[Lecture Notes in Economics and Mathematical Systems] Equilibrium Models in an Applied Framework...

Chapter 5

An Applied Model: The CGE Mini Model

In this chapter a CGE model (the CGE mini model1) is presented. The model is

simple enough to be presented in a few pages and yet complicated enough to

demonstrate the application of the general CGE structure. In short, the focus of

this chapter is to provide examples of structural adjustment in an open economy.

The numerical applications of this chapter will be an examination of the sensitivity

of the model to systematic variation in key variables of the adjustment process.

Here we emphasise the effect of changes (government intervention) in the fixed rate

of real exchange and growth in the capital stock.

5.1 The Basic Structure of the CGE Model

The behaviour of economic agents in this model is designed according to neoclas-

sical microeconomic theory with relative prices playing a major role in the deter-

mination of economic activities. Producers minimise costs subject to a given

production technology, and consumers maximise utility given their total expendi-

ture determined as a constant fraction of their income. Firms (within 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. The model assumes perfect competition in all markets and domestic

and foreign commodities are treated as imperfect substitutes according to

1 The CGE mini-model is included in the GAMS model library which is distributed with the

GAMS system. The CGE mini-model is a minor version of an equilibrium model that originally

comes from Chenery, Lewis, de Melo, and Robinson in their work in designing an equilibrium

development model for Korea. The model is originally designed for the study of three develop-

ment strategies. The first option was the strategy of export expansion, the second option was the

strategy of import substitution, and the third option was a strategy between the two extreme cases.

This model illustrates the basic use of CGE models. See further: Chenery et al. (1986),

pp. 311–347.

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

DOI 10.1007/978-3-642-34994-2_5, # Springer-Verlag Berlin Heidelberg 2013

73

Armington’s (1969) specification. Exports are determined by an exogenous foreign

demand and the relative export price is measured in foreign currency.2 Prices in the

foreign markets are linked but need not be identical to the domestic market.

However, the world price in foreign currency (dollars) is assumed to be exogenous,

i.e., the small country assumption.3

Thus, the CGE model simulates the working of a market economy. In each

period, it solves for wages and prices that clear the markets for labour and

commodities. The model is Walrasian in that only relative prices matter. The

numeraire against which all relative prices are measured is defined as an index of

domestic prices. The model satisfies Walras’s law, which implies that there cannot

be a situation of aggregate excess supply or demand. However, the model also

comprises non-tradable commodities. Non-tradable commodities are commodities

that are not subject to international trade. Government service as well as housing fit

this category. Intermediate inputs are required according to fixed input–output

coefficients; aggregate labour and capital are combined to create value added

according to a Cobb-Douglas production function. The labour market is segmented

in three distinct categories. Each labour category linked to respective sector. There

is no mobility of labour between sectors within periods. 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.

Sectoral capital stocks are fixed within periods, but they change over time given

aggregate growth of the capital stock. Investment is allocated endogenously to

make sectoral rental rates equal. These general characteristics of the CGE model

were stipulated in the preceding chapter. Applications of theoretical models will

often involve a number of compromises in order to make the models more realistic

and more useful in an applied setting.

However, the model does not take into account future markets despite the fact it

explicitly considers time. There is no intertemporal optimisation4 and the agents

have no expectations about future prices. Given this formulation, the model does

not embody the true concept of a dynamic model but rather is akin to comparative

static’s, which analyses periods as a number of discrete moments, using a static

model for each of these moments. Our study is focused on structural adjustment in

pure market variables only. In this model, that implies that improvements in

technology and technological substitution in the process of production, an impor-

tant source of industrial innovation and structural renewal (Freeman 1974), is

omitted as an endogenous variable in the analysis. The explanation is the technical

2 Note, that the export demand function (Eq. 4.35) is not included in the CGE mini model.3 In other words the word price in foreign currency is given. The reader must note, that price

incentive policy such as taxes, subsides, and tariffs are now explicitly incorporated. Domestic

prices can be altered by the government by changes in price incentive policy, and hence, affect the

economic structure.4 In intertemporal models, agents have rational expectations and future markets are considered

when optimising. Endogenous variables follow an optimal path over time and there are no

incentives to deviate from this path at any point of time.

74 5 An Applied Model: The CGE Mini Model

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assumptions that underlie the input–output accounting system. By systematically

generating and incorporating changes in the aggregate technical coefficients, tech-

nological substitution and improvements in technology can be introduced exoge-

nously. Moreover, all investments are in established industries and hence,

according to the specification of the model, directed to the production of a given

set of commodities. In this model a balance between savings and investment is

achieved by setting total investment equal to the sum of domestic and foreign

savings. Thus, total investment is determined by savings in the economy (saving

determined investment). A fixed fraction of the foreign capital inflow is assumed to

enter directly into savings. The reminder being saved by the sectors and a portion of

it being used as private consumption. Domestic savings is made up of government

and private savings. Private savings is in this model specified as a rising function of

GDP. That implies that a rising GDP will increase investment. In the total savings

equation, Eq. 5.33, total depreciation expenditure is included. For example, an

increase in total depreciation expenditure would increase savings, and thus the total

level of investment.

