Chapter 4

A Market with Autonomous Economic Decision

Makers: Features of the CGE Model

Alternative to the standard linear programming model in the previous chapter,

where the central planner is the maximising actor, economic models have been

developed that attempt to capture the endogenous role of prices and the workings of

the market system, where the essence of the general equilibrium problem is the

reconciliation of maximising decisions made separately and independently by

various actors. The objective of this literature is to convert the Walrasian general

equilibrium structure, from an abstract representation of an ideal economy (Arrow

and Debreu model 1954) into numerical estimates of actual economies.

In the construction of applied general equilibrium models two different

approaches must be emphasised.1 On one hand, the computable general equilibrium(CGE) models introduced by Adelman and Robinson (1978), extending the

approach of Johansen (1960),2 which, given a set of excess demand equations,

simulate the behaviour of producers and consumers to study the competitive

adjustment mechanism of a system of interdependent markets. One the other

hand, the activity analysis general equilibrium (AGE) models introduced by

Ginsburgh and Waelbroeck (1975) and Manne (1977), which are characterised by

inequality constraints and specified as a mathematical programming problem to

examine the optimisation solutions of which are a competitive equilibrium. The

linear programming model, based on the traditional Koopmans activity model, was

presented in the previous chapter. Now, we will present the basic features of the

CGE-model.

1 See Bergman (1990) for a survey of the development of the computable general equilibrium

model. See also Borges (1986).2 The first successful implementation of an applied general equilibrium model is due to the

pathbreaking study by Johansen (1960) of the Norwegian economy. Johansen retained the fixed-

coefficients assumption in modeling intermediate demand, but employed Cobb-Douglas produc-

tion functions in modeling the substitution between capital and labour services and technical

change.

R. Noren, Equilibrium Models in an Applied Framework,Lecture Notes in Economics and Mathematical Systems 667,

DOI 10.1007/978-3-642-34994-2_4, # Springer-Verlag Berlin Heidelberg 2013

55

4.1 The Basic Structure

Rather than being a single maximisation problem, the CGE model involves the

interaction and mutual consistency of a number of maximisation problems sepa-

rately pursued by a variety of economic actors. The problem involves the reconcili-

ation of distinct objectives and not only the maximisation of a single indicator of

social preference.3 As we know from Chap. 2, the duality theorem ensures that the

objective function of the dual will equal, at optimum, the objective function of the

primal. Thus, an overall budget constraint is satisfied. Nothing guarantees, how-

ever, that the budget constraints of the individual actors in the economy are

satisfied. The essence of the general equilibrium problem is the reconciliation of

maximising decisions made separately and independently by various actors in an

economic system. In that sense, this problem is absent from the standard linear

programming model, where the central planner is the only maximising actor. That

is to say, the problem arises when one attempts to go from the shadow prices of

linear programming model to the market-clearing prices of general equilibrium

theory.4 Theoretically, market equilibrium prices are prices at which the demand

and supply decisions of many independent economic actors maximising their

profits and utilities given initial endowments are reconciled.

In the CGE model we incorporate the fundamental general equilibrium links

representing the decentralised interaction of various actors in a market economy.

Thus, prices in the CGE model must adjust until the decisions by the producers are

consistent with the decisions made by the various actors representing final demand.

This implies that the model includes a general feedback mechanism that would

require an adjustment in prices, i.e., and the workings of market-clearing processes.

In addition, the CGE model can accommodate different types of distortions, such as

taxes and tariffs or monopolistically fixed factor prices. However, most CGE

models conform only loosely to the theoretical general equilibrium paradigm.

The CGE model seems to address issues we recognise from macro-econometric

models. But what are then the differences between the traditional macro-

econometric models and the CGE models? In short, the macro-econometric models

have a very high content of statistics, but almost no content based on economic

theory. In other words, one tries to find a pattern in the data, i.e., subsequently

explained by economic phenomena. The macro-econometric models are located

somewhere in between, drawing both on classical statistical methods as well as

some economic theory. The macro-econometric models usually address macro

issues such as the role of inflation or Keynesian unemployment. In this respect,

the empirical content is crucial in the macro-econometric model but the connection

to economic theory (optimisation behaviour) is small.

