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A CONJECTURAL VARIATION COMPUTABLE GENERAL
EQUILIBRIUM MODEL WITH FREE ENTRY
by Roberto A. De Santis*
The Kiel Institute of World Economics
Düsternbrooker Weg 120, 24105, Kiel, Germany
E-mail: r.desantis@ifw.uni-kiel.de
ABSTRACT: This paper proposes a procedure to incorporate the conjectural variation approach in
Computable General Equilibrium (CGE) analysis such that the strategic interaction among rival firms
in international markets can be modelled. It shows how to calibrate the conjectured reactions of rival
domestic and foreign firms. It also shows that the approach suggested by Harrison, Rutherford and Tarr
(henceforth, HRT) is valid if Cournot competition prevails among domestic firms, among foreign
firms, and between domestic and foreign firms. A conjectural variation CGE model applied to Turkey
indicates that, if Cournot competition prevails between domestic and foreign firms, the results obtained
under the HRT approach are very similar to those obtained under the conjectural variation approach.
However, if foreign firms expect that rival domestic firms would react to their own action, then the
results change dramatically. In a more competitive context, a large welfare gain from trade
liberalisation can be generated.
KEYWORDS: Price cost margin, Conjectural variation, CGE analysis.
JEL classification: D43, D58.
* I am indebted to Glenn Harrison, Thomas Rutherford, Frank Stähler and John Whalley for their valuable comments on an
early stage of this paper. All errors are my responsibility.
1
1. Introduction
The CGE modelling literature has developed quite markedly in the last two decades. Initially, these
models were constructed under the assumption of perfect competition and constant returns to scale
(CRS). In the middle eighties, under the wave of the ‘new trade theory’,1 models with industrial
organisation features were used to study the impact of trade policy actions when industries are
characterised by endogenous market structure, and the economies to scale are exploited at firm level.
These models, with imperfect competition and increasing returns to scale (IRS) at firm level, usually
employ the Lerner formula to set endogenously the price markup above the marginal cost. Examples of
small open economy CGE models of this kind are those built by Harris (1984) and Devarajan and
Rodrik (1989, 1991). Harris (1984) assumes that a firm of protected oligopolistic industries sets its
price as a weighted average of the monopolistic Lerner price and the tariff-inclusive price of the
importing competing goods. Devarajan and Rodrik define the inverse of the price cost margin in the
domestic (export) market, as a product between the endogenous number of firms and the constant
absolute value of the domestic (foreign) demand elasticity faced by the industry as a whole.2 Examples
of multicountry CGE models with industrial organisation features are those built by Gasiorek, et al.
(1992) and by HRT (1996, 1997b). In these studies, the price cost margin is defined as an inverse
function of the endogenous price elasticity of demand perceived by the representative firm. Gasiorek, et
al. assume that the aggregate demand is isoelastic;3 whilst HRT derive the perceived price elasticity of
1 The ‘new trade theory’ began with models facing imperfect competition and increasing returns to scale. Alongside the
gains from trade due to the conventional comparative advantage, it is argued that, by enlarging markets, international trade
raises competition and allows greater exploitation of economies of scale (Krugman, 1979, 1981; Lancaster, 1980; Dixit and
Norman, 1980; Helpman, 1981; Ethier, 1982).
2 Devarajan and Rodrik (1991) calibrate the price elasticity of domestic demand as a positive function of the ratio between
the price of imports and the price of domestic goods.
3 It must be stressed that the original algebraic formulation of the price elasticity of demand perceived by a firm with an
isoelastic demand curve has been developed by Smith and Venables (1988), under the alternative Cournot and Bertrand
conjectures. However, these models are of a partial equilibrium nature.
2
demand under the assumption that domestic goods and imports are imperfect substitutes. This latter
finding is very important as, in order to capture intraindustry trade, most of CGE models employ the
Armington specification, which states that goods produced by industries located in different countries,
but which compete in the same market, are imperfect substitutes (Armington, 1969). The studies by
HRT are based upon the assumption that firms compete in a quantity setting oligopoly with constant
conjectures. The latter are endogenously calibrated. They express the optimal markup for each sector in
each national market as a function of elasticities of substitution and firms’ market share, and assume
that the price elasticities of demand perceived by a firm in the domestic and export markets are
independent of conjectural variations parameters (De Santis, 1999). In this paper, I suggest a way to use
the conjectural variation approach in CGE models, where the price elasticities of demand perceived by
a firm in the domestic and export markets do depend upon strategic expectations among firms.
The criticisms made by theoretical industrial economists to the conjectural variation approach
are well known. It is argued that the notion of conjectural variation is ad hoc (Daughety, 1985), or that
strategic responses require a temporal setting (Makowski, 1987). However, it is also understood that the
conjectural variation approach is an approximation of the solution which emerges from the equilibrium
of a dynamic oligopolistic game (Schmalensee, 1989; Ferrel and Shapiro, 1990).4 Certainly, the
conjectural variation models are used by empirical industrial economists because they can cover the
entire range of market performance from competition to monopoly (Cowling, 1976; Cowling and
Waterson, 1976; Slade, 1987; Machin and Van Reenen, 1993).
The conjectural variation approach is rarely used in CGE models for two main reasons: firstly,
the demand tree of a typical CGE model is of a multi-stage type and the strategic behaviour of domestic
3
and foreign firms can occur at different stages of the demand tree; secondly, the calibration of the key
parameters of the markups equations can be tricky and is certainly demanding, causing problems
associated with the convergence of the model.5 In order to understand the problem, let me sketch a
figure where the strategic interactions among domestic and foreign firms are clearly identifiable. Figure
1 depicts a typical three stage demand tree for the imperfect competitive good employed in the CGE
literature (see for example HRT, 1996, 1997b). At the first stage, the final demand of the representative
consumer and the intermediate demand of industries are satisfied by the supply of composite
commodities. At the second stage, the aggregate demand for composite commodities is satisfied by the
supply of domestic goods and imports, treated as imperfect substitutes. At the third stage, having
decided the demand for domestic goods and for imports, consumers and industries purchase a variety of
domestic goods and a variety of imports. Hence, domestic firms (as well as foreign firms) compete
against each other at the third stage of the demand tree. Whereas domestic firms and foreign firms
compete against each other at the second stage of the demand tree. This implies that the expectation of
a domestic (foreign) firm about the action of other domestic (foreign) firms to their own actions is
formed at the third stage of the demand tree; whereas the expectation of domestic (foreign) firms about
the action of the foreign (domestic) firms to their own actions is formed at the second stage of the
demand tree.