In the real world, investments made to increase the total capacity as well as the

replacement and scrapping of old production units change the production

characteristics. New capacity have in general input–output proportions different

from those of existing production units due to changed relative prices and technical

progress, and in the long run, production of commodities which cannot be found

within the initial production possibility set.

As the reader will recall, the numeraire against which all prices are measured is

defined as an index of domestic prices. Thus, variations in the nominal exchange

rate in the model directly affect the ratio of the price – in domestic currency – of

imports and exports to the price of domestic sales and in that way represent a

change in the real exchange rate. A devaluation increases the domestic price of

imports and exports relative domestic sales, and thus, encourages exports and

import substitution.5 With the price normalisation, the formal presentation of the

core equations of our extended CGE model is complete. The description above

sketches only the particular characteristics of our model. A detailed description of

all mathematical equations is presented in an appendix to this chapter.

5.2 The Numerical Experiments

Given the specification above, we will now be equipped with a numerical general

equilibrium model designed as a tool to determine the optimum resource allocation

and, given the numerical results, the significance of equilibrium. The equilibrium

conditions in the model include a supply–demand balance in three different types of

market: labour, commodity, and foreign exchange. A fourth macroeconomic

5 For a discussion, see Dervis et al. (1982), pp. 192–197.

5.2 The Numerical Experiments 75

equilibrium condition is the balance between saving and investment, i.e., the macro

closure of the model.6

With reference to Dervis et al. (1982)7 the model can easily degenerate into a

magic black box that yields quantitative results but do not really add to our

understanding of the mechanisms governing the model. Considering this comment,

the experiments are designed to outline the basic adjustment mechanisms that will

determine the direction, and hence, the fundamental structure of the solutions.

Following Chenery et al. (1986) the model contains three institutions, namely

production sectors, factors of production, and household types. The production

system comprises three production sectors. The production sectors; agriculture,

industry, and service, represent the whole economy. The production sectors are

associated with a specific labour category, namely agricultural labour, industrial

labour, and service labour.8 Each household category is characterised by a single

type of factor it owns and supplies. Here, there will be two categories of

households; labour household and capitalist household. The labour household

supplying the three different kind of labour and receive the wage rate of value

added, and the capitalist household being the owners of capital and receive the

residual value added.9

Given the assumptions of the model the economy is assumed to be in equilib-

rium, a so called benchmark equilibrium. A benchmark equilibrium data set is a

collection of data in which equilibrium conditions of an assumed underlying model

are satisfied. The benchmark dataset is calibrated to the base year data.10 Calibra-

tion is the process of assignment of numerical values to the model parameters. The

purpose of calibration procedure is to make sure that the solution of the model

reproduces exactly the observed statistics of the base year, and then we only use

base year data as input.11 The method is to calculate values of shift and share

parameters of production functions, Armington functions, and CET functions.12

Since we do not accomplish an empirical comprehensive study, but only use the

6 The choice of which variables are to be exogenous is called the model closure. In all experiments

in this book the exchange rate is fixed and the net flow of foreign borrowing is unfixed. Following

this specification, the trade deficit is free to vary.7 Dervis et al. (1982), p. 183.8 Alternatively, the sectors can be defined in terms of input characteristics; labour-intensive,

capital-intensive, and knowledge-intensive commodities.9 Note, that in equilibrium the expenditures of each household exhaust its income. However, in this

chapter we consider saving. In any case, total income generated in the system always equals total

national product at market prices.10 To compute benchmark equilibrium can also be an alternative if the benchmark year is not

accepted as a representative equilibrium.11 This assumes that the benchmark year is a representative equilibrium.12 The parameters of the functions are calibrated “backwards” from the benchmark dataset

(Petersen 1997). See Shoven and Whalley (1984, 1992). See also Condon et al. (1987).


model as an illustration, we shall use the data supplied with the CGE mini-model.13

As anyone who deals with empirical studies knows, obtaining adequate and reliable

data for the model is the most time-consuming task faced in the study. Therefore the

data collection in this numerical study is reduced to a minimum. The first task is to

present Table 5.1. The table below represents the benchmark equilibrium as it is

presented in the GAMS program library.14 The variables in Table 5.1, together with

the computations in each experiment, will make Tables 5.1, 5.2, 5.3, 5.4, and 5.5

self-contained.

Real exchange rate, general price level, foreign savings, and government con-

sumption are fixed. Capital stock has an upper limit in the short run. Since the CGE

mini model is applied for a particular country, Korea, the computations are in

billion won. Exchange rate is defined as won per dollar. Foreign savings, net

Table 5.1 Benchmark equilibrium

Agriculture Industry Services

Domestic prices 1.000 1.000 1.000

Rate of capital rent 1.000 1.000 1.000

Value added price 0.737 0.291 0.662

Composite commodity supply 711.644 930.351 497.443

Domestic output 657.368 840.050 515.430

Domestic sales 641.704 812.222 492.031

Exports 15.664 27.828 23.399

Imports 69.941 118.129 5.412

Capital stock 657.575 338.708 1548.519

Depreciation by sector 0 0 0

Intermediate uses 256.645 464.166 156.260

Private consumption 452.176 307.856 202.042

Government consumption 2.823 9.881 128.448

Investment by origin – 148.449 10.693

Investment by destination 20.688 46.151 92.302

Domestic price of imports 1.000 1.000 1.000

Domestic price of exports 1.000 1.000 1.000

Average output price 1.000 1.000 1.000

Price of composite commodities 1.000 1.000 1.000

Real exchange rate 1.000, General price level 1.000, Government revenue 194.555, Tariff revenue