3 A presentation of the theoretical structures underlying the CGE models and their relationship to

economic theory, see: Dervis et al. (1982).4 Taylor (1975).

56 4 A Market with Autonomous Economic Decision Makers: Features of the CGE Model

With CGE modelling, however, one starts with a theoretical model, i.e.,

maximisation behaviour of the individual actors in the economy, and then finds

data that fits the model. The used data are estimated independently and which are

reported in the literature and are then calibrated to represent a situation close to

general equilibrium. The CGE model cannot address macro issues such as the role

of inflation or Keynesian unemployment but market-clearing prices, and thus,

questions of economic efficiency, is important. Consequently, the content of eco-

nomic theory is crucial but the weakness is the lack of empirical validation of the

model.

The empirical implementation of general equilibrium models starts with Leif

Johansens (1960) path-breaking MSGmodel of the Norwegian economy. However,

it was in the early 1970s that a major breakthrough made possible the development

of detailed and complex general equilibrium models, which could be solved

computationally. The breakthrough was the introduction of an algorithm for the

solution of the general equilibrium problem, i.e., for the computation of equilibrium

prices – which was developed by Herbert Scarf (1967). The most striking aspect of

this algorithm was its general nature. In fact, it was guaranteed to converge, i.e., find

the equilibrium vector of prices, under most general conditions. Since the algorithm

is based on the proof of existence of equilibrium prices, and actually follows the

steps used in that proof, it is guaranteed to work without any constraints on the

specification of the model, apart from the general requirement that excess demand

functions be continuous and that Walras’s law be observed.5

There is no precise definition of a CGE model. The group of related numerical

multisectoral economic models usually referred to as CGE models has a set of

common features. One of these is that both quantities and prices are endogenously

determined within the models. In this respect CGE models differ to a great extent

from input–output and programming models. Another feature is that CGE models

in general can be numerically solved for market clearing prices for all product and

factor markets. CGE models are generally focused on the real side of the economy,

although financial instruments and financial markets are included in some models.

The CGE approach descends directly from the work of Arrow and Debreu

(1954) and uses the Walrasian general equilibrium framework calibrated by real-

world data to ensure consistency with observed empirical facts. CGE models can

also be seen as a logical culmination of a trend in the literature on planning models

to add more and more substitutability and nonlinearity to the basic input–output

model.

Nevertheless, existing CGE models have often retained the assumptions of fixed

coefficients for intermediate technology and the compositions for capital

commodities. In contrast, the production technology for primary factors is

described by a neoclassical production function that allows smooth substitution

among several factor inputs. The degree of substitution is governed by the elasticity

of substitution specified. Intermediate inputs are required according to fixed

5 For a general discussion, see Shoven and Whalley (1992), pp. 37–68.

4.1 The Basic Structure 57

input–output coefficients; aggregated labour and capital are combined to create

value added according to a specified production (Cobb-Douglas or CES) function.

Aggregate labour is an aggregation of labour of different types, and the aggregate

capital used in each sector is a linear aggregation of capital commodities from

different sectors. Sectors are assumed to maximise profits, and labour demand

functions come from the first order conditions equating the wage with the marginal

revenue product of labour of each category.

For each sector, the production function describes the technology available.

Given the level of demand by sector, producers minimise costs by using optimal

quantities of primary factors and intermediate commodities as a function of their

relative prices. Once the optimal combination of inputs is determined, sectoral

output prices are calculated assuming competitive supply conditions in all markets.

Since each sector supplies inputs to other sectors, output prices and the optimal

combination of input are determined simultaneously for all sectors. The assumption

of perfect competition in commodity markets amounts to assuming that firms take

commodity price as given. Under these circumstances one can treat each sector as

one large price-taking firm.

Domestic supply of each sector is given by a constant-returns Cobb-Douglas or

CES production function with labour of different skill categories and sector-specific

capital stocks, which is assumed fixed within each period, subject to depreciation.

This implies that current investment will add to capacity only in future periods.

Hence the production function (ex post) will exhibit decreasing returns to scale in

labour, the only variable. Unit production costs will be a function of the level of

output, and a given sector can always maintain international competitiveness by a

suitable change in the scale of operation. Thus, complete specialisation is avoided.