[Insert Fig. 1]
In this paper, I derive a general formulation for the price markup, where the price elasticity of
demand is a function of the conjectured reactions of both the rival domestic and foreign firms. I show
4 Note that, in linear oligopolies and for an open set of values of the discount factor, the conjectural variation solution is the
reduced form of the equilibrium of a quantity-setting repeated game with minimax punishments during T periods (Cabral,
1995).
5 By calibration procedure I mean the estimation of unknown parameters, such that the observed values of endogenous
variables constitute an equilibrium of the CGE model.
4
that the price cost margin formula used by HRT can be obtained in the specific case when firms behave
in a Cournot fashion. I also show how to calibrate the conjectural variation of the domestic (foreign)
firm about the behaviour of the rival domestic (foreign) firms. In order to understand how welfare and
output might be affected by the use of alternative conjectural variations, a single country open economy
CGE model has been built for the Turkish economy, and the effects of a unilateral partial trade
liberalisation policy are examined.
The remaining sections of this paper have been organised as follows: Section 2 describes the
modelling framework; Section 3 derives the price elasticities of demand perceived by a representative
firm in the domestic and export markets; Section 4 describes the numerical model, the benchmark data
set and the calibration procedure, and discusses the numerical results obtained applying an CGE model
to the Turkish economy; Section 5 presents a summary.
2. The structure of the model
Consider an open economy with a single representative consumer whose consumption decisions are
taken by solving a multi-stage CES demand system. Assume that the industry is imperfectly
competitive, the technology exhibits IRS at firm level and the equilibrium number of firms is
determined by the zero profit condition. Finally, assume that the production function entails the use of
intermediate inputs and primary inputs, such as labour and capital. This structure implies that final
demand is equal to the sum between consumer demand and intermediate demand. The final demand is
satisfied by the supply of domestic goods and imports, which are in turn assumed to be imperfect
substitutes as in Armington (1969).
2.1. The supply behaviour
5
Assume that within an industry i a firm s faces fixed costs, fi, and produces two differentiated
commodities, one supplied in the domestic market, ~
dis , and the other exported, ~
eis . Note that i denotes
the sectors facing IRS, whereas j denotes all economic sectors.
The profit function of a representative domestic firm, πi, takes the following form:
(1)
()
πiis
dis is
eis i is is i
pd pe c d e f=+−+−
~~~~ ~~,
where ~
pis
d and ~
pis
e denote the brand prices of domestic output and exports, respectively; and ci the
marginal cost, which is assumed to be independent of output. The first order conditions yield the price
cost margins in both the domestic and export markets
(2) ~
~
pc
p
is
di
is
dis
−=1
τ,τis <−1,
(3) ~
~
pc
p
is
ei
is
eis
−=1
δ,δis <−1,
where τis and δis represent the price elasticities of domestic and export demands perceived by a
domestic firm s, respectively. HRT (1997b) argue that
()()
~~
pcp
is
diis
di
dis
−=+1Ωτ and
()()
~~
pcp
is
eiis
ei
eis
−=+1Ωδ, where Ωi
d and Ωi
e denote the conjectural variations in the domestic and
export markets, respectively (with ΩΩ
i
di
e
==0 representing the Cournot case). However, they
implicitly assume that τis and δis are independent of conjectural variations parameters. Conversely, as
suggested by Smith and Venables (1988), τis and δis also depend on the perceived effect of the firm’s
action on industry aggregate supply. More precisely, I show in the next section that τis and δis are each
a function of two conjectural variations parameters, since domestic firms also have conjectures about
how foreign firms respond.
6
2.2. The demand behaviour
A typical CGE model with imperfect competition and IRS is characterised by the three stage demand
system as depicted in Figure 1. At the first stage, the final demand of the representative consumer, Ci,
and the intermediate demand of industries, Xi, are satisfied by the supply of composite commodities,
Qi:
(4) CIp
iii
=α
(5) XaY
iij
j
j
=∑
(6)
()
()
()
[]
()
QCX D M
iii ii ii
ii ii
ii
=+= +−
−−
−
ϕϕ
εε εε
εε
11
1
1,
where αi denotes household budget shares, I household income, pi the price of the Armington goods,
Yj sectoral output, aij the input requirements by sectors j which are supplied by the IRS sectors, Di
domestic output, Mi imports, εi the elasticity of substitution between imports and domestic goods, and
ϕ
i the share parameter of the Armington function. Equation (4) is derived by maximising the
consumer’s Cobb-Douglas utility function subject to his budget constraint, whereas the derivation of
(5) is based upon the assumption that intermediate inputs are net complements (i.e. Leontief
specification). Equation (6) gives the equilibrium in the goods market.
At the second stage, the aggregate demand for composite commodities is satisfied by the supply
of domestic goods and imports, according to the CES Armington specification. At the upper level, the
solution of the Armington-dual problem yield the demand for domestic goods, Di, the demand for
imports, Mi, and the Armington price, pi:
(7) DppQ
iii
dii
iii
=−
ϕεεε,
7
(8)
()
MppQ
iii
mii
iii
=− −
1ϕεεε,
(9)
()
()
()
{}
()
pp p
iii
dii
m
iiiii
=+−
−−
−
ϕϕ
εεεεε
11
11
1,
where pi
d denotes the domestic price index and pi
m the import price index.