28.657, Indirect tax revenue 65.275, Total household savings 66.569, Government savings 53.380,

Total depreciation expenditure 0.000, Total savings 159.142., Total investment 159.142, Foreign

savings 39.174, Net flow of foreign borrowing 58.759, Household tax revenue 100.617, and

Private GDP 1129.261

13As noted, the mini-equilibrium-model is included in the GAMS model library, which is

distributed with the GAMS system. Readers who have access to the GAMS program can thus

take an active part of the model developed here. Readers who also are interested in downloading

the current version of the GAMS distribution will find necessary information in the appendix of

this chapter and Chap. 4.14 See the end of the appendix for this chapter.


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remittances from abroad, and net flow of foreign borrowing is, however, expressed

in billion dollars.

With each equilibrium experiment, follows a presentation of the employment

results. LABOUR1 is agricultural labour, LABOUR2 is industrial labour, and

LABOUR3 is service labour.

Summary matrix with sectoral employment results

LABOUR1 LABOUR2 LABOUR3

Agriculture 2515.900 442.643 –

Industry – 767.776 –

Services – 355.568 948.100

Summary matrix with aggregate employment results


Average wage rate 0.074 0.140 0.152

Labour supply 2515.900 1565.987 948.100

We are now prepared to draw attention to the elaboration of the experiments, and in

this context, evaluate the results of the computations. As is well known, the choice of

Table 5.2 Physical deterioration of the capital stock






Domestic output 643.646 902.741 437.371

Domestic sales 620.343 875.410 423.609

Exports 22.424 27.320 13.311

Imports 44.568 129.840 4.560

Capital stock 657.575 338.708 1032.484

Depreciation by sector 40.964 52.689 160.796












Total depreciation expenditure 254.449, Total savings 343.935, Total investment 343.935, Foreign

savings 39.174, Net flow of foreign borrowing 48.280, Household tax revenue 72.461, and Private

GDP 813.256


endogenous variables are crucial when illustrating the equilibrium mechanism of the

model, and hence implicitly, the specification of numerical experiments.15 Remember,

in all experiments we assume that the exchange rate is fixed and the balance of trade is

endogenous, so that foreign capital inflow adjusts. This redefines the balance of

payments constraint. As a consequence, the value of imports no longer has to be

exactly equal to the value of exports. Further, the foreign capital inflow (net flow of

foreign borrowing) constitutes an addition to the income generated within the econ-

omy, and is also incorporated in the capital income equation.

5.2.1 Capital Stock Subject to Physical Deterioration

As well known to the reader, the capital stock is subject to physical deterioration.

The physical deterioration, depreciation expenditure rates (DEPRj), in this model

are now assumed to be 6 % in agriculture, 15 % in industry, and 15 % in services.

These coefficients have now been added in the equation representing the total

Table 5.3 Devaluation of domestic currency






Domestic output 644.007 899.780 430.067

Domestic sales 605.879 858.884 411.207

Exports 33.190 39.872 18.873

Imports 28.724 111.742 4.103

Capital stock 657.575 338.708 988.527












28.355, Indirect tax revenue 66.867, Total household savings 43.299, Government savings

�4.918, Total depreciation expenditure 249.678, Total savings 355.068, Total investment

335.068, Foreign savings 39.174, Net flow of foreign borrowing �10.169, Household tax revenue

65.460, and Private GDP 734.685

15 The model is solved by the GAMS program. A description of how the system of equations can

be implemented in GAMS, see Condon et al. (1987). See also Lofgren et al. (2002).


depreciation expenditure. That inclusion influences the basic numerical values of

the model. Since we only use this model as an illustration, the assumed values are

without empirical significance. The result from the new computation is presented in

Table 5.2 below.

Table 5.1 provides a comparative benchmark for this experiment. Notice, that

the value of marginal product of capital (rate of capital rent) is the same for all three

sectors. However, the issue of structural transformation naturally emphasises the

importance of including investment as well as disinvestment. Hence, the focus of

the presentation is principally directed to the depreciation expenditure and the

investment by destination. By the introduction of capital depreciation expenditure

rates in the equilibrium model part of the capital stock is not used for domestic

output. In model terms that part is now used for depreciation expenditure. The

direct effect will be a reduction in domestic output in agriculture and services, but

an increase in industry. The capital stock has physically been reduced in the

services sector (Table 5.2). Hence, the strong decrease in domestic output. Effi-

ciency in reallocation has not succeeded to compensate for this loss. The increased

investment in the first period is only the demand for investment. The physical

increase in real capital will be added to the capital stock in the subsequent period.

The assumed state of technology is determined by the production function shift

parameter in the production function. The next period will be presented in Table 5.5.

But we will first focus on the change in the real exchange rate.