4.2 The Construction of a Simple CGE Model

In this section we will discuss the construction of a simple computable general

equilibrium model (CGE model).6 Our example is a model of constant to returns to

scale production functions. We use the Cobb-Douglas production function with

constant returns to scale to illustrate the fact that with a linear homogenous

production function it is possible to derive factor demand functions and unit cost

equations. First we set up a formal model for an economy with constant returns to

scale in production, and then extends the analysis by showing how inter-industry

flows (input–output flows) and a foreign sector can be included in the model.

The nature of supply and demand functions is dictated by economic theory. The

consumer is assumed to maximise utility subject to a budget constraint which states

that the household’s total expenditure on commodities (consumption, denoted X)must be equal to the consumer’s income R.

6 The model is based on Dinwiddy and Teal (1988).

58 4 A Market with Autonomous Economic Decision Makers: Features of the CGE Model

Maximise U ¼ UðX1; Xi; . . .XnÞ (4.1)

Subject to p1X1 þ piXi; . . . pnXn ¼ R (4.2)

From the solution to the consumer’s constrained optimisation problem come the

demand relations

X1 ¼ X1ðp1X1 þ piXi; . . . pnXn;RÞ (4.3)

showing that consumption depends upon commodity prices and income.

The Cobb-Douglas production function is assumed to be linear and homogenous,

increasing all the factor inputs by a given proportion will lead to an equi-

proportionate increase in output (Zj), i.e., there are constant returns of scale.

Zj ¼ Kαj L

1�αj (4.4)

Using the v and w to represent respectively the prices of capital and labour the

total cost (TC) of the representative firm is given by

TCj ¼ vKj þ wLj (4.5)

From Eq. 4.4 we can solve for Kj in terms of Zj and Lj:

Kj ¼ ZJ

LJ1�α

� �1α

(4.6)

Substituting Eq. 4.6 in Eq. 4.5, and minimising this function with respect to Lj,gives the necessary condition:

@TCJ

@LJ¼ �v

1� α

α

� �ZJLJ

� �1α þ w ¼ 0 (4.7)

Solving for Lj, to find the conditional demand for labour:

Lj ¼ 1� α

α

v

w

� �α

Zj (4.8)

Similarly, we can solve for Lj, from Eq. 4.4 in Eq. 4.5, and minimising this

function with respect to Kj, gives the necessary condition:

Lj ¼ ZJKJ

α

� � 1

1� α(4.9)

4.2 The Construction of a Simple CGE Model 59

Substituting Eq. 4.9 in Eq. 4.5 gives a functioning that is minimised with respect

to Kj and thus gives the necessary condition:

@TCJ

@KJ¼ v� w

α

1� α

� � ZJ

KJ

� � 1

1� α ¼ 0 (4.10)

Enables us to derive the conditional demand for capital:

Kj ¼ α

1� α

w

v

� �1�αZj (4.11)

The two Eqs. 4.8 and 4.11 represent the two conditional demands for the factors

of production labour and capital when the firm’s production function is given by the

constant returns of scale version of the Cobb-Douglas function.

These two equations (unit cost equations) can be written in terms of factor

demand per unit of output (value added) by dividing both sides of the equation by

Zj. Denoting the per unit factor demands for capital and labour by the lower case

letters kj and lj, we have

kj ¼ KJ

ZJ

� �¼ α

1� α

w

v

� �1�α(4.12)

lj ¼ LJZJ

� �¼ 1� α

α

v

w

� �α

(4.13)

showing that the per unit factor demands are functions of the two factor prices rand w. By using these two equations the expression defining the firm’s profit can be

written in terms of kj and lj, i.e., the unit profit equation

Πj ¼ pjZj � vkjZj � wljZj (4.14)

This makes it clear that the perfectly competitive profit-maximising firm with

constant returns to scale will make zero profits. Only with zero profits can a firm

with a constant return to scale technology be in equilibrium, and this equilibrium is

compatible with any one of the set of possible output levels. The unit cost (price)

equation can also be written in terms of k and l.

Pj ¼ vkj þ wlj (4.15)

Note, that there is no supply function with constant returns to scale. This implies

that we must use the unit cost function above.