At the third stage, having decided the demand for domestic goods and for imports, consumers
and industries purchase a variety of domestic goods and a variety of imports, based again on CES
functions:
(10)
() ()
Dd
iis
s
n
ii
ii
=
−
=
−
∑~/
/
ςς
ςς
1
1
1
,
ς
i>1,
(11)
() ()
Mm
iir
r
k
ii
ii
=
−
=
−
∑~/
/
ξξ
ξξ
1
1
1
,ξi>1,
where
ς
i and ξi represent the elasticities of substitution among n domestic varieties and k imported
varieties, respectively; and ~
mir denotes output of each foreign brand r. Given (10) and (11), the solution
of the dual problems yields
(12) ~~
dppD
is idis
di
ii
=−ςς
,
(13)
()
()
()
pp
idis
d
s
n
i
i
=
−
=
−
∑~/
1
1
11
ςς
,
(14)
()
[]
~~
mpp t M
ir imir
mii
ii
=+
−
ξξ
1,
(15)
()
[]
()
()
ppt
imir
mi
r
ki
i
=+
−
=
−
∑~/
11
1
11
ξξ
,
where ~
pir
m denotes the price of the imported brand r, and ti the ad valorem tariff rate.
8
3. The strategic interaction among firms
As suggested by Smith and Venables (1988), τis and δis also depend on the perceived effect of the
firm’s action on industry aggregate supply. In this section, I will show that τis and δis are each a
function of two conjectural variation parameters, since a domestic firm also has conjectures about how
rival domestic and foreign firms respond. Thus, assume that domestic and foreign firms do respond to
rivals’ output choices with constant conjectures.
From (12), the inverse demand function can be log-linearised as
(16) ln ~ln ln ~lnpDdp
is
dii iis i
d
=−+11ςς .
By definition the derivative of (16) with respect to ln ~
dis yields the inverse of the price elasticity
of domestic demand perceived by a firm:
(17) 11 1
τς ς
is i
i
is i
i
d
is
dD
dd
dp
dd
=−+
ln
ln ~ln
ln ~.
The appendix shows that under symmetry among domestic firms and constant conjectures
(18)
()
11111 11
111
11
1
τ ς ες χε
ϕ
ϕµλ
ες
ς
iiiii
i
ii
i
i
i
i
i
it
ts
is
i
n
M
D
d
d
i
i
i
=− − − + −
+−
+
−−
≠−
∑
Ψ
~
~,
where
[]
Ψii
dii
dii
mi
pD pD pM=+
represents the domestic industry market share in the domestic
market;
χ
i is the absolute value of the price elasticity of aggregate demand; λ∂ ∂
iitis
dd=~~
denotes the
conjectured reaction of rival domestic firms, tn=−11,....., ; and
µ
∂∂
iii
MD= can be interpreted as
the conjectured reaction of foreign firms to the domestic firms’ action in the domestic market.
Regarding the price elasticity of aggregate demand, by using (4)-(6), it can be shown that
χ
iii
CQ=
(see appendix). This implies that
χ
i is endogenous and ranges between zero and one.
9
Similarly, the appendix shows that the inverse of the price elasticity of export demand perceived
by a representative firm is:
(19) 11111 11
111
11
1
δξ εξ χε
ϕ
ϕµλ
εξ
ξ
iiiii
i
ii
i
i
i
i
i
it
ts
is
i
n
D
E
e
e
ii
i
=− − − + −
+−
+
−−
≠
−
∑
***
***
*
*
***
**
*
~
~
Ψ,
where
()
Ψii
eii
eii
di
pE pE p D
***
=+ denotes the domestic industry market share in the foreign market;
pi
e is the price index of exports, Ei; pid* is the domestic price index of foreign goods, Di*; χi
* the
absolute value of the price elasticity of aggregate demand in the foreign market; λ∂∂
*~~
=ee
it is denotes
the conjectured reaction of rival domestic firms; µ∂ ∂
**
=DE
ii
can be interpreted as the conjectured
reaction of foreign firms to the domestic firms’ action in the foreign market; εi
* and ϕis
* are the foreign
Armington elasticity of substitution and share parameter, respectively; and ξi
* is the elasticity of
substitution among n exported brands.6
Also the foreign industry is assumed to be imperfectly competitive. It can be easily shown that
the inverse of the price elasticity of import demand perceived by a representative foreign firm (
γ
i<−1)
is
(20)
()
()
11111
111
111
11
1
γξ εξ χε
ϕ
ϕµλ
εξ
ξ
iiiii
i
ii
i
i
i
i
i
m
iz
zr
ir
i
m
k
D
M
m
m
i
i
i
=− − − + − −
+−
+
−−
≠
−
∑
Ψ
~
~,
6 Note that in a multiregional framework, δi is also affected by the ratio between domestic firms’ exports and total exports
to a given region r. In a single country case, this ratio is obviously equal to one.
10
where λ∂∂
i
miz is
mm=~~
denotes the conjectured reactions of rival foreign firms, zk=−11,....., ; and
µ∂∂
i
mii
DM= can be interpreted as the conjectured reactions of domestic firms to the foreign firms’
action in the domestic market.
It is interesting to note that
()
lim
nii
→∞ =−11τς,
()
lim *
nii
→∞ =−11γξ and
()
lim
kii
→∞ =−11γξ. In
other words, the price cost margin of a firm would be equal to the inverse of the elasticity of
substitution among individual producers, as the number of brands converges to infinite. This result is in
line with the monopolistic competitive literature (Dixit and Stiglitz, 1977; Krugman, 1979).
The absolute value of (18)-(20) correspond to the price cost margin formula employed by HRT
(1997b) if, and only if, λµλµλµ
iiiii
mi
m
===== =
** 0 (Cournot competition). The formulas
employed by HRT (1997b) are therefore a specific case of the general formulation presented in this
study.
Equations (18)-(20) are consistent with the theory, which argues that a more collusive outcome
is obtained for positive conjectural variations, if
ς
ε
χ
ii i
>>, ξεχ
ii i
** *
>> and ξεχ
ii i
>>.
