lower prices.5

Like Lahiri and Ono (1998, 2003), we analyze optimal LCR policy. However, there are a number of

important differences. Most importantly, unlike them we consider exchange rate volatility. Second,

unlike Lahiri and Ono, in our analysis consumers’ surplus is absent as FDI is purely export oriented. In

addition, unlike Lahiri and Ono, we do not consider another producing country and strategic interaction

with it. An important part of our analysis is to examine the role of free and exit of foreign firms on

optimal policies and how that interacts with exchange rate uncertainty. One of our findings is that an

increase in the volatility foreign exchange rate increases optimal LCR under both free entry and exit of

foreign firms and when the number of foreign firms is fixed. We also find that the government uses a less

strict LCR policy when the number of foreign firms is endogenous than when it is exogenous.

The lay out of the paper is as follows. The formal structure of the model is spelled out in the next

section. The effects of exchange rate uncertainty on equilibrium variables are examined in Section 3.

Section 4 is concerned with optimum public policy with respect to LCR. The last section offers some

concluding remarks.

2. The formal framework

There are m identical domestic firms and n identical foreign firms all located in the domestic (host)

country and they compete in a Cournot oligopolistic market of a homogeneous good in a consuming

country where there are no producers for this good. The outputs of each domestic and foreign firm are Xd

and Xf, respectively. Firms maximize their profits with respect to quantities under uncertain conditions

about exchange rates.6 The exchange rate between the host country currency and the consuming

country’s currency is e1, that between the foreign country’s currency and the consuming country’s

3The paper’s conclusion is that there is little evidence that large international corporations could have adverse effects on exchange rates of

large economies, although this conclusion could not be applied to small economies.

5A paper with a somewhat similar framework is Raff and Srinivasan (1998) which analyzes FDI decisions when the host government uses

taxes as a signaling instrument in order to give information about economic advantages in the host country.6For all variables, subscripts or superscripts d and f denote the variables for a domestic or a foreign firm, respectively.

4Lahiri and Ono (2003) consider the strategic use of LCR in the well-known Brander–Spencer framework with two producing countries and a

third consuming country and deterministic exchange rates.

S. Lahiri, F. Mesa / International Review of Economics and Finance 15 (2006) 346–363 349

currency is e2. The exchange rate between the domestic and the foreign country is deduced in terms of

the two exchange rates as e2/e1. Both exchange rates are exogenous to the model and randomly

determined.7 Ex-post profit of each domestic firm pd and the profit for each foreign firm p f are measured

in terms of the currencies in the respective countries, and these are:

ppd ¼ ee1P4� Cdð ÞXd;

ppf ¼ ee2P4� CC� �

Xf ;

where P* is the price of the good measured in the currency of the consuming country.

A domestic firm’s marginal (average) cost (Cd) is constant and non-random because exchange rates

do not effect this cost. This cost is the sum of unit labor costs, ld, and unit intermediate input costs, kd,

both being bought locally. That is,

Cd ¼ ld þ kd:

The marginal cost (C) of each foreign firm in terms of its parent country’s currency is given by

CC ¼ ee2

ee1l þ dkð Þ þ l � dð Þkf ;

where l and k are, respectively, the unit labor cost and unit cost of intermediate input bought locally in

terms of the host country’s currency, kf is the unit cost of intermediate input bought from the parent

country, and the local content requirement is given by the policy variable d. Note that the part of the

marginal cost for a foreign firm which is due to inputs not bought in its parent country is stochastic.

In order to keep the analysis tractable, we shall henceforth assume that the demand function for the

good is linear:

P4 ¼ a� bD; ð1Þwhere D is the demand in the consuming country. The market clearing condition for the good is:

mXd þ nXf ¼ D: ð2Þ

The certainty equivalence of profits of each domestic and foreign firm are given, respectively, as:8

pdc ¼ E ee1P4Xd � CdXd½ � � cdSD ee1P4Xd½ �; ð3Þ

pfc ¼ E ee2P4Xf � CCXf

� �� cf SD ee2P4Xf � CCXf

� �; ð4Þ

where E(d ) and SD(d ) represent the expected value and the standard deviation, respectively.9

7The tilde over the letters refers to the random nature of the variables.