In the open economy model it is assumed, for simplicity, that commodity 1 is

exported (E) and commodity 2 is imported (M). Thus

E ¼ Z1 � X1 (4.16)

M ¼ X2 � Z2 (4.17)

60 4 A Market with Autonomous Economic Decision Makers: Features of the CGE Model

With this in mind, we have now to incorporate inter-industry flows

(input–output) in the model. We assume two firms and two commodities, 1 and 2.

Total output (Z) of the two firms is given by:

Z1 ¼ a11Z1 þ a12Z2 þ X1 þ E1 (4.18)

Z2 ¼ a21Z1 þ a22Z2 þ X2 �M2 (4.19)

We can now more closely see the relationship between total output (Z) and

value added. The assumption of fixed coefficients for intermediate inputs implies

that there is no substitution possible between these inputs. The production function

now compromising the intermediate inputs zij together with the value-added

components, i.e., Kj and Lj. This can be written:

Zj ¼ zij;K:αj L

:1�αj i ¼ 1; 2 (4.20)

In order to preserve full-employment of our model, we shall assume that

substitution between the primary factors K and L is possible, and that it still

represents a linear homogeneous function. This will again mean that price the per

unit of output will be equated with the unit cost of production. In the input–output

model, cost per unit will include not only capital and labour costs, but also the cost

per unit of inter-industry inputs. Thus, the unit prices for the two firms are:

p1 ¼ a11p1 þ a21p2 þ vk1 þ wl1 (4.21)

p2 ¼ a12p1 þ a22p2 þ vk2 þ wl2 (4.22)

In this simple model we are assuming that the total quantity of capital and labour

are fixed. The market clearing equations therefore take the form:

K1 þ K2 ¼ K� (4.23)

L1 þ L2 ¼ L� (4.24)

The household’s income R has to be defined. The household not only supplies

the factor service (labour), but is also the sole shareholder in the economy. The

income of the household is therefore defined by the following equation:

R ¼ vðK1 þ K2Þ þ wðL1 þ L2Þ (4.25)

The economy engaged in world trade is presented with given world market

prices, p1W and p2

W, which will not be affected by the country’s level of exports (E)and imports (M). Thus, the open economy includes two set of prices, endogenous

domestic production costs and exogenous world market prices. The open economy

4.2 The Construction of a Simple CGE Model 61

also includes the exchange rate (ER). Hence, the world market prices are converted

to domestic prices by:

p1 ¼ ER p1W (4.26)

p2 ¼ ER p2W (4.27)

The world market prices, p1W and p2

W , are treated as exogenous variables in a

small open economy. For commodities in trade, the domestic production costs

are, in equilibrium, equal to the exogenous world market prices. ER is, however,

an endogenous variable.

Assuming here that capital flows are excluded from the model, the balance of

payments equation may be described as:

p1WE� p2

WM ¼ 0 (4.28)

The general equilibrium system is now complete. It consists of 20 equations in

the following 20 endogenous variables: X1, X2, Z1, Z2, K1, K2, L1, L2, k1, k2, l1, l2, p1,p2, w, v, R, E, M. and ER. In addition there are eight exogenous variables: a11, a12,

a21, a22, p1W , p2

W , K*, and L*.The model:

Commodity markets

Household demand X1 ¼ X1(p1, p2, R) (1)

X2 ¼ X2(p1, p2, R) (2)

Unit price equations p1 ¼ a11p1 þ a21p2 þ vk1 þ wl1 (3)

p2 ¼ a12p1 þ a22p2 þ vk2 þ wl2 (4)

Market clearing: (Commodity markets) X1 ¼ a11Z1 þ a12Z2 � E (5)

X2 ¼ a21Z1 þ a22Z2 þ M (6)

Factor markets

Demand k1 ¼ k1(w,v) (7)

K1 ¼ k1Z1 (8)

k2 ¼ k2(w,v) (9)

K2 ¼ k2Z2 (10)

l1 ¼ l1(w,v) (11)

L1 ¼ l1Z1 (12)

l2 ¼ l2(w,v) (13)

L2 ¼ l2Z2 (14)

Market clearing: (Factor markets) K1 þ K2 ¼ K* (15)

L1 þ L2 ¼ L* (16)

Household’s income

R ¼ v(K1 þ K2) þ w(L1 þ L2) (17)

Foreign sector

Price equations p1 ¼ ER p1W (18)

p2 ¼ ER p2W (19)