In order to get further insights regarding the expressions which define the price markups in the
domestic and foreign markets, it is very useful to compute the total differential of (18), (19) and (20).
Since, they are very similar expressions, I report only the total differential of (18), which is:
(21)
()
()
dnAdn nGB d d CdD
M
i
i
ii
i
ii
ii
ii
i
ii
i
i
11111
22
τλ
χε χ
χ= −+−
−
+
ΨΨ,
where
()
Gn
ii i
=− +11λ,
()
AB
iiiiiii
=−+ −11 11ες χεΨ,
()
()
BMD
ii
iiii i
i
=+ − −
11 1
ϕϕ µ
ε and
()()()()
()
CMD
iii i iiiii i
ii
=−− −
Ψ111 1
χε ϕεϕ µ
εε . This exercise allows one to arrive at the following
conclusions under the assumptions that
ς
ε
χ
ii i
>>:
11
• new entry of domestic firms leads to a fall in the domestic price markup if
()
λii
A−<10;
• a larger aggregate price elasticity (in absolute value) in the domestic market implies a larger price
elasticity of demand perceived by a domestic firm (in absolute value) in the domestic market if
BG
ii
>0;
• an increase in the market share of the domestic industry implies a rise in the price markup in the
domestic market if BG
ii
>0;
• a rise of domestic sales relative to the import volume implies a rise in the price markup in the
domestic market if CG
ii
>0.
All these conditions are fulfilled if
µ
i≥0 and
()
11
1
−<<
−
nii
λ. However, a variety of possibilities are
given to modellers, if they believe that the imperfect competitive industry behaves according to
different strategic interactions. Similar results can be obtained by calculating the total differential of
(19) and (20). Hence, a check on the value of λi, λi
*, λi
m,
µ
i, µi
* and µi
m is very useful to understand
and interpret the numerical results.
4. A CGE model for Turkey
The single country 3-sector CGE model presented in this section examines how robust is the model to
alternative conjectural variation parameters. Given the fact that the model is working at an extremely
aggregate level, one should interpret the results simply as numerical exercises to test the capacity of the
model. Nevertheless, the outcome might result to have an useful empirical application, because Turkey
has markedly reduced its trade barriers on industrial goods in the 1990’s. Hence, the construction of a
12
CGE model with imperfect competition and scale economies, and the study of the elimination of
Turkish tariffs on industrial goods can be empirically relevant.7
The CGE model contains two categories of industries: those where perfect competition and
CRS are assumed to prevail (agriculture and services), and that which is characterised by IRS
(industry). The production function has a two stage nested CES structure. At the first stage, I assume a
Leontief function among primary factors of production and intermediate inputs, which are in turn
assumed to be net complements. At the second stage, the elasticity of substitution among the mobile
labour and the mobile capital is assumed to be positive. The production possibility frontier of the
industries facing perfect competition and CRS is a CET specification of domestic products and exports,
treated as imperfect substitutes. On the demand side, the representative household demand, government
spending, and the intermediate demand are satisfied by a composite of domestic and imported goods, as
described in section 2.2. Government spending is set exogenously, so it does not play any role. The
household demand is derived from a Cobb-Douglas utility function. The country is assumed to be price
taker for the commodities traded internationally, with the exception of exports produced by sectors
facing IRS, for which a downward sloping demand curve is supposed. The latter has been derived by
assuming that an hypothetical foreign consumer purchases a variety of domestic goods and a variety of
Turkish exports, treated as their substitutes (see the appendix). Foreign domestic production is set
exogenously. The trade balance and the public budget balance are always in equilibrium. With regard to
the sectors facing imperfect competition and IRS, expressions (1), (2), (3), (7), (10), (A8) and (A10)
endogenously determine ni, ~
pis
d, ~
pis
e, Di, ~
dis , Ei and ~
eis . Similarly, the zero profit condition and the
7 CGE studies, which have examined the economic implications of Turkish trade policies in the 1990’s, are those of HRT
(1997a), Mercenier and Yeldan (1997), and De Santis (2000).
13
price cost margin for the foreign firm, plus (8) and (11) determine ki, ~
pir
m, Mi and ~
mir . I postulate that
the Turkish trade liberalisation policy does not have any impact on foreign factor prices.
Regarding the numéraire of the model, the domestic price of agricultural goods is normalised to
unity. It is well known that the choice of the numéraire matters in general equilibrium models with
imperfect competition (Gabszewicz and Vial, 1972; Dierker and Grodal, 1986; Ginsburgh, 1994).
However, as suggested by Ginsburgh (1994) and Ginsburgh and Keyzer (1997), in models where
markets are competitive for some commodities, all agents take the prices on the competitive markets as
given. Hence, a numéraire among the prices of these goods can be chosen. This choice does not solve
the problem per se, but at least the behaviour of oligopolists would not be affected (Cripps and Myles,
1988).
4.1 Benchmark and calibration
The theoretical model outlined above and applied to Turkey requires a benchmark data set to calibrate
unknown parameters, such that the observed value of endogenous variables constitutes an equilibrium
of the numerical model. The main bulk of the data comes from the official 1990 Input-Output table for
Turkey (see Table 1). The activities and commodities are disaggregated into 3 different types:
agriculture, industry and services.
[Insert Table 1 here]
In order to calibrate the variables of the sector facing IRS, the algebraic structure of the model
required further information on price-cost margin, fixed costs and the number of symmetric firms. I
assume that labour and capital inputs used in fixed proportion are 60% of the primary factor inputs.
This allows me to calibrate the marginal cost and the cost disadvantage ratio, which is equal to 16.3%. I
also assume that the number of domestic and foreign firms is 50 each. The number of firms is large
14
enough to avoid problems associated with integer values. The elasticity of substitution among domestic
brands and among foreign brands is set equal to 7, such that
()
11
01
−<<
−
nii
!
λ,
()
11
01
−<<
−
nii
!*
λ and
()
11
01
−<<
−
kii
m
!
λ, which yield !