8See, e.g., Newbery and Stiglitz (1981, ch. 6) for a discussion on this concept. As has been shown in Newbery and Stiglitz, the formulation

below does not need any approximation if the utility function is of a particular type and the random variables follow a Normal distribution.

However, they have also shown that this formulation provides a good approximation with any utility function or distribution provided the

variance of the random variable is small. We have chosen a log-normal distribution as it has the property that it always takes non-negative

values. However, all our results will hold if the distribution is Normal.9Appendix A defines, inter alia, mathematical expressions for the expected, variance, and covariance values of the random

variables.

S. Lahiri, F. Mesa / International Review of Economics and Finance 15 (2006) 346–363350

Eqs. (3) and (4) can be written as:

pdc ¼ adP4� Cd½ �Xd; ð5Þ

pfc ¼ afP4� h½ �Xf ; ð6Þ

where

ad ¼ le1� cdre1N0;

af ¼ le2� cfre2N0;

h ¼ ae2e1

l þ dkð Þ þ 1� dð Þkf ;

ae2e1

¼ le2e1

þ cfre2e1

:

and le1and le2

are the expected values, and re1and re2

the standard deviations, of domestic and foreign

exchange rates respectively. Relative risk aversion coefficients of the firms in the two countries are given

by cd and cf.10 A foreign firm’s certainty equivalent marginal cost is h above.11

The first-order conditions, assuming Cournot conjectures, are given by:

P4� bXdð Þad ¼ Cd; ð7Þ

P4� bXfð Þad ¼ h: ð8Þ

The left-hand side of Eqs. (7) and (8) represents marginal revenues, whereas the right-hand side

represents marginal costs.

We now consider two different equilibria depending on whether the number of foreign firms is

exogenous or endogenous. These are done in the following two subsections.

2.1. The case of exogenous number of foreign firms

For simplicity, we assume that there is only one domestic firm and only one foreign firm

competing in the third country. The reaction functions are obtained with the two first-order conditions

(7) and (8) as:

Xd ¼1

2ba� Cd

ad

� �� Xf

2; ð9Þ

Xf ¼1

2ba� h

af

� �� Xd

2: ð10Þ

10For a meaningful solution of the equilibrium, it is assumed that adN0 and afN0.

11We assume that ae2/e1 kNkf, as otherwise the foreign firms would not want to buy intermediate inputs from its home country.

S. Lahiri, F. Mesa / International Review of Economics and Finance 15 (2006) 346–363 351

Eqs. (9) and (10) represent each firm’s best response to an arbitrary strategy by the other firm. The

two firms’ outputs are positively related to the market size (a), but negatively related to both their own

costs and their rival firm’s output. The slopes of the reaction functions are negative because an increase

in the rival’s output reduces a firm’s profits; that is, the firms are strategic substitutes. The Nash

equilibrium output levels are:

X Ed ¼

1

3baþ h

af� 2

Cd

ad

� �;

X Ef ¼

1

3baþ Cd

ad� 2

haf

� �:

Note that a higher value of market size (a) and a foreign firm’s (domestic firm’s) marginal cost

increases the domestic firm’s (foreign firm’s) output, while a higher value of a firm’s own marginal cost

reduces its output.

The equilibrium price is derived by substituting the two Nash equilibrium outputs in Eq. (1):

PE ¼ 1

3aþ Cd

adþ h

af

� �:

Note that an increase in marginal costs or the volatility of exchange rates increases the equilibrium

price.

2.2. The case of endogenous number of foreign firms

Following Lahiri and Ono (1998), the endogenous number of foreign firms is determined by a free

entry and exit condition; that is, in equilibrium, the expected profit of being in the host country is equal

to the profit of some benchmark international activity. The latter is henceforth called reservation profits.

Foreign firms move into (out of) the host country if profits they make there (pf) are larger (smaller) than

the reservation profit (p) so that, in equilibrium:12

pfc ¼ pp; ð11Þ

where certainty equivalent profit (pcf) is defined in Eq. (6).13

12An alternative interpretation of p is that it is a fixed cost for each foreign firm. As long as these costs are incurred outside the host country,

this interpretation will not affect any of our results.13

If we allow free entry and exit of domestic firms as well as foreign firms, the equilibrium will be such that less efficient of the two sets of

firms will be driven out of the market. Lahiri and Ono (2004, ch. 10) allow for endogeneity of the numbers of both groups of firms by

considering differentiated products.