Balance of payments p1W E � p2

W M ¼ 0 (20)

62 4 A Market with Autonomous Economic Decision Makers: Features of the CGE Model

We often assume that exports and domestically sold commodities, as above, are

perfect substitutes. This specification of export supply, however, over-states both

the links between exports and domestic prices and the responsiveness of exports to

demand shifts on world markets. With the possibility to specify foreign trade, not

only as perfect substitutes as in the linear model, but as a close substitute to

domestic production, and a substitution that can vary according to specification,

the CGE model offers a greater capacity to reflect empirical evidence. As a result,

export prices for any commodity may differ from world market prices as well as

from prices paid on the domestic market, and a country may export and import

commodities in a given sector. In this way the model captures the phenomena of

intra-industry trade. This represents a significant departure from the “small country

assumption” of traditional trade theory in which countries can export any amount

of a given commodity at a given price and nothing at a higher price. Since the

possibility to specify substitution (in production, foreign trade and demand) is very

essential in the CGEmodelling approach, the technique is presented more closely in

the next section. We choose the just discussed, and most frequent, example –

foreign trade.

4.3 Foreign Trade: The CES and CET Specification

In the closed economy the basic technological and demand variables determine the

domestic shadow price system. However, the situation is quite different in a free

trade economy where the domestic market is small in relation to the world market.

Given the assumption of perfect substitutability between imported and domestically

produced commodities, the small-country assumption implies that the individual

country becomes a price taker facing exogenous world market prices. The theory of

international trade suggests that, as far as some commodities are actually imported

or exported, the domestic shadow prices among them tend to converge to their

relative world market prices. Consequently, world market prices determine the

domestic shadow prices of tradables, and a given commodity has (at equilibrium)

the same price whether it is imported or produced domestically. Hence, whereas

supply and demand determine domestic shadow prices in a closed economy, they

will adjust to world market prices in the small open economy.

Needless to say, extreme specialisation in production and trade conflicts with

empirical evidence, which on the contrary, shows a relatively little specialisation on

the sector level. However, the observed combination of domestic production and

trade may be in complete accordance with the theoretical model. First, the country

under study consists of many regions, which implies that a commodity may be

imported to one region and exported from another, but never be both imported to

and exported from one single region. Second, the same argument is applicable

to the fact that the model is specified to cover a period of some length. Hence, a

commodity may be both produced and traded at different points of time during the

4.3 Foreign Trade: The CES and CET Specification 63

period of specification. Finally, the commodities of the model are aggregates of

different commodity categories. For each of these commodities the theoretical

requirement may be fulfilled.

In the standard small-country assumption, often made in international trade

theory, a traded commodity is assumed to be one for which the single country is

a price-taker and the domestically produced commodity is a perfect substitute for

that sold in the world market. The earlier discussion has already stressed that the

small-country assumption leads to the result that the domestic price of a traded

commodity is equal7 to its world price (PWi). Moreover, we also stressed that

assuming perfect substitutability implies that there is no product differentiation

between imports and domestic products and that a commodity will either be

exported or imported but never both (intra-trade is eliminated). This implies that

changes in world market prices, exchange rates and tariff rates, are entirely trans-

lated into changes in domestic prices, and hence, exaggerate the effects of trade

policy over the domestic price system and the domestic economic structure. Fur-

thermore, the small country assumption together with an assumption of constant

returns to scale in production, leads to a tendency toward extreme specialisation in

production that is not always desirable.8 In the discussion above we have repeatedly

stressed that extreme specialisation in production and trade conflicts with empirical

evidence (Flam 1981; Lundberg 1988), which on the contrary shows a considerable

amount of intra-industry trade even within rather disaggregated production sectors.