Biv>0 and !
Civ≥0 (v denotes the domestic market, the import market
and the export market); except for the scenario labelled ‘CV4’, where I assume a more competitive
behaviour among domestic and foreign rivals firms, µi
m<0, which yields !
Bim=0, !
Cim<0 and
()
!
λi
mi
k<− −
101 if ξi=3.8 This permits the calibration of the firms’ perceived price elasticities in each
market.
The conjectural variation parameters Ωi
v and λi
v are endogenously calibrated. Under the HRT
formula, the conjectural variation parameters in the domestic ( !
Ωi), export market ( !*
Ωi) and import
market ( !
Ωi
m) are calibrated as follows: !!
!
Ωiii
=−θτ 1, !!
!
*
Ωiii
=−θδ 1, and !!
!
Ωi
mii
=−θγ 1, where !
θi
denotes the calibrated price cost margin, which is assumed equal to the cost disadvantage ratio for both
domestic and foreign firms. Thus, !
θi is equal to 0,163. Under the correct approach, the conjectural
variation parameters in the domestic ( !
λi), export market ( !*
λi) and import market ( !
λi
m) are calibrated as
follows:
(21)
()
()
()
()
[]
()
!
!
!!!!
,
λθς
ες χε ϕϕ µ
ε
i
ii i
iiiii iiii i
i
n
MD n
i
=−
−+ − +− −
−
−
−
0
00
10
01
1
11 1111 11
Ψ
(22)
()
() ()
()
()
!
!
!!!
,
*
*
*** * * *
**
*
λθξ
εξ ε ϕ ϕ µ
ε
i
ii i
iii i i iii i
i
n
DE
n
i
=−
−+ − + −
−
−
−
−
0
00
10
01
1
11 111 1
11
Ψ
8 Variables and parameters with ^ mean that they are calibrated, whilst variables with 0 are observed in the base year.
15
(23)
()
()
()
()
()
[]
()
!
!
!!!!
.λθξ
εξ χε ϕ ϕ µ
ε
i
mii i
ii iii i iii i
mi
k
DM k
i
=−
−+− − + − −
−
−
−
0
00
10
01
1
11 1 111 1 11
Ψ
The conjectural variation parameters
µ
i, µi
* and µi
m are set exogenously. It is important to note that
(21) can be re-arranged as
()
!!!
Gn A
iii ii
=−
01θς . If !
θς
ii
>1,
!
Gi has the same sign of !
Ai. Hence, if !
Ai
is required to be positive and !
Gi is required to be negative, then !
θς
ii
<1 . This result can be extended
to the other markets. This is the reason why the elasticity of substitution among imported brands is set
equal to 3 in ‘CV4’. Note also that if the benchmark values of the relative prices are equal to one, as it
is often postulated in the literature, then (21)-(23) reduce to
(21a)
()
()
[]
()
!
!
!!,λθς
ες χε µ
ipp
ii i
iiiii i
i
i
di
m
nn
00
0
0
01
1
11 111 11
=
−
=−
−+ − +−
−
Ψ
(22a)
()
()
[]
()
!
!
!,
*
*
***** *
*
λθξ
εξ χε µ
ipp
ii i
iiiii i
i
i
di
e
nn
00
0
0
01
1
11 1 11 11
=
−
=−
−+ − +−
−
Ψ
(23a)
()
()
()
[]
()
!
!
!!.λθξ
εξ χε µ
i
m
pp
ii i
ii iii i
mi
i
di
m
kk
00
0
0
01
1
11 1 1 11 11
=
−
=−
−+− − + −
−
Ψ
Table 2 shows the calibrated quantity conjectures [(21a)-(23a)] and the price elasticities
perceived by domestic and foreign firms under the HRT approach and the correct approach. The
conjectural variation parameters are very close to the Cournot case, though those under the HRT
approach are slightly larger. The price elasticities are also very similar among the two approaches. Note
that the approach proposed in this study permits one to set the absolute value of the price elasticity
perceived by firms equal to the inverse of the price cost margin, and to calibrate the conjectured
reactions of rival firms. The study considers four alternative constant quantity conjectures:
16
µµ µ
ii i
m
00 0
0===
* (i.e. CV1 scenario); µµ
ii
00
6==
* and µi
m
00= (i.e. CV2 scenario); µµ
ii
00
0==
*
and µi
m
030= (i.e. CV3 scenario); µµ
ii
00
0==
* and µi
m
01=− (i.e. CV4 scenario).
[Insert Table 2 here]
Table 3 reports the sign of the calibrated expressions, which affect the price markups in the
three markets. Note that ςεχ
ii i
>>
!, ςε
ii
**
>>1 and ξεχ
ii i
>>
!. As a result, the individual producer
can charge a larger price cost margin in the three markets if: (i) the conjectural variations parameters
are positive; (ii) its industry concentrates; (iii) the market share of its industry increases; (iv) the sales
of its industry rise relative to the sales of the rivals; (v) the absolute value of the price elasticity of
aggregate demand becomes smaller.
[Insert Table 3 here]
4.2. Scenarios: Partial trade liberalisation in Turkey
The policy experiment consists of eliminating the tariff rate levied on Turkish industrial imported
goods (i.e. the benchmark ad valorem tariff rate is 20.74%), under the hypothesis that the firm’s output
choice on how to react to its rivals’ output choices is given a priori and is independent of the trade
policy impact. As public revenues decline with a tariff fall, endogenously determined net transfers to
the representative consumer ensure that the government budget is in equilibrium. The CGE model
assumes free entry/exit. Hence, the benchmark generates a long run reference equilibrium by setting
pure profits to zero. This reference equilibrium is then the basis for comparison in counterfactual trade
policy analysis. Four alternative constant quantity conjectures have been employed: µµ µ
ii i
m
00 0
0===
*
(i.e. CV1 scenario); µµ
ii
00
6==
* and µi
m
00= (i.e. CV2 scenario); µµ
ii
00
0==
* and µi
m
030= (i.e.