S. Lahiri, F. Mesa / International Review of Economics and Finance 15 (2006) 346–363352

The equilibrium values of the endogenous variables Xd, Xf, n, and P*, can be solved as:

X Ef ¼

ffiffiffiffiffiffiffiffippafb

s; ð12Þ

PE ¼

ffiffiffiffiffiffibppaf

sþ h

af; ð13Þ

X Ed ¼

1

b

ffiffiffiffiffiffibppaf

sþ h

af� Cd

ad

!; ð14Þ

nE ¼ 1ffiffiffiffiffiffiffiffiffiffibppafp aþ m

Cd

ad

� �af � 1þ mð Þh

� 1þ mð Þ: ð15Þ

The equilibrium output of each foreign firm depends positively on reservation profit and the

volatility of foreign exchange rate, and negatively on the slope of the demand function. As for the

international price, it is explained by factors external to domestic firms such as reservation profits,

foreign firms’ marginal cost and the volatility of foreign exchange rate. The output of each domestic

firm depends positively on reservation profits, the marginal cost of foreign firms and the volatility of

foreign exchange rate, but negatively on own marginal cost and volatility of host country exchange

rate. The equilibrium number of foreign firms is increasing (decreasing) in domestic (foreign) firms’

marginal cost and the volatility of domestic (foreign) exchange rate, and it is decreasing in the level of

reservation profit.

3. Exchange rate volatility and market equilibrium

The effects of changes in the variances and the covariance of exchange rates on both the price and

quantities are examined, first, under the assumption of a exogenous number of foreign firms, and then

for the case where the number of foreign firms is endogenously determined.

Before proceeding with any further with our analysis, we make the following assumption:14

Assumption. adr21b0; afr2

2b0; adr12

N0; and afr12N0:

14In appendix A, it is shown that this assumption will hold if the relative risk aversion coefficients are not very small.

S. Lahiri, F. Mesa / International Review of Economics and Finance 15 (2006) 346–363 353

3.1. The case of exogenous number of foreign firms (m=n=1)

To examine how exchange rate variations affect output levels (Xd, Xf) and the international price (P*),

the first-order conditions (7) and (8) are totally differentiated to obtain:

dXd ¼1

3b2Cdadr2

1

adð Þ2þCr2

1

!dr2

1 �hafr2

2

afð Þ2�Cr2

2

!dr2

2 þCr12dr12

" #; ð16Þ

dXf ¼1

3b�

Cdadr21

adð Þ2þ 2Cr2

1

!dr2

1 þ 2hafr2

2

afð Þ2�Cr2

2

!dr2

2 � 2Cr12dr12

" #; ð17Þ

where

Cr21¼ l þ dkð Þ

ae2e1

r2

i

afN0; ð18Þ

Cr12¼ l þ dkð Þ

ae2e1

r12

afb0: ð19Þ

In general, a change in the variance of the foreign exchange rate (dr22) increases the domestic firm’s

output Xd, and reduces the foreign firm’s output Xf. A change in the covariance between e1 and e2, r12,

lowers Xd and raises Xf. A change in r12 however has ambiguous effects on Xd and Xf.

The above results can be explained intuitively as follows. When a firm is risk averse, the volatility of

exchange rate increases uncertainty in the international market and thus the firm predicts a lower

international price level measured in their own currency. This subjective prediction by the firm is

equivalent to a fall in its marginal benefit caused by uncertainty, and so the firm reduces, and its rival

increases, its output. An increase in either of the two variances increases the expected costs of imported

inputs for the foreign firm, and this lowers the output of the foreign firm and raises that of the domestic

one. Thus, the effect of an increase in r12 is ambiguous on both output levels, but the effect of an increase

in r22 unambiguously reduces Xf and raises Xd. An increase in the covariance reduces the marginal cost

of the foreign firm as the effective marginal cost of the foreign firm, h, depends on the ratio of the two

exchange rates, and this unambiguously increases Xf and reduces Xf.