At a level of high aggregation, each sector represents a bundle of different

commodities. In this model,9 we solve this problem by relaxing the perfect substi-

tutability assumption. Instead, we stipulate that for any traded commodity, imports

Mj (perfectly elastic in supply) and domestically produced commodities xZj are not

perfect but relatively close substitutes. Thus, we relay on the Armington (1969)

assumption that commodities of different origin are qualitatively different

commodities. Formally, we define for each tradable commodity category a com-

posite (aggregate) commodity xj, which is a CES utility function of commodities,

produced abroad (imports, Mj) and commodities produced domestically, xZj . We

have:

xj ¼ ACj δjM�ρjj þ ð1� δjÞxZ�ρj

j

h i�1=ρj(4.29)

where ACj is the CES function shift parameter, δj , the value shares (distribution

parameter) of imports in total domestic expenditure is a constant, and σj , the

7Differences may exist due to transportation costs and tariff rates.8 Samuelson (1952).9 The computable general equilibrium (CGE) model to be described is a variant of the model

developed by Dervis et al. (1982). This section is, in certain parts, based on Condon, Dahl and

Deverajan (1987).

64 4 A Market with Autonomous Economic Decision Makers: Features of the CGE Model

elasticity of substitution between the two sources of supply in all domestic uses, is

given by σj ¼ 1=ð1þ ρjÞ.This formulation implies that consumers (at home as well as abroad) will choose

a mix of Mj and xZj (inputs in the CES utility function “producing” the composite

output xj) depending on their relative prices.10 Minimising the cost of obtaining a

unit of utility (the composite commodity xj):

pjxj ¼ pZj xZj þ pMj Mj (4.30)

Subject to Eq. 4.29 yields:

Mj

xZj¼ pZj

pMj

!σjδj

1� δj

� �σj

(4.31)

where pZj denote the domestic commodity price and pMj denote the domestic currency

price of imports (domestic currency outlay of imports). Thus, the solution is to find a

ratio of inputs (Mj to xZj ) so that the marginal rate of substitution equals the ratio of the

price of the domestically produced commodity to the price of the imported commod-

ity. In standard trade theory the trade substitution elasticity is infinity so that pZj ¼ pMj. If pZj exceeds p

Mj , x

Zj would have to be zero. Equation (4.3) allows for a richer set of

responses,11 but as σj gets larger, the responsiveness of Mj=xZj to changes in pZj =p

Mj

rises. In that case pZj =pMj will stay close to its base value and we approximate the case

wherepZj , at the equilibrium, will stay fixed topMj . On the other hand, ifσj is very low,

large changes in pZj =pMj may take place.12 Thus, as a result of this specification, pZj is

no longer fixed to pMj , it is endogenously determined in the model. The variable pMj ,

however, is linked to the exogenously fixed world market price, pWj by:

pMj ¼ pWj ER (4.32)

where ER is the exchange rate (fixed initially in the model). This implies that we

maintain the assumption of exogenously fixed world market prices of imports.

Turning to export demand standard trade theory assumes that a small country

faces a perfectly elastic demand for its exports. This implies that any balance of

payment problem can be solved by an indefinite expansion of exports at constant

10 Consequently, there can be both import and export of each category of tradable commodities in

equilibrium.11 If the trade substitution elasticity equal unity, the CES utility function reduces to a Cobb-

Douglas utility function.12 In the extreme case where sigma is zero, Mj=x

Zj would be fixed, and imports become perfect

complements of domestic products.

4.3 Foreign Trade: The CES and CET Specification 65

world market prices of the most profitable commodities. This profile of trade may

not be realistic for many countries. While they may not be able to affect the world

market prices with their exports, the countries may register a declining market share

as their domestic costs rise. In addition, increasing selling costs will normally

reduce the net return from exports as the quantity is increased. The most satisfying

way to reflect this situation would be a specification were export demand Ej is a

decreasing function of the domestic export costs (prices) in foreign currency. If we

let pEj denote the domestic currency price of exports (domestic currency receipts of

exports)13 and pWj , as above, the world market price in foreign currency (exoge-

nously fixed), we would have:

pEj ¼ pWj ER (4.33)

Given the assumptions of standard trade theory, the variable pEj is linked to the

exogenously fixed world market price pWj . However, assuming product differentia-

tion leads to less than infinitely elastic demand functions for exports. The individual

country is still regarded as a small country in the world market, hence, pWj is

assumed exogenously fixed. But the foreign currency price of a particular country’s

exports, denoted pWEj , is endogenously determined by its domestic production costs

pZj (average output price), and exchange rate policy ER. We get:

pWEj ¼ pZj

ER(4.34)

Consequently, we consider the following constant elasticity export demand

function:

Ej ¼ Eoj

PWj

pWEj

!nj

(4.35)

where nj is the price elasticity of export demand and Eoj is a constant term reflecting

total world demand for each commodity category and the country’s market share

when, at equilibrium,pWj ¼ pWEj . Logically, the domestic currency price of exports is:

pEj ¼ pWEj ER (4.36)

Given the fact that our country is small, changes in pWEj will not affect pWj , but it

will have effects on our country’s market share for aggregate commodity category j.