CV3 scenario); µµ
ii
00
0==
* and µi
m
01=− (i.e. CV4 scenario). The results are shown in Table 4.
17
[Insert Table 4 here]
Firstly, I run a scenario where all sectors are perfectly competitive and have CRS (i.e. CRS
scenario). In accordance with the CGE literature, the welfare gains (measured by the Hicksian income
equivalent variation) are very small: 0,3% of the consumer income. According to the benchmark data
set, 36% of industrial imported goods are used as intermediate inputs by the industry. Hence, despite
the rise of the import volume in industrial goods by 11,6%, industrial production rises by 0,5%, driven
by cheaper imported intermediate inputs and by a large increase in exports.
The imperfect competitive models (i.e. HRT, CV1, CV2, CV3 and CV4) present a completely
different picture compared to the CRS scenario with regard to both welfare and sectoral production.
The results indicate that the approach suggested by HRT, which implicitly assumes Cournot
competition among domestic and foreign firms, produce similar findings compared to those obtained
with the conjectural variation approach, where Cournot competition is explicitly postulated (CV1).
However, if domestic firms believe that foreign firms will increase their production as they growth
(CV2), or if foreign firms believe that domestic firms will change production as they expand, that is
µi
m≠0 (CV3 and CV4), then the results can change even dramatically.
Firstly, let me discuss the scenario HRT and CV1, as the results are very similar. A fall in tariff
in industrial goods leads to an increase in industrial imports by 14,7-14,9% and reduces the protection
enjoyed by domestic firms. As a result, the equilibrium number of domestic firms declines by 5,3-5,5%,
while the number of foreign firms increases by 13,5-14,2%. However, a fall in the protection rate does
not imply a large output contraction, because of the scale effect due to the use of intermediate imported
goods in the production process of industrial goods. The welfare level, however, remains constant
because market concentration leads to two opposite effects which seem to offset each other: a more
efficient use of the economic resources, but higher domestic prices. Given the revealed comparative
18
advantage in industry and services compared to agriculture, the trade balance equilibrium is achieved
via an increase in exports in these two sectors. Resources are therefore pulled out from both agriculture
and industry, and shifted to services which expands by 3,6%. It must be stressed that an increase in
output per firm in the domestic market (1,6-2,1%) does not imply a decline in the price cost margin (as
suggested by Horstmann and Markusen, 1986), because the negative impact on the number of firms
(which leads to an increase in the price cost margin) dominates both the negative impact on the
domestic industry market share and the positive impact on the aggregate price elasticity (which lead to
a decrease of the price cost margin). With regard to the export market, since the number of firms
declines and the market share increases, then the price cost margin in the export market increases,
despite firm’s exports rise by 26,9-27,1%. In the import market, the market structure effect seems to
dominate slightly the industry market share effect. As a result, the price cost margin of the foreign firms
declines.
If, by contrast, some form of collusion between domestic and foreign firms is hypothesised
(CV2 and CV3), then a welfare loss can be generated, as a result of the trade liberalisation policy. The
scenario ‘CV2’ is based upon the assumption that domestic firms believe that foreign firms will expand
their output if they growth. This more collusive behaviour is reflected in a higher price cost margin in
the domestic market, which rises by 3,2%, and a smaller output per firm, which declines by 1,1%.
Technically this is due to the fact that !
Ai is almost six times that in ‘CV1’ (see Table 3). Hence, the
negative market structure effect plays a bigger role in determining the higher equilibrium price markup
in the domestic market. The consequent fall in domestic sales in the industrial sector by 4,8% is the
main reason why welfare declines by 0,2%. The scenario ‘CV3’ is based upon the assumption that
foreign firms expect the rival domestic firms to expand their production, as imports increase due to a
tariff fall. This conjecture limits entry of foreign firms, whose number rises by only 4,3% and causes a
19
large expansion of the size of existing firms by 13,4%. The fact that µi
m>0 implies that !
Bim>1 and
!
Cim>0 . Hence, the foreign industry market share effect and the effect of the import volume relative to
domestic sales play a bigger role compared to the previous scenarios. This is the reason why the price
cost margin of the foreign firms declines by 10,1%. As a result of a fall in foreign prices, domestic
demand is satisfied by a larger volume of industrial imports, which increases by 18,4%. Despite that,
welfare declines by 0,1%.
If foreign firms expect the rival domestic firms to reduce their output as they expand (i.e.
µi
m<0), then the results change dramatically (CV4). This conjecture favours the entry of new foreign
brands in the domestic economy. The equilibrium number of foreign firms increases by 35,3%. The
scale effect on industrial production is so large that manufacturing output expands by 3,2%. The fact
that µi
m=−1 implies that !
Bim=0 and that !
Aim is very small. Hence, if the market structure effect has a
small role in affecting the price markup, the foreign industry market share effect does not play any role
to explain the 28,6% increase in the price cost margin. What matters is the effect of the import volume
relative to domestic sales, which contracts. As a consequence of the scale and variety effects, and of the
better allocation of resources within the Turkish economy (i.e. domestic firm’s output increases by
8,1% and the number of domestic firms declines by 4,5%), welfare rises by 2,7% of the consumer
income, a large increase compared to the previously discussed scenarios.
5. Summary
This study proposes a procedure to embody the conjectural variation approach in CGE models, which
are characterised by scale economies and free entry in order to capture the strategic interactions among
rival firms in international markets. The model is similar to that used by HRT (1997b) to examine the
20
regional impact on output and welfare of the reforms of the Uruguay Round, when firms compete in a
quantity setting oligopoly with calibrated constant conjectures. It assumes that the price cost margin
faced by national firms is endogenous, and derives the price elasticities of demand perceived by a firm
in a multistage demand system.