As for the effects on price, we have:

dP4 ¼ � 1

3

Cdadr21

adð Þ2�Cr2

1

!dr2

1 þhafr2

2

afð Þ2�Cr2

2

!dr2

2 �Cr12dr12

" #: ð20Þ

The international price is increased by the volatility of both exchange rates. The reason is that own

effects—the effect of an increased volatility of an exchange rate on the output level of the firm directly

affected by it—dominate cross-effects—the effect of an increased volatility of an exchange rate on the

output level of the rival of the firm directly affected by it—insofar as the effect on aggregate output, and

therefore the market price is concerned. An increase in the covariance reduces the price.

S. Lahiri, F. Mesa / International Review of Economics and Finance 15 (2006) 346–363354

3.2. The case of endogenous number of foreign firms

The effects of changes in r12, r2

2, and r12 on Xd, Xf and n are derived from Eqs. (7), (8) and (11) as

follows:

dXd ¼1

bCd

ad

adr21

adþCr2

1

� �dr2

1 þCr12dr12 �

1

2

ffiffiffiffiffiffibppaf

sþ h

af

!afr2

2

af�Cr2

2

!dr2

2

" #; ð21Þ

dXf ¼ �1

2

ffiffiffiffiffiffiffiffipp

baf

safr2

2

afdr2

2; ð22Þ

dn ¼ffiffiffiffiffiffiaf

bpp

r� m

Cd

ad

adr21

adþ mþ 1ð ÞCr2

1

� �dr2

1 þ"

mþ nþ 1ð Þ 12

ffiffiffiffiffiffibppaf

sþ mþ 1ð Þ h

af

!(

�afr2

2

af� mþ 1ð ÞCr2

2

#dr2

2 � mþ 1ð ÞCr12dr12

):

ð23Þ

Because of free entry and exit of foreign firms in this case, the output level of a foreign firm depends

only on the volatility of the foreign exchange rate [see Eq. (12)], and thus the volatility of domestic

exchange rate and the covariance of the two exchange rates have no effect on Xf. Moreover, an increase

in r22 in fact increases Xf, although it also unambiguously reduces the number of foreign firms. The

reason for the latter is that an increase in the volatility of the foreign exchange rate, for reasons

mentioned before, unambiguously reduces the profits of foreign firms resulting in an outflow of the

foreign firms. An increase in r22 also increases Xd unambiguously. The effect of an increase in r1

2 has

ambiguous effects on both Xd and n for reasons mentioned before. Finally, the covariance increases the

inflow of foreign firms and reduces the output of the domestic firm. The effects of the volatility of the

exchange rates on the international price of the final good are derived by totally differentiating the

inverse demand function, and substituting dXd, dXf, and dn from Eqs. (12)–(23):

dP4 ¼ Cr21dr2

1 þCr12dr12 �

hafþ 1

2

ffiffiffiffiffiffibppaf

s !afr2

2

af�Cr2

2

!dr2

2: ð24Þ

As in the case of fixed number of foreign firms, the volatility of both exchange rates increases the

equilibrium price. Finally, the price falls if the covariance between the exchange rates increases.

Stating the above results formally, we can state the following propositions:

Proposition 1. In the absence of free entry and exit of foreign firms, we have the following results:

(i) An increase in r22 decreases the foreign firm’s production level, but increases the domestic firm’s

output and the price.

S. Lahiri, F. Mesa / International Review of Economics and Finance 15 (2006) 346–363 355

(ii) An increase in r12 decreases domestic firm’s output level and the price, but increases the foreign

firm’s output.

(iii) An increase in r12 increases equilibrium price, but its effect on the two output levels in ambiguous.

Proposition 2. In the presence of free entry and exit of foreign firms we find:

(i) An increase in r22 increases all firms’ output levels and the price, and decreases the number of

foreign firms.

(ii) An increase in r12 increases the international price, has ambiguous effects on Xd and n, and no

effect on Xf.

(iii) An increase in r12 decreases the domestic firm’s output level and the price, increases the number

of foreign firms, and has no effect on output level of a foreign firm.

Having described the model and carried out some comparative static exercises, we shall now consider

optimal LCR policy of the host-country government in the following section.