13 Foreign currency is here regarded as an intermediate commodity (not desired in itself), where

the import process requires foreign currency as input, and foreign currency is the output of the

export process.

66 4 A Market with Autonomous Economic Decision Makers: Features of the CGE Model

For example, a devaluation of the exchange rate leads to a fall in pWEj and hence,

with constant pWj , an increase in its market shares. Conversely, an increase in

domestic production costs, pZj , leads to an increase in pWEj , and with constant pWj , its

market share will decline. This implies that export prices pEj (or pWEj ) are no longer

fixed to the world market price in foreign currency pWj . The small-country assump-

tion, requiring fixed terms of trade, will no longer hold. Consequently, the small

country assumption is retained only in the sense that world market prices pWj on

international traded commodities is to be regarded as given.

On the supply side exports is usually derived residually by subtracting domestic

demand from total domestic production. Given the standard small-country assump-

tion, domestic production will expand until domestic production costs rise to the

world market price level. As long as domestic production costs are lower than

established world market prices, it will be profitable to expand domestic production

for exports.14 As a result, export supply may exhibit an excessively strong response

to changes in domestic prices. When a domestic price rises, producers are induced to

increase supply and domestic consumers to reduce their demand. The net result is a

dramatic increase in exports. However, in reality, exports may not rise this fast,

because the domestically consumed and exported commodities in the same sector

may be quite different. Thus, the small-country assumption together with the

assumption that the supply of exports is simply the difference between total domestic

production and domestic absorption may in several cases greatly overestimate the

responsiveness of export supply, and again, the problem increases with the degree of

aggregation. Hence, we postulate a constant elasticity of the transformation (CET)

function between domestically consumed xZj and exported Ej commodities:

Zj ¼ ATj γjEjϕj þ ð1þ γjÞxjZ

ϕjh i1=ϕj

(4.37)

Zj is domestic output, ATj is the CET function shift parameter, γj is a constant,

and the elasticity of transformation τj is given by: τj ¼ 1=ð1� ϕjÞ.Maximising the revenue from a given output:

pZj Zj ¼ pZj xZj þ pEj Ej (4.38)

Subject to Eq. 4.37 yields the following allocation of supply between domestic

sales and exports:

Ei

xZi¼ pEi

pZi

� �τi 1� γiγi

� �τi

(4.39)

14On the other hand, if the domestic price is greater than the world market price, the commodity

will not be produced.

4.3 Foreign Trade: The CES and CET Specification 67

This leads to the export price pEj (or pWEj ) diverging from the domestic price pZj .

The supply of exports by sector is a function of the ratio of the price in domestic

currency of exports. This treatment partially segments the export and the domestic

markets. Prices in the two markets are linked together but need not be identical.

Imports and domestic products are assumed to be imperfect substitutes. Imports and

domestic commodities are combined according to a CES trade aggregation func-

tion, with consumers demanding the composite commodity. The trade substitution

elasticity determines the extent to which import shares adjust in response to changes

in relative prices. For both exports and imports, the word price in foreign currency

is assumed to be constant – the small country assumption.

4.4 Concluding Remarks

The model is Walrasian in that only relative prices matter. This proposition reflects

the well-known fact that if all prices increase in the same proportion, but relative

prices are unaltered, the relationships in the economy remain unchanged. On order

to solve the model to find the equilibrium prices, we arbitrarily set one price equal

to one, and then solve the system for all other prices. The commodity with price set

equal to unity is known as the numeraire commodity, and the prices of all other

commodities are determined in terms of the numeraire. Provided the general

equilibrium is homogeneous of degree zero it does not matter which commodity

is chosen to be the numeraire. However, in applied models it is convenient to use a

price-normalisation rule that provide a no-inflation benchmark against which all

price changes are relative price changes.15

According to Walras’s law, there cannot be a situation of aggregate excess

demand or supply. In other words, if one market has positive excess demand,

another must have excess supply, to such an extent that in value terms they cancel