I show that the price elasticities of demand perceived by a firm in the domestic and export
markets are a function of the conjectured reactions of the rival domestic and foreign firms. I show also
that the formulas suggested by HRT can be obtained under the hypothesis of Cournot competition. I
indicate an approach to calibrate the conjectural variation parameters, and I set up a CGE model for
Turkey for the empirical analysis. The numerical simulations indicate that the HRT approach, which
implicitly assumes Cournot competition among domestic and foreign firms, leads to the same outcome
produced with the conjectural variation approach of this study, when Cournot competition is explicitly
postulated. However, if foreign firms believe that domestic firms reduce their output as they expand
due to trade liberalisation, then the results change dramatically, and a large welfare gain can be
generated. One of the contributions of this study is that the conjectural variation of domestic and
foreign firms can be modelled within large-scale applied general equilibrium models. This would allow
modellers to assess better the effects of economic policies once the strategic interactions among
domestic and foreign firms are known.
21
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24
Appendix
• Derivation of (18)
Given (10)
(A1)
()
∂
∂λ
ςς
ς
ς
D
dDd
d
d
i
is
iis
it
ts
is
ii
i
i
~~
~
~
=+
−
−
≠−
∑
11
1
1
1,
Since from (12) Dd p p
iis is
di
d
ii
11ςς
~~
−=, then
(A2)
()
dD
dd
pd
pD
d
d
i
is
is
dis
idi
it
ts
is
i
i
ln
ln ~~~~
~
=+
−
≠−
∑
1
1
1
ς
ςλ.
Since, by using the chain rule, ∂
∂
∂
∂
∂
∂
p
d
p
D
D
d
id
is
id
i
i
is
~~
=, then
(A3)
()
dp
dd
pd
pD
D
p
p
D
d
d
id
is
is
dis
idi
i
idid
i
it
ts
is
i
i
ln
ln ~~~~
~
=+
−
≠−
∑
∂
∂λ
ς
ς
1
1
1.
Given the symmetry assumption, (A3) and (A2) into (17) yield
(A4)
()
1111 1
1
1
τς ς
∂
∂λ
ς
ς
iiii
i
id
id
i
it
ts
is
n
D
p
p
D
d
d
i
i
=− + +
+
−
≠−
∑~
~.
By applying similar steps at the second stage of the demand tree, then
(A5) D
p
p
D
M
D
i
id
id
ii
i
ii
i
i
i
i
i
∂
∂εεχ
ϕ
ϕµ
ε
=− + −
+−
−
111
111
Ψ,
where
()()
χ∂∂
iiiii
pQ Q p=− . Equation (A5) into (A4) yields expression (18).
25
• Derivation of the price elasticity of aggregate demand
The price elasticity of aggregate demand can be derived by using (4)-(6), as follows:
χ∂
∂
∂
∂
∂
∂
∂
∂
ii
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
Q
p
p
Q
p
Q
X
p
C
p
p
Q
X
p
C
Q
=− =− +
=− + .
Under a Leontief specification ∂∂Xp
ii
=0 . To show this assume that production is undertaken by
using intermediate inputs only, which are substitutes. Then, the intermediate demand can be written as
XapqY
bbb
=−, where
()
[]
()
qap ap
bb bbb
=+−
−−
−
11
11
1, p is the price of intermediate goods X, p the
price of other intermediate good, a a share parameter, and b the elasticity of substitution among inputs.
In this case,
()
[]
∂∂Xp baYp q apq
bbb b b
=− −
−− −
11
1 , which means that
()
lim ∂∂Xp
b→
=
00 . Since I assume
a Leontief specification between value added and intermediate inputs, which are in turn assumed to be
net complements, then ∂∂Xp
ii
=0 . Given the Cobb-Douglas utility function, the price elasticity of
aggregate demand reduces to 01≤= ≤
χ
iii
CQ .
• Derivation of (19)
Assume that an hypothetical foreign consumer purchases a variety of domestic goods, ~*
dir , and a variety
of goods exported by the country under analysis, ~
eis , which are treated as their substitutes. I can
describe the three-stage foreign utility function (U*) as follows:
(A6) UQ
jj
j
**
*
=
Πα,αj
j
*
∑=1
(A7)
()
()
()
()
QD E
iii ii
ii ii
ii
*** *
** **
**
=+−
−−−
ϕϕ
εε εεεε
111
1,
(A8)
() ()
Ee
iis
s
n
ii
ii
=
−
=
−
∑~**
**
//
ξξ
ξξ
1
1
1
, ξi
*>1,
26
(A9)
() ()
Dd
iir
r
k
ii
ii
**
//
~**
**
=
−
=
−
∑ςς
ςς
1
1
1
,ςi
*>1.
Qi
* denotes foreign total sectoral demand and ςi
* the elasticity of substitution among k varieties
produced and consumed abroad.
The first order condition of the second-stage utility maximisation problem yields the vector of
the export demand functions, which is employed in the numerical model:
(A10) Ep
pD
ii
i
id
iei
ii
=−
−
ϕ
ϕ
εε
*
*
*
*
**
1.
The first order conditions of the third-stage utility maximisation problem yield the lower level
demands:
(A11) ~~
**
epp E
is i
e
is
e
i
ii
=−ξξ
,
()
()
pp
ieis
e
s
n
i
i
=
−
=
−
∑~*
*
/
1
1
11
ξξ
,
(A12) ~~
*** *
**
dppD
ir idir
di
ii
=−ςς
,
()
()
pp
idir
d
r
kii
**
/
~*~
=
−
=
−
∑1
1
11
ςς
.
By using the same technique shown to derive (18), one gets expression (19).