4. Optimal local content policy

Social welfare can be written as

WW ¼ Gþ mCdXd þ n dk þ lð ÞXf þ mppd;

where G is the real income generated elsewhere in the economy and it is assumed to be deterministic and

exogenous for the purpose of this paper. The second and the third terms represent wage income

generated in the host country by domestic and foreign firms respectively.15 Finally, the last term gives

profits by domestic firms. An important feature in this expression is the inclusion of unemployment in

the domestic economy as in Brander and Spencer (1987) and Lahiri and Ono (1998).

Simplifying the above equation, we obtain the following expression for social welfare:

WW ¼ Gþ mee1P4Xd þ n dk þ lð ÞXf ;

where the exchange rate e1 is a random variable. The certainty equivalence of the social welfare function

is:

Wc ¼ E WW� �

� cgSD WW� �

¼ Gþ magP4Xd þ n dk þ lð ÞXf ; ð25Þ

where

ag ¼ le1� cgre1

� �;

and cg is the government’s relative risk aversion parameter.

15It is implicitly assumed that one unit spend on intermediate inputs locally creates the same amount of wage income.

S. Lahiri, F. Mesa / International Review of Economics and Finance 15 (2006) 346–363356

The certainty equivalence of social welfare function is totally differentiated in order to derive

optimum LCR on intermediate inputs:

dWc ¼ agmP4dXd � agmXdbdX þ n dk þ lð ÞdXf þ nkXf ddþ dkXf dn: ð26Þ

We shall now consider the cases of exogenous and endogenous number of foreign firms in turn in the

following two subsections.

4.1. The case of exogenous number of foreign firms (m=n=1)

The slope of the social welfare (W) in relation to LCR on intermediate inputs (d) is obtained as

dWc

dd¼ 2

3

ag

b1

2

k

agþ 1

3

hd

af

� �a� hd

af

dk þ lð Þag

� k

ag� 1

3

hd

af

� �haf� 1

2

Cd

ad

� � ; ð27Þ

where hd is the partial derivative of the marginal cost of a foreign firm with respect to d and it is given

by:

hd ¼ ae2e1

k � kfN0:

An increase in d increases Xd and reduces Xf, and increases domestic employment for given Xd and

Xf. The reduction in Xf in turn reduces domestic employment and increases domestic profits. Thus, an

increase in d has ambiguous effect on Wc.

It is easy to show that the value of the above derivative given in Eq. (27) is unambiguously positive

when d=0. This together with the concavity of the Wc (with respect to d) implies that optimal value of din this case is positive.16 The optimum LCR (dx*) is obtained from Eq. (27), by setting the right-hand

side to zero, i.e.,

dx4 ¼

k

agþ 2

3

hd

af

� �a� k

ag� 1

3

hd

af

� �2kf þ ae2=e1 l

af� Cd

ad

� �� 2

l

ag

hd

af

2 2k

ag� 1

3

hd

af

� �hd

af

; ð28Þ

where the subscript x refers to the case of exogenous number of foreign firms.

The optimum LCR increases with market size (a) and with the domestic firm’s marginal cost. In

contrast, there is a negative relationship between optimal LCR and each foreign firm’s marginal

costs.

16It can be verified that the second-order condition is satisfied if and only if k/adNhd/(6le2

).

S. Lahiri, F. Mesa / International Review of Economics and Finance 15 (2006) 346–363 357

4.2. The case of endogenous number of foreign firms

By totally differentiating the market clearing condition (15), the two first-order conditions (7) and (8),

and the FDI equilibrium condition (11), we solve for dXd, dXf, dX and dn, and then substituting these in

Eq. (26), we get:

dWc

dd¼ ag

b

(k

agaþ m

k

ag� hd

af

� �Cd

ad� 1þ mð Þ dk þ l

ag

hd

af

� 1þ mð Þ kag� 2m

hd

af

� �hafþ

ffiffiffiffiffiffibppaf

s !):

ð29Þ

As in the case of exogenous number of foreign firms, this slope is increasing in the market size and in

domestic firms’ marginal costs. It is also decreasing in foreign firms’ marginal costs and, additionally, in

the reservation profits. It is once again easy to check that the right-hand side of Eq. (29) is

unambiguously positive when evaluated at d=0. Thus, the optimal value of d once again is positive.17

The optimum level of dn* is obtained as:

dn4 ¼

k

agaþ m

k

ag� hd

af

� �Cd

ad� 1þ mð Þ k

ag� 2m

hd

af

� �F � 1þ mð Þ l

ag

hd

af

2 1þ mð Þ kag� m

hd

af

� �hd

af

; ð30Þ

where the subscript n refers to the case of free entry and exit of foreign firms, and the parameter F in Eq.