out. To see that Walras’s law always hold, it is sufficient that, the total value of

output, and the total value of expenditures balances. This result will always be true

if all economic agents meet their budget constraints. Because each spending unit’s

demand are subject to a budget constraint which says that outlay must equal

income, it is clear that such a budget constraint also hold in the aggregate and

will hold not only at equilibrium, but for all allowable price vectors. The static

model as presented above has no formal link between capital formation and

production capacity. Capital commodities are assumed exogenous without any

correspondence to the effect that is created by the supply of investment from sectors

producing capital commodities (investment in final demand).

15 See Dervis et al. (1982), p. 150.

68 4 A Market with Autonomous Economic Decision Makers: Features of the CGE Model

Appendix: A Summary of Models Presented

The presentation of multisectoral general equilibrium models in this study is now

complete. Here follows a summary of the most essential features:

The Linear Model

The central planner is assumed to be the only maximising actor.

No market (prices and quantity) interaction. In the linear programming model

we interpret the shadow prices that result as a by-product of the solution as

equilibrium prices.

These prices cannot be interpreted as market-clearing prices of general equilib-

rium theory because endogenous prices and general equilibrium interaction to

simulate competitive market behaviour cannot be achieved.

Foreign trade specified as perfect substitutes to domestic production. Only inter-

trade, i.e., full specialisation.

An optimum solution may only be at a vertex or an extreme point.

The Quadratic Model

The quadratic model is an improvement of the welfare function.

The model in Chap. 3 is formulated in terms of the maximisation of the sum of

consumer’s and producer’s surplus. See also page 317–319 in Nicholson. But still

the central planner is assumed to be the only maximising actor.

The existence of a two way feedback in which quantity can influence price and

price can influence quantity for each sector (market interaction), is developed.

Foreign trade specified as perfect substitutes to domestic production. Only inter-

trade, i.e., full specialisation (because the linear constrains are retained).

The optimum value of the objective function might occur anywhere in the

feasible set, but not necessarily at a vertex or an extreme point.

The Computable General Equilibrium (CGE) Model

Alternative to the standard linear (and quadratic) programming model, where the

central planner is the only maximising actor, the CGE model has been developed to

capture the endogenous role of prices and the workings of the market system.

Decisions: The essence of the CGE model is the reconciliation of maximising

decisions made separately and independently by various actors.

Appendix: A Summary of Models Presented 69

Prices: The model includes a general feedback mechanism that would require an

adjustment in prices, i.e., the workings of market-clearing processes. Theoretically,

market equilibrium prices are prices at which the demand and supply decisions of

many independent economic actors maximising their profits and utilities, given

initial endowments, are reconciled.

Foreign trade: With the possibility to specify foreign trade, not only as perfect

substitutes as in the models above, but as a close substitute to domestic production,

and a substitution that can vary according to specification, the CGE model offers a

more close relation to empirical evidence. In this way the model captures the

phenomena of intra-industry trade.

The reader has to note, that both a neo-classical production function of the value

added component, and inter-industry flows (the input–output flows) in the com-

modity balance equations can be incorporated in the CGE model.

Real World Applications: The GAMS Program

If you are interested in the practical application of real word problems the GAMS

computer program is recommended. GAMS homepage is www.gams.com. Here

you will find the GAMS program library. Here you will also find reference to

literature, tutorials, and course outlines on GAMS.

A short, and here recommended, description on programming in GAMS is AGAMS Tutorial. The handbook A Standard Computable General Equilibrium(CGE) Model in GAMS can be used as a reference book for further studies. Note,

that some references are rather extensive in the number of pages. Hence, study the

reference first on screen, and then print out only the selected parts you need.

The GAMS program itself (student version) can be installed on your computer. It

is possible to download the program (student version) on your own private com-

puter from the GAMS homepage. If you choose to download the GAMS program

from the GAMS homepage, read the instructions carefully.

MPSGE is a mathematical programming system for general equilibrium analy-sis which operates as a subsystem within GAMS. MPSGE simplifies the modelling

process and makes AGE modelling accessible to any economist who is interested in

the application of these models. http://www.gamsworld.org/mpsge/index.htm.

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