Table 5.4 Appreciation of domestic currency






Domestic output 642.468 910.525 446.218

Domestic sales 628.567 892.097 435.946

Exports 13.891 17.037 8.539

Imports 73.868 155.595 5.158

Capital stock 657.575 338.708 1090.138














savings 39.174, Net flow of foreign borrowing 120.041, Household tax revenue 79.507, and

Private GDP 892.332




Agriculture 2515.900 323.690 –


Services – 363.908 948.100




Labour supply 2515.900 1565.987 948.100

5.2.2 A Change in the Real Exchange Rate

In the second experiment we start with an increase in the real exchange rate, i.e., a

devaluation of domestic currency (here won). We assume arbitrarily devaluation

Table 5.5 Growth in the domestic capital stock






Domestic output 646.272 941.866 444.970

Domestic sales 624.184 912.035 431.173

Exports 23.439 29.844 13.296

Imports 47.195 133.174 4.658

Capital stock 659.675 382.196 1063.822














savings 39.174, Net flow of foreign borrowing 51.953, Household tax revenue 73.938, and Private

GDP 829.836


by 20 %. We start from the computed equilibrium data in Table 5.2. Thus, Table 5.2

provides a comparative benchmark for this experiment. Table 5.3 presents the

results obtained.

What will be the consequences? Firstly, we have to consider the activities in

foreign trade. The devaluation affects exports and import prices uniformly. That is

confirmed in Table 5.3. Secondly, the devaluation is expected to expand the

production of exportables. For exports to expand, however, their foreign price

must decline on foreign markets. However, to get a more specific answer, we

must carry out a more detailed empirical study under a longer period of time.

That means that the capital stock must be permitted to adjust.

With fixed import prices in foreign currency, a devaluation leads to a deteriora-

tion in the terms of trade because the increased import prices in domestic currency

implies a fall in imports (short run effect) and an increased domestic import

substitution (long run effect). Thus, adjustment by devaluation affects both exports

and imports in each sector. Regarding the results in Table 5.3 (trade deficit

decrease) the beginning of such a change has started. The composite commodity

supply is decreasing in agriculture, industry and services. Domestic output has

increased in agriculture but decreased in industry and service. As a result of these

effects, GDP have decreased. This implies that devaluation in the short run has, in

most cases, a decreasing initial effect on output. We can only look at initial effect

because capital stocks are restricted to the predetermined values of one singe

period. Moreover, the foreign currency price of a particular country’s exports is

generally endogenously determined by its domestic production costs and exchange

rate policy. However, in this mini CGE model the export demand function,

discussed in Chap. 4 (Eq. 4.35), is not included. To reveal if the current account

follows a J-curve pattern,16 the study must include an elasticity export demand

function and comprise subsequent periods.



Agriculture 2515.900 326.396 –


Services – 366.583 948.100




Labour supply 2515.900 1565.987 948.100

In the next experiment (Table 5.4 below) we have a decrease in real ex-change

rate, i.e., an assumed appreciation of domestic currency by 20 %.

16 The J-curve describes the time lag with which a real currency devaluation improves the current

account.


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Again, we start from the computed benchmark equilibrium data. As expected,

the reverse to the experiment above is the case, i.e., all of the features from the

earlier experiment are preserved but in opposite direction. The experiments in this

section have illustrated an important trade-off in the open economy, namely the

trade-off between competitiveness, i.e., between increased import substitution

versus domestic structural renewal, and hence, potential export expansion. The

change in the real exchange rate has an influence on that balance. First we present

the summary, and then the Table itself.



Agriculture 2515.900 315.015 –


Services – 358.366 948.100




Labour supply 2515.900 1565.987 948.100

5.2.3 Growth in the Domestic Capital Stock

In the next experiment (Table 5.5 below) we go back to the first experiment

(Table 5.2), and ask ourselves what will be the consequences of growth in the

capital stock. Table 5.2 provides a comparative benchmark for this experiment.

Operationally, the solution for the first period is used to create the next period’s

model parameters. It will solve the market for equilibrium prices and quantities for

one period and then add the solution obtained to the pre-determined variables that

are needed to obtain the market equilibrium solution for the next period. The

sequence with links to equilibria does not refer to the calendar time. The outcome

sequence time index is named ‘period’. Thus, the solution for each period,

depending only on current and past variables, is used to create the next period’s

variables in the model. The model is solved as a sequence of static equilibrium, with

no intertemporal optimisation. Thus, the model is comparable with the approach

used and discussed in Chap. 3, the quadratic programming model. Dynamics appear

through changes in domestic and international conditions.17 The static equilibrium

represents an optimum for producers and consumers. The updated exogenous

variables and parameters specify cumulative dynamic process such as factor accu-

mulation and productive growth. The model is thus solved forward in a dynamically

17 For details, see the discussion in Chap. 3.


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recursive fashion.18 However, one important difference occurs, disinvestment

(depreciation expenditures) is specified in the CGE model, but was not in the

quadratic programming model.

For each period the sector capital stocks are adjusted. Given the computed data

of investment by destination minus computed total depreciation expenditure by

sector, added to the current sector capital stocks, will become the next period’s

sector capital stocks. The net sum of these changes in capital will be our definition

of growth.