(30) is given by:

F ¼kf þ ae2=e1 l

afþ

ffiffiffiffiffiffibppaf

s:

We conclude this section by comparing dx* and dn*. For this we evaluate the right-hand side of Eq.

(27) at d=dn*:

dW

dd

�����d¼dn4

¼ 2

9

ag

b

�2k

ag

af

hd� 1

�(�

k

ag� hd

af

� aþ 6

k

ag

af

hd

ffiffiffiffiffibpaf

s !

� k

af

�2kf þ a e2=e1ð Þl

af� Cd

ad� 2

l

ag

hd

af

�): ð31Þ

It can be shown that the right-hand side of Eq. (31) is unambiguously positive.18 From the concavity

of the welfare function, it then follows that dx*Ndn*. Formally,

18Note that, k

ag� hd

af

� aþ 6 k

ag

afhd

ffiffiffiffiffibppaf

q� N k

ag2

kfþa e2=e1ð Þ laf

� Cd

ad

� .

17It can be verified that the second-order condition is satisfied if and only if k/adNhd/(2le2

).

S. Lahiri, F. Mesa / International Review of Economics and Finance 15 (2006) 346–363358

Proposition 3. The host-country government imposes a stricter LCR in absence of free entry and exit of

foreign firms than in the presence of it.

4.3. Comparative statics

In this section, we shall examine the effects of changes in r12, r2

2 and r12 on the opti-

mum level of d.19 In order to keep the analysis at a tractable level, we make the assumptions that

the relative risk preference for the host government and domestic firms are equal, i.e., ad=ag, and

that m=1.

In all the cases, we shall examine if (dW/dd) increases or decreases as a result of changes in the

variances or covariance of the exchange rates. If (dW/dd) increases, the optimal value of d will increase

as well.

4.3.1. The case of exogenous number of foreign firms (m=n=1)

First, we examine the effect of a change in r12 when r2

2=r12=0. We assume that k/adNhd/(2le2) so that

the second-order condition is satisfied (see footnote 16). In addition, we make the assumption that this

inequality will be satisfied if the home country had the foreign country’s stochastic parameters, i.e., k/

afNhd/(2le1). To summarize, we assume:

k

adN

hd

3le2

; andk

afN

hd

3le1

: ð32Þ

Differentiating Eq. (27) with respect to the variance of the domestic exchange rate (r12) we get:

d

dr21

dW

dd

����d¼dx4

¼ 2

3

hd

le2

k

b

� Hx þ dx4þ

l

k

� �1� 1

3

hd

le2

ad

k

� �� � k ae2e1

r21

hd

� Hx þ 3dx4þ1

2

le2

hd� 1

3

ad

k

� �Cd

ad� l

k

� �adr2

1

ad

;

ð33Þ

where

Hx ¼1

2aþ Cd

ad

� �� h

af

� �af

hdN0:

Since ae2/e1, r12N0 and Eq. (32) is satisfied, the first expression inside the curly brackets which comes via

changes in foreign cost, is negative.20 Since Eq. (32) is satisfied and adr12b0, the second expression in

brackets is in fact positive when l/k is relatively small, and thus the right-hand side of Eq. (33) in general

has an ambiguous sign.

20As is shown in Appendix A, kae2

e1r2i¼ hdr2

iN0.

19Note that the effect of a rise in cd (cf) on d has the same sign as that in r1

2 (r22).

S. Lahiri, F. Mesa / International Review of Economics and Finance 15 (2006) 346–363 359

For the effect of a change in r22 when r1

2=r122=0, we find:

d

dr22

dW

dd

����d¼dx4

¼ 2

3

k

bHx þ dx4 1� 1

3

hd

af

le1

k

� �� � kae2e1

r22

af� hd

af

afr22

af

!(

þ 1� 1

3

hd

af

le1

k

� � lae2e2

r22

af� ae2

e1

l þ k4� afr2

2

a2f

!):

Since Eq. (32) is satisfied, afr22b0 and ae2

e1r22N0, the sign of ddx*/dr2

2 is unambiguously negative.