27
Fig. 1 The Demand System
Consumer demand Intermediate demand FIRST STAGE
Armington good SECOND STAGE
- Competition among domestic
and foreign firms
Imports Domestic goods THIRD STAGE
- Competition among domestic firms
- Competition among foreign firms
Brand ................... Brand Brand ................... Brand
(1) (k) (1) (n)
28
Table 1: The benchmark data set for Turkey
Share
Billion of
1990 TL Agriculture Industry Services
Domestic sales 514105 0,177 0,360 0,463
Exports 52060 0,048 0,513 0,439
Imports 69033 0,038 0,903 0,059
Import duties 13396 0,035 0,965 0,000
Labour 96257 0,316 0,134 0,551
Capital 178661 0,180 0,250 0,570
Intermediate demand for agricultural goods 40060 0,373 0,554 0,074
Intermediate demand for industrial goods 158654 0,053 0,588 0,358
Intermediate demand for services 92533 0,083 0,420 0,498
Private consumption 262204 0,204 0,368 0,427
Government spending 43083 0,012 0,118 0,870
Elasticities
Labour / Capital 1,4 1,4 1,4
Domestic goods / Imports 2,0 2,0 2,0
Domestic goods / Exports 2,0 - 2,0
Domestic brands 7,0
Foreign brands 7,0 (3,0)
Source: SIS (1994) for the national account statistics.
29
Table 2: Calibrated conjectures and firms’ price elasticities
Conjectural variation parameters Price elasticities
Domestic Export Import Domestic Export Import
market market market market market market
HRT 0,036 0,085 0,065 - 6.365 - 6.664 - 6.541
CV1 -0,010 0,036 0,000 - 6,144 - 6,144 - 6,144
CV2 -0,019 0,033 0,000 - 6,144 - 6,144 - 6,144
CV3 -0,010 0,036 - 0.019 - 6,144 - 6,144 - 6,144
CV4 -0,010 0,036 - 1.065 - 6,144 - 6,144 - 6,144
HRT: Harrison-Rutherford-Tarr approach;
CV1: Correct approach under the assumption that µµ µ
ii i
m
00 0
0===
*;
CV2: Correct approach under the assumption that µµ
ii
00
6==
* and µi
m
00=;
CV3: Correct approach under the assumption that µµ
ii
00
0==
* and µi
m
030=;
CV4: Correct approach under the assumption that µµ
ii
00
0==
* and µi
m
01=− .
Table 3: The sign and the size of !
Giv, !
Aiv, !
Biv and !
Civ
!
Gi!
Ai!
Bi!
Ci!*
Gi!*
Ai!*
Bi!*
Ci!
Gim!
Aim!
Bim!
Cim
CV1 + 0,52 + 1,92 + 1,00 0,00 + 2,76 + 0,36 + 1,00 0,00 + 1,03 + 0,99 + 1,00 + 0,00
CV2 + 0,09 + 11,28 + 7,00 18,06 + 2,62 + 0,38 + 7,00 0,00 + 1,03 + 0,99 + 1,00 + 0,00
CV3 + 0,52 + 1,92 + 1,00 0,00 + 2,76 + 0,36 + 1,00 0,00 + 0,05 + 20,02 + 31,00 + 2,47
CV4 + 0,52 + 1,92 + 1,00 0,00 + 2,76 + 0,36 + 1,00 0,00 - 51,2 + 0,17 0,00 - 0,08
CV1: Correct approach under the assumption that µµ µ
ii i
m
00 0
0===
*;
CV2: Correct approach under the assumption that µµ
ii
00
6==
* and µi
m
00=;
CV3: Correct approach under the assumption that µµ
ii
00
0==
* and µi
m
030=;
CV4: Correct approach under the assumption that µµ
ii
00
0==
* and µi
m
01=− .
30
Table 4: The impact of the elimination of tariffs on industrial imported goods
CRS HRT CV1 CV2 CV3 CV4
Welfare 0,003 0,000 0,000 -0,002 -0,001 0,027
AgrIndSerAgrIndSerAgrInd SerAgrInd SerAgrInd SerAgrInd Ser
Output -0,019 0,005 0,005 -0,056 -0,006 0,036 -0,058 -0,008 0,036 -0,061 -0,017 0,036 -0,063 -0,014 0,040 -0,009 0,032 0,009
Domestic sales -0,020 -0,017 -0,005 -0,056 -0,036 0,015 -0,058 -0,038 0,014 -0,061 -0,048 0,013 -0,063 -0,047 0,016 -0,009 0,015 0,005
Export volume 0,046 0,158 0,108 -0,056 0,201 0,248 -0,058 0,202 0,251 -0,061 0,199 0,256 -0,063 0,214 0,278 -0,009 0,144 0,050
Import volume -0,058 0,116 -0,067 0,056 0,147 -0,175 -0,058 0,149 -0,177 -0,061 0,151 -0,183 -0,063 0,184 -0,192 -0,009 -0,006 -0,039
Domestic industry market share -0,056 -0,078 -0,079 -0,080 -0,083 -0,069
Export industry market share 0,157 0,090 0,091 0,091 0,096 0,065
Foreign industry market share 0,165 0,233 0,234 0,238 0,245 0,205
Number of domestic firms -0,055 -0,053 -0,037 -0,058 -0,045
Number of foreign firms 0,142 0,135 0,136 0,043 0,353
Domestic firm’s domestic output 0,021 0,016 -0,011 0,012 0,064
Domestic firm’s exports 0,271 0,269 0,246 0,289 0,198
Domestic firm's aggregate output 0,052 0,048 0,021 0,047 0,081
Foreign firm's output 0,004 0,013 0,013 0,134 -0,265
PCM in the domestic market 0,004 0,008 0,032 0,008 0,007
PCM in the export market 0,003 0,002 0,003 0,003 0,002
PCM in the import market -0,003 -0,011 -0,011 -0,101 0,286
Aggregate demand price elasticity 0,016 0,016 0,017 0,016 0,047
Agr: Agriculture; Ind: Industry; Ser: Services. PCM: Price cost margin.
CRS: All sectors have constant returns to scale and are perfect competitive; HRT: Harrison-Rutherford-Tarr approach; CV1: Correct approach under the assumption that
µµ µ
ii i
m
00 0
0===
*; CV2: Correct approach under the assumption that µµ
ii
00
6==
* and µi
m
00=; CV3: Correct approach under the assumption that µµ
ii
00
0==
* and
µi
m
030=; CV4: Correct approach under the assumption that µµ
ii
00
0==
* and µi
m
01=− .
31