Capital stock 657.575 338.708 1032.484

New capital stock 659.675 382.196 1063.822

The first period, the starting point of the temporary equilibrium computations, is

represented by the equilibrium solution presented in Table 5.2. The subsequent

period (Period 2) is presented in Table 5.5 below. In the second period the domestic

prices have increased in agriculture and services but have decreased in industry.

The composite commodity supply has increased in agriculture, industry and

services. Domestic output has increased in all three sectors, but it is most apparent

in industry. GDP has increased. The explanation is the growth in capital stocks.

Since the capacity expansion in capital stocks are assumed proportional, the result

has not demonstrated a change in the structure of production.

Depreciation expenditure by sector has decreased in agriculture but has

increased in industry and service. However, investment by destination has

increased in all three sectors. Rate of capital rent has decreased. The explanation

is again the growth in capital stocks. Exports have increased in agriculture and

industry but have decreased in service. Imports have increased in all three sectors.



Agriculture 2515.900 335.020 –


Services – 374.909 948.100




Labour supply 2515.900 1565.987 948.100

18 Recursive-dynamic CGE models are those which can be solved sequentially (one period at a

time): they assume that behaviour depends only on current and past states of the economy.


5.3 Concluding Remarks

Although we do not here present an exhaustive set of experiments, the workings of

the model have been clarified, and at the same time, the model has indicated how

future empirical applications might be implemented. Thus, we have been able to

examine the importance of different initial conditions and the economic structure

within a framework that imposes inter-sector consistency. The three numerical

experiments presented in this chapter would need to be justified by an empirical

analysis. However, the numerical input values have only been used as a concept in

our CGE model, in other words, the numerical values have not been derived from

any empirical observation.

This type of model can accommodate different types of distortions, such as taxes

and tariffs or monopolistically fixed factor prices. Consequently, the model used

here incorporates price-incentive variables that represent tools of policy makers.

These tools have not been discussed, and not been used as policy instruments in the

numerical experiments. However, in empirical application where the evaluation of

economic policy is essential, the situation will become somewhat different. The

structure of the model provides here a comprehensive and efficient technique for

accomplishing this type of analysis.

In most CGE models capacity expansion and the process of structural adjustment

are restricted to the existing technical structure of production. Structural adjustment

is the key to understanding the importance of individual and collective motivations,

and thereby provide the framework for the entrepreneur in economic analysis.19

From an evolutionary theoretical point of view20 the equilibrium models are

inadequate to capture the specification of the mechanisms that creates incentives

for the entrepreneur to enforce new activities to maintain the capacity for growth.

However, one thing is to have knowledge of the problem, another is to make the

problem operational. To start with the structure of ownership of the business

sectors, and then specify the incitement behaviour that is assumed to follow that

type of ownership, may be a good point of departure to make entrepreneurship

operational in an economic model. In later years the structure of ownership in the

business sectors has rapidly changed. That change may have many causes, but the

strong increase in structural transformation, recorded in the past two decades, is

probably closely connected to this development.

Disinvestment is an important component in the transformation process, and

even a condition for investment and growth. To under-stand the importance of this

argument a model of the economic transformation process is developed. Economic

transformation will be specified as endogenous, and it will become an integral part

of a steady-state equilibrium mechanism. In the next chapter, Chap. 6, a model of

the fundamental structure of the transformation process of the open economy in an

equilibrium framework is carried out.

19 The perfect competition theory defines the equilibrium state and not the process of adjustment.

(Kirzner 1973).20 Schumpeter 1942 and 1976.

5.3 Concluding Remarks 85

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Appendix 1: The Mathematical Equations of the Model

Prices

Definition of Domestic Import Prices

pMj ¼ pWMj � ER� ð1þ tmj þ prjÞ (5.1)

pWMj is the world market price of imports, ER is the real exchange rate, tmj is the

tariff rate on imports, and prj is the import premium rate. Note, that the world

market price of imports pWMj and the tariff rates are fixed. Depending on the

exchange rate, the domestic import price pMj is flexible or fixed.

Definition of Domestic Export Prices

pEj ¼ pWEj � ð1þ tejÞ � ER (5.2)

pEj is the domestic price of exports, pWEj is the world market price of exports, tej are

the export duty rates, and ER is the real exchange rate. Note, the world market price

of exports pWEj and the duty rates are fixed. Depending on the exchange rate, the

domestic export price pEj is flexible or fixed.

Value of Domestic Sales

Pi � xi ¼ pZj � xZj þ pMj �Mj (5.3)

pi is the price of composite commodities, xi is the composite commodity supply, pZjis the domestic price, xZj are the domestic sales, pMj is the domestic price of imports,

and Mj is imports by sector.

Value of Domestic Output (Market Value)

pZj � Zj ¼ pZj � xZj þ pEj � Ej (5.4)


pZj is the average output price by sector, Zj is the domestic output by sector, xZj are

domestic sales, pEj is the domestic price of exports, and Ej is exports by sector.

Definition of Activity Prices

pZj � 1� ITAXj

� � ¼ PVAj þ Σj; aij � pi (5.5)

pZj is the average output price by sector, ITAXj is the indirect tax rate, PVAj is the

value added price by sector, aij are the input–output coefficients, and pi is the priceof composite commodities.