Finally, for the effect of a change in r12 when dr12=dr2

2=0, we get

d

dr12

dW

dd

����d¼dx4

¼ � 2

3

hd

le2

k

bHx þ dx4þ

l

k

� �1� 1

3

hd

af

ad

k

� � kae2e1

r12

hd:

Since Eq. (32) is satisfied and ae2/e1r12b0, the sign of ddx*/dr12 is unambiguously positive.

The above results can be formally stated as:

Proposition 4. When all economic agents are risk averse, and in the absence of free entry and exit of

foreign firms in the host country, an increase in r22 reduces the optimal level of LCR, but an increase in

r12 increases this level. The effect of r12 is ambiguous.

The reason why the effects of r22 and r12 are unambiguous, but that of r1

2 is ambiguous, lies in our

finding earlier that the effects of r12, r2

2 and r12 on output levels (Xd and Xf) have similar patterns.

4.3.2. The case of endogenous number of foreign firms

For this case, in place of Eq. (32), we assume that

k

adN

hd

le2

; andk

afN

hd

le1

; ð34Þ

so that the second-order condition is satisfied (see footnote 17).

For a change in r12 when r2

2=r12=0, we get

d

dr21

dW

dd

����d¼dn4

¼ � 2k

bHn þ dn4þ

l

k

� �1� hd

le2

ad

k

� �� � kae2e1

r21

le2

(

þ Hn þ1

2

le2

hd� ad

k

� �Cd

ad� dn4þ

l

k

� �� �hd

le2

adr21

ad

;

where

Hn ¼1

2aþ Cd

ad

� �� h

af�

ffiffiffiffiffiffibppaf

s !af

hdN0:

Once again since ae2e2

r21N0 the first expression of this equation is negative. Since afr2

1b0, the second part

of the equation could be positive. Therefore, the sign of ddn*/dr12 is ambiguous. Thus, the qualitative

result is the same as in the case of fixed number of foreign firms.

S. Lahiri, F. Mesa / International Review of Economics and Finance 15 (2006) 346–363360

When r12=r12

2 =0, and r22 changes, we get:

d

dr22

dW

dd

����d¼dn4

¼ � 2k

bHn þ dn4 1� hd

af

le1

k

� �� �hd

af

kae2e1

r22

af�

afr22

af

!( )

þ 1� hd

af

le1

k

� � l ae2e1

r22

af�

ae2e1

l þ kf

afþ 1

2

ffiffiffiffiffiffibppaf

s !afr2

2

af

" #):

Because afr22b0 and ae2

e1r22N0 then we have ddn*/dr2

2b0.

Finally, for a change in r12 when dr12=dr2

2=0, we have:

d

dr12

dW

dd

����d¼dn4

¼ � 2k

bHn þ dn4þ

l

k

� �1� hd

af

le1

k

� � k

afae2=e1r12

:

Since ae2/e1r12b0 and the term inside the parenthesis is positive, we get ddn*/dr12N0.

These results are summarized as follows.

Proposition 5. When all economic agents are risk averse, and in the presence of free entry and exit of

foreign firms in the host country, an increase in r22 reduces the optimal level of LCR, but an increase in

r12 increases this level. The effect of r12 is ambiguous.

Thus, the qualitative nature of the comparative static exercises does not depend on whether or not

there is free entry and exit of foreign firms. However, as mentioned before, the level of optimal policies

does depend on endogeniety or otherwise of the number of foreign firms.

5. Conclusions

The aim of this paper has been to investigate the implications of exchange rate volatility on optimal

local content requirement (LCR) on foreign firms in an oligopolistic market setting. Two main issues have

been addressed in this paper. First, we have examined how changes in the volatility of exchange rates

affect the equilibrium quantities and price. Second, we have characterized optimum host-government

policy on local content requirement and examined how it is affected by exchange rate volatility.

Uncertainty in exchange rates generates extra costs, and firms have to adjust outputs

appropriately. The costs are incurred on two fronts: via revenue and via unit costs of production.

The effects via the revenue channel are symmetric. A firm’s exports are affected negatively if the

volatility of domestic exchange rate increases, but positively if it increases. Furthermore, when the

number of foreign firms is endogenous, a higher domestic exchange rate volatility makes the

market more competitive by increasing the inflow of FDI. However, if foreign exchange rate

volatility increases, the number of foreign firms falls. The effect via the second channel is not

symmetric, as an increase in the volatility of either exchange rate increases the unit cost of

production of each foreign firm (which imports some of its inputs from the host country) but does

not affect the unit cost of domestic firms (which buy all their inputs domestically). Because of

this, the volatility of domestic exchange rate has ambiguous effects on output levels and the

S. Lahiri, F. Mesa / International Review of Economics and Finance 15 (2006) 346–363 361

number of firms, but as far as the foreign exchange rate is concerned, the effects via the revenue

channel is reinforced by that via the costs channel.

For the same reasons, an increase in the volatility of domestic exchange rate has an ambiguous effect

on optimal LCR. However, an increase in the volatility of the foreign exchange rate unambiguously

decreases optimal LCR. The qualitative results are the same whether the number of foreign firms is

exogenous or endogenous. However, optimal LCR is unambiguously lower when there is free entry and

exit of foreign firms than when the number of foreign firms is exogenous.

Acknowledgement

We are grateful to Peter Sinclair for helpful comments and suggestions.

Appendix A. Mean, variance and certainty equivalence

If the exchange rates follow log-normal distributions, i.e., lnei~N(li,ri2), (i=1, 2), then the expected

values and variances of the exchange rates are:

le1¼ el1þ1

2r21 ; ðA:1Þ

le2¼ el2þ1

2r22 ; ðA:2Þ

le2e1

¼ el2�l1þ12

r22þr2

1ð Þ�r12 ; ðA:3Þ

r2e1¼ e2l1þr2

1 er21 � 1

� ; ðA:4Þ

r2e2¼ e2l2þr2

2 er22 � 1

� ðA:5Þ

r2e2e1

¼ e2 l2�l1ð Þþr22þr2

1�2r12 er2

2þr2

1�2r12 � 1

� ; ðA:6Þ

where r12 is the covariance between e1 and e2.

The certainty-equivalence parameters are:

aj ¼ lei� cjreiN0; j ¼ d; f ; g; i ¼ 1; 2: ðA:7Þ

which, using Eqs. (A.1–A.5), can also be written as:

aj ¼ lei1� cj er2

i � 1� 1

2

� �N0: ðA:8Þ

S. Lahiri, F. Mesa / International Review of Economics and Finance 15 (2006) 346–363362

Then the derivative of aj with respect to ri2 is derived as

ajr2i¼ 1

2aj � cj

leier2

i

er2i � 1

� �12

0@

1A ¼ 1

2lei

1� cj2er2

i � 1

er2i � 1

� �12

0@

1A; ðA:9Þ

from which it follows that if the relative risk aversion parameter (cj) is not to small, we have the

following

daj

dr2i

¼ ajr2ib0: ðA:10Þ

The certainty equivalence parameter for the foreign firm in relation to its marginal costs is given by:

ae2e1

¼ le2e1

1þ cj er22þr2

1�2r12 � 1

� 12

� �; ðA:11Þ

from which we obtain

ae2e1

r2i¼ 1

2ae2

e1

þ cjle2

e1

er22þr2

1�2r12

er22þr2

1�2r12 � 1

� �12

0@

1A ¼ 1

2le2

e1

1þ cj2er2

2þr2

1�2r12 � 1

er22þr2

1�2r12 � 1

� �12

0@

1A; ðA:12Þ

from which it follows that if the relative risk aversion parameter (cj) is not to small, we have the

following

dae2e1

dr2i

¼ ae2e1

r2iN0: ðA:13Þ

We also find that

ae2e1

r12¼ � 2ae2

e1r2i¼ � le2

e1

1þ cj2er2

2þr2

1�2r12 � 1

er22þr2

1�2r12 � 1

� �12

0@

1Ab0: ðA:14Þ

As the derivative of a foreign firm’s marginal costs with respect to d, we get

dhdd¼ hd ¼ ae2

e1

k � kfN0;

and then that:

dhd

dr2i

¼ hdr2i¼ kae2

e1r2iN0;

dhd

dr12

¼ hdr12¼ � 2

dhd

dr2i

b0:

S. Lahiri, F. Mesa / International Review of Economics and Finance 15 (2006) 346–363 363

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