Definition of Capital Commodity Price

pKj ¼ Σi; pi � cij (5.6)

pKj is the rate of capital rent by sector, pi is the price of composite commodities, and

cij is the capital composition matrix.

Definition of General Price Level

pindex ¼ Σi; pwtsi � pi (5.7)

pindex is the general price level, pwtsi are the CPI weights, and pi is the price of thecomposite commodity.

Output and the Factors of Production

Production Function (Cobb-Douglas)

Zj ¼ ADj ΠlcLj;lc αj;lc Kj1�Σlc; αj;lcð Þ (5.8)

Appendix 1: The Mathematical Equations of the Model 87

Zj is the domestic output by sector, ADj is the production function shift parameter,

αj,lc is the labour share parameter, Lj,lc is the employment by sector and labour

category (lc), and Kj is the capital stock by sector.

First Order Condition for Profit Maximum

PLlc �Wdist � Lj;lc ¼ xZj � PVAj � αj;lc (5.9)

PLlc is the average wage rate by labour category (lc), Wdist are the wage

proportionality factors, Lj,lc denote the employment by sector and labour category,

and PVAj is the value added price by sector.

Labour Market Equilibrium

Σj; Lj;lc � Llc (5.10)

Lj,lc denote the employment by sector and labour category, and Llc is the labour

supply by labour category (lc).

CET Function: Exports (Domestic Output)

Zj ¼ ATj γj Eϕj

j þ ð1� γjÞxZϕj

j

h i1=ϕj

(5.11)

Zj is the domestic output by sector, ATj is the CET function shift parameter,

GAMMA is the CET function share parameter, Ej is exports by sector, ϕj is the

CET function exponent, and xZj are the domestic sales. This function applies to

commodities that are both sold domestically and exported. The equation above

reflects the assumption of imperfect transformability between domestic sales and

exports.

Export Supply

Ej

xZj¼ pEj

pZj� 1� γj

γj

1ϕj�1 (5.12)


pEj is the domestic price of exports, and pZj is the domestic price.

CES Function: Composite Commodity Aggregation Function

xi ¼ AC: j δj M�ρjj þ ð1� δjÞxjZ:�ρj

h i�1=ρj(5.13)

xi is the composite commodity supply, ACj is the Armington function shift param-

eter,δj is the Armington function share parameter,Mj is imports, ρj is the Armington

function exponent, and xZj are the domestic sales. This function applies to

commodities that are both produced and sold domestically and imported, i.e.,

composite commodities. The equation above reflects the assumption of imperfect

substitutability between imports and domestic produced commodities sold

domestically.

Cost Minimisation of Composite Good

Mj

xZj¼ pZj

pMj� δj1� �δj

11þρj

(5.14)

pZj is the domestic prices, and pMj is the domestic price of imports.

Domestic Sales for Non-traded Sectors

A first step toward more realism has been taken by introducing non-tradable

commodities. Non-tradable commodities are commodities that are not subject to

international trade. In general, most service as well as housing and construction fit

this category.

xZj ¼ Zj (5.15)

xZj are the domestic sales, and Zj is the domestic output by sector.


Composite Commodity Aggregation for Non-traded Sectors

xi ¼ xZj (5.16)

xi is the composite commodity supply, and xZj are domestic sales.

Demand

Total Intermediate Uses

xij ¼ Σj; aij � Zj (5.17)

xij are the intermediate uses, aij is the input–output coefficients, and Zj is the

domestic output by sector. The sector balances of intermediate inputs (inter-

industry matrix) form the basis of the input–output table. The input–output matrix

is derived from the inter-industry matrix, by dividing each element in a column by

the row sum of the corresponding row. The Leontief matrix is obtained from the

input–output matrix by subtracting it from an n by n identity matrix. This changes

the sign of all off-diagonal elements and makes all diagonal elements into their

complements to one. Theoretically, the input coefficients are in physical terms.

Empirically, the coefficients are in monetary terms. As long as we assume that

prices are constant, the input coefficients should be the same either in physical or

monetary terms.

The transactions may be valued at either the price received by the producer,

producer’s value, or at the price paid by the consumer, purchaser’s value. Thedifference between these values is that transport margins, net indirect commodity

taxes, i.e., indirect taxes less subsides, and trade margins are added to the basic

producer’s values in the national accounts. Since the demand components are

computed at purchaser’s values, production and imports are converted to these

values too.

Inventory Investment

DSTj ¼ DSTRj � Zj (5.18)

DST j is inventory investment by sector, DSTR j is the ratio of inventory investment

to gross output, and Zj is the domestic output by sector.


Private Consumption Behaviour

Pj � CDj ¼ Σh; CLESj;h � ð1�MPShÞ � YHh � ð1� HTAXhÞ (5.19)

pj are the price of composite commodities, CDj is the final demand for private

consumption, CLESj,h are the private consumption shares, MPSh is the marginal

propensity to save by household type, YHh is the total income by household type,

and HTAXh is the income tax rate by household type

Private GDP

Y ¼ Σh YHh (5.20)

Y is private GDP, YHh is the total income by household type.

Total Income Accruing to Labour

YHh ¼ Σlc; PlcL � Llc þ REMIT � ER (5.21)

YHh is the total income by household type, PlcL is the average wage rate by labour

category, Llc is the labour supply by labour category, REMIT is the net remittances

from abroad, and ER is the real exchange rate.

Total Income Accruing to Capital

YHh ¼Σj; PVAj � Zj � DEPRECIA � Σlc;PlcL � Llc

þ FBOR � ERþ YPR (5.22)

YHh is the total income by household type, PVAj is value added price by sector, Zj is

the domestic output by sector, DEPRECIA is total depreciation expenditure, PlcL is

the average wage rate by labour category, Llc is the labour supply by labour

category, FBOR is the net flow of foreign borrowing, ER is the real exchange

rate, and YPR is total premium income accruing to capitalists.


Saving and Income

Household Savings

HSAV ¼ Σh; MPSh � YHh � ð1� HTAXhÞ (5.23)

HSAV are the total household savings, MPSh is the marginal propensity to save by

household type h, YHh is the total income by household type, and HTAXh is the

income tax rate by household type.

Government Revenue

GR ¼ TARIFF� NETSUBþ INDTAX þ TOTHTAX (5.24)

GR is the government revenue, TARIFF is the tariff revenue, NETSUB is the export

duty revenue, INDTAX is the indirect tax revenue, TOTHTAX is the household tax

revenue.

Government Savings

GR ¼ Σj; pj � GDj þ GOVSAV (5.25)

GR is the government revenue, pj are the price of composite commodities, GDj is

the final demand for government consumption, and GOVSAV are government

savings. It is an essential assumption for a real equilibrium model that the govern-

ment must balance its budget.

Government Consumption Shares

GDj ¼ GLESj � GDTOT (5.26)

GDj is the final demand for government consumption, GLESj is the government

consumption shares, and GDTOT is the total volume of government consumption.


Tariff Revenue

TARIFF ¼ Σj; TMj �Mj � pWMj � ER (5.27)

TARIFF is the tariff revenue, TMj are the tariff rates on imports,Mj are imports,pWMj

are world market price of imports, ER is the real exchange rate.

Indirect Taxes on Domestic Production

INDTAX ¼ Σj; ITAXj � pZj � Zj (5.28)

INDTAX is the indirect tax revenue, ITAXj is the indirect tax rates, pZj is the average

output price by sector, and Zj is the domestic output by sector.

Export Duties

NETSUB ¼ Σj; tej � Ej � pWEj � ER (5.29)

NETSUB is export duty revenue, tej are export duty rates, Ej are exports by sector,

pWEj is the world market price of exports, ER is the real exchange rate.

Total Import Premium Income

YPR ¼ Σj; pWMj �Mj � ER� pr (5.30)

YPR is the total premium income accruing to capitalists, pWMj is the world market

price of imports, Mj are imports, ER is the real exchange rate, and pr is the import

premium.

Total Household Taxes Collected by Government

TOTHTAX ¼ Σh; HTAXh � YHh (5.31)

TOTHTAX is the household tax revenue,HTAXh is the income tax rate by household

type h, YHh is the total income by household type h.


Capital Formation

Depreciation Expenditure

DEPRECIA ¼ Σj; DEPRj � pKj � Kj (5.32)

DEPRECIA is the total depreciation expenditure, DEPRj is the depreciation rate, Kj

is the capital stock by sector, pKj is the rate of domestic capital rent by sector, ER is

the exchange rate. As the capital stock gets older, the quasi-rent in the Marshallian

sense falls and eventually becomes zero. The economic decision is then taken to

scrap the capital object as obsolete.

Total Savings

SAVINGS ¼ HSAV þ GOVSAV þ DEPRECIAþ FSAV � ER (5.33)

SAVINGS are total savings, HSAV are total household savings, GOVSAV are

government savings, DEPRECIA is total depreciation expenditure, FSAV are

foreign savings. Thus, the sum of domestic and foreign savings in domestic

currency.

Domestic Investment by Sector of Destination

In the CGE mini-model domestic investment by sector of destination is given by:

pKj � IDj ¼ KIoj � INVEST � KIoj � Σj; DSTj � pj (5.34)

Thus, pKj is rate of capital rent by sector, IDj is volume of investment by sector of

destination,KIoj are the shares of investment by sector of destination, INVEST is the

total investment,DSTj is inventory investment by sector, pj is the price of composite

goods. The sector share parameters for investment are assumed fixed. Total invest-

ment is determined by savings in the economy (saving determined investment).

The sector capital stocks Kj are fixed within periods. However, they change over

time given aggregate growth of the capital stock and the sector allocation of invest-

ment. Sector share parameters of investment by sector of destinationKIoj are assumed

to be fixed. For information, the numerical values of the sector share parameters of

investment are in these applications arbitrary assumed to be: 0.13 for agriculture, 0.29

for industry, and 0.58 for services. The sum is equal to one. However, the sector

allocation of investment is here assumed to be adjusted over time (endogenously) to

equate rental rates pKj in the industrial sectors by the terminal year.


Investment by Sector of Origin

The request for the volume of investment by sector of destination IDj (the sector

capital accumulation) is translated into a demand for investment commodities by

sector of origin ISi (producing sectors of capital commodities), thus investment by

sector of origin:

ISi ¼ Σj; IMATij � IDj (5.35)

ISi is the final demand for productive investment, IMATIJ is the capital composi-

tion matrix, and IDj is the volume of domestic investment by sector of destination. In

accordance with the production structure, as represented by the input–output model,

the investment by sector of origin ISi is also known as final demand for productive

investment. The summation of the capital composition matrix IMATIJ is, as the

sector share parameters of investment, equal to one. Following this application, the

two sectors producing capital commodities are industry (the dominating sector),

and a small fraction from services.

Balance of Payments

Σj; pWMj �Mj ¼ Σj; pWE

j � Ej þ FSAV þ REMIT þ FBOR (5.36)

pWMj is the world market price of imports, Mj are imports, pWE

j is the world market

price of exports, Ej are exports by sector, FSAV are foreign savings, REMIT are net

remittances from abroad, and FBOR is the net flow of foreign borrowing. In the

experiments in this book the exchange rate is fixed and the net flow of foreign

borrowing is unfixed. Following this specification, the trade deficit is free to vary.

Market Equilibrium

Commodity Market Equilibrium

xi ¼ xij þ CDj þ GDj þ ISi þ DSTj (5.37)

xi are the composite commodity supply, xij are intermediates uses, CDj is the final

demand for private consumption, GDj is the final demand for government con-

sumption, ISi is the final demand for productive investment, and DSTj is the

inventory investment by sector.


Objective Function

OMEGA ¼ Πj CDjCLESj;h (5.38)

OMEGA is the objective function variable, CLESj,h is the private consumption

shares, and CDj is the final demand for private consumption.

For full specification of the numerical input in the original input version of the

model, see the computer program of the CGE mini-model. The CGE mini-model is

a minor version of an equilibrium model that originally comes from Chenery,

Lewis, de Melo, and Robinson in their work on designing an equilibrium develop-

ment model for Korea. The model illustrates the basic use of CGE models. See

further: Chenery et al. (1986). The model is included in the GAMS model library

(korcge.gms). The reader can reach the GAMS homepage at www.gams.com.

Appendix 2: Some Parameters Assignments of the Model

PARAMETER ASSIGNMENTS

INCOME TAX RATE BY LABOUR ¼ 0:08910

INCOME TAX RATE BY CAPITALIST ¼ 0:08910

LABOUR SHARE PARAMETER IN THE PRODUCTION FUNCTION


Agriculture 0.38258 0.06740 0.00000

Industry 0.00000 0.53476 0.00000

Services 0.00000 0.16234 0.42326

INPUT–OUTPUT COEFFICIENTS


Agriculture 0.12591 0.19834 0.01407

Industry 0.10353 0.35524 0.18954

Services 0.02358 0.11608 0.08390

CAPITAL COMPOSITION MATRIX


Agriculture 0.00000 0.00000 0.00000

Industry 0.93076 0.93774 0.93080

Services 0.06924 0.06226 0.06920


http://www.gams.com

WAGE PROPORTIONALITY FACTORS


Agriculture 1.00000 0.52780 0.00000

Industry 0.00000 1.21879 0.00000

Services 0.00000 1.11541 1.00000

PRIVATE CONSUMPTION SHARES

LAB-HH CAP-HH

Agriculture 0.47000 0.47000

Industry 0.31999 0.31999

Services 0.21001 0.21001

References

Armington P (1969) A theory of demand for products distinguished by place of production. IMF

Staff Pap 16:159–178

Chenery H, Lewis J, de Melo J, Robinson S (1986) Alternative routes to development. In: Chenery

H, Syrquin M (eds) Industrialization and growth: a comparative study. Oxford University

Press, New York

Condon T, Dahl H, Devarajan S (1987) Implementing a computable general equilibrium model on

GAMS – the Cameroon model, DRD discussion paper 290. The World Bank, Washington, DC

Dervis K, de Melo J, Robinson S (1982) General equilibrium models for development policy.

Cambridge University Press, Cambridge

Freeman C (1974) The economics of industrial innovation. Penguin Books, Harmondsworth,

Middlesex

Kirzner IM (1973) Competition and entrepreneurship. The University of Chicago Press, Chicago

Lofgren H, Harris RL, Robinson S (2002) A standard computable general equilibrium (CGE)

model in GAMS, vol 5, Microcomputers in policy research. International Food Policy

Research Institute, Washington, DC

Petersen TW (1997) An introduction to CGE-modelling and an illustrative application to Eastern

European Integration with the EU. The Institute of Economics at the University of

Copenhagen, Denmark. The working paper is only available on www.dreammodel.dk/

Schumpeter J (1942, 1976) Capitalism, socialism and democracy. Harper & Row, New York

Shoven J, Whalley J (1984) Applied general equilibrium models of taxation and international

trade: an introduction and survey. J Econ Lit XXII:1007–1051

Shoven J, Whalley J (1992) Applying general equilibrium. Cambridge University Press,

Cambridge

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http://www.dreammodel.dk/

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