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so-called Computable General Equilibrium (CGE) models which were introduced into the ... equilibrium, macro models that are antecedent to the contemporary.
March, 1986

Bulletin Number 86-1

ECONOMIC DEVELOPMENT CENTER

I -k•• \•z,,-

I

-

I

7•. .."-.

A COMPUTABLE GENERAL EQUILIBRIUM MODEL FOR DEVELOPMENT POLICY ANALYSIS A. Erinc Yeldan

ECONOMIC DEVELOPMENT CENTER Department of Economics, Minneapolis Department of Agricultural and Applied Economics, St. Paul UNIVERSITY OF MINNESOTA

A COMPUTABILE GENERAL EQUILIBRIUM

MODEL

FOR DEVELOPMENT POLICY ANALYSIS

A.

Erinc Yeldan

February,

1986

Graduate student and Research Assistant, Department of Agricultural and Applied Economics, University of Minnesota. paper has been supported in part by a grant Research for this from The Cargill Foundation and the International Economics version of the paper was presented An earlier Division of ERS. as a seminar at the Agricultural Development workshop, University of Minnesota. I am grateful to Professors Edward Schuh, Terry Roe, of the Agricultural %JamesHouck, and the participants Development Workshop for valuable comments and suggestions. however, are solely mine. All the remaining errors,

A COMPUTABLE GENERAL EQUILIBRIUM MODEL FOR DEVELOPMENT POLICY ANALYSIS

The purpose of so-called introduced

this paper is

Computable General

to present an example of the

into the Applied Economics

more than a decade ago and proved medium/long-term planning exercises. ari sen

in

a little for both

policy analysis

for such modelling has

r-esp-onse to the well.-known short-comings and

world economies,

equilibrium constructs. the interwoven structure

of the

applied policy analysts have always

about the anaLlytical

models. Thus, the growing has led

just

to be very useful

The underlying motivation

Due to the complexities and

skeptical

literature

and development

limitations of the partial

real

(CGE) models which were

Equilibrium

to the explicit

powers of

need for

aim of

was formalized by Kenneth Arrow,

equilibrium

increasingly

converting

equi librium system from an abstract

195)0s) into a realistic

partial

been

general

models

the Walrasian

mathematical

general

apparatus

Gerard Debreu and others

and applicable

model

(as in

the

of actual

economi es. The CGE Mode:l.s have, until many countries,

some examples,

the existing

to:

Taylor & Black

(1974,

Dervis & Robinson

Malaysia) ; Lanka).

(1978,

(1980,

questions.- :L

models include,

Chile) ; Adelman

Cardoso & Taylor

Feltenstein

policy

different

addressing

cite

Korea);

now, been successfully applied to

Turkey);

& Robinson Ahluwalia

(1979, Brazil); Argentina).

but not

To limited

(1978,

& Lysy

S. (1979,

de Melo (1980, Sri

de Melo & Robinson

Colombia),

Lewis & Urata

(1983,

Turkey) ; Lundborg

Malaysia);

Gupta & Togan

(1984,

India,

(1984,

Kenya and Turkey).

(1980,

The paper

first introduces the broad

class

of

general

equilibrium, macro models that are antecedent to the contemporary CGE formulations.

There,

I try

to provide an interpretative

essay on such early multi-sector constructs and follow the path to the evolution of the idea of building price-endogenous, nonlinear macro models that can capture both the market-optimization behavior of

individual

agents and the commanding nature of the

exogenously specified government The second and third segments of the CGE model.

policies.

sections in

turn, build the different

The paper concludes with a compact

presentation of the core CGE equations and two Appendices, one on the Linear Expenditure derivation

and another on the endogenous

System:

of the price elasticity

of

demand,

both of which

will

be used in the modelling process.

1.

INTRODUCTION:

A PRELUDE TO THE CGE MODELS

The earliest multisector planning models were based on the simple input-output linkages among economy.

various sectors of the

With these models, assuming a fixed-cofficients --

Leontieff --

Technology for each

sector, and given

the estimates of

input-output coefficients across sectors, the planner was in a position to calculate the necessary output

level at each sector

in order to satisfy a targeted final consumption bundle. To be more concise, letting A be the matrix input-output coefficients as.ij,

with a±j

being the amount of

input i necessary to produce 1 unit of opuput j; gross output vector by X, and the final

of fixed

and denoting

consumption vector by C,

the material-balance

X

AX

Now, bundle,

can be written

as:

+ C

(I-1)

suppose- the planner

has some targeted

indicated by the vector

problem can for

equation

C

be found by solving

'Then the

consumption

"solution" to the

the material-balance

equation

X:

X =

Equation satisfy

(I

-

A) .

C

(1-2)

(1-2) gives gross production requirements the targeted

Leaving the static,

consumption

aside the rather fixed

of such models

criteria

for setting

the absence

simplistic

has been

of the gross output

and cumbersome ng,

an optimization

consumpti-on

bundle,

the determination

vector

X,

nature of

thIe most. i mportan t

the lack of

the targeted

of such criteria,

to

demand.

i n put-"out p ut model.i

drawback

i.n order

becomes an ad

of C,

C.

Yet,

in

and hence

hoc exercise in

matrix algebra. Later,

another

class

of

F'rogr-ammin ig Models succeeded shortcomings of

the early

multisector in

models,

overcoming

input-output

exercises.

explicit

objective function was introduced

involved

optimizing this Again,

constraints. static

linear Max

RX s.t.

X

and cr

retaining

:i:B 0 U::

model

many other Here an

and the problem

function subject to certain

programming Ax

th i s,

known as Linear

(linear)

the same notation for can be formulated

X and A,

as follows:

the

a vector of objective function weights and B is

where R is

Given data on R,

vector of resource constraints. feasible set F =

{XIAX :i B;

a solution vector X* Linear

problem

interesting implications for

particular,

Min WB s.t.

WA W

R C)

problem;

and only if

X*,

the Duality Theorem

for the primal problem

is

the dual

a feasible vector W exists for

such that,

-

R) X*

Equations

(I-3)

= 0

W* AX*--B) (WA

Now,

a vector of constants.

if

economic

given the above linear programming

states that a feasible vector, optimal

then

the dual problem could be written as:

(primal),

where W is

bounded and non-empty,

the

Models coupled with the so-called Duality

Programming

In

is

: 0

if

can be found to the above problem. 0

Bj

> 0

La)jX"j j

-

X" > 0

implies

EW"ia,..a i

-

Thus,

in

R

> 0

general

Ea.i j

-

X'*

implies

W*

-

EW'*aAj i

at optimum,

4

= O

(1-5)

= 0

(I-6)

Rj == 0 X~*

implies

if,

BE

0C=

(I-7)

(I-8)

any one of the constraints

in

either

problems

is

not binding

negative or strictly variable

positive)

carries

(i.e.

function weights, of

and

positive

(I-5)

and

levels,

(1-8)

allows us to interpret "input prices".

(1-6)

state

that

the associated

state

In

the dual

this

only fully

context,

used inputs have

that

price

must be zero.

only those activities

supply Further,

which

be carried

(1-

do not incur out at

levels. Thus,

insights

the linear

programming

for the general

modelled economies.

However,

the fact

the heuristic physical

First

assumption

a wellI-defined

of all,

that

mixed economies

constraints,

the multipliers

at

the opt:i.mum,

properties

of

models are based planner,

on

in

command

of

yet

subject

to

seeks to maximize

for the whole society.

designed

where individual

the dual

of the economy,

and natural

nor

such

a fictitious

welfare function

Cit. .. well-suited,

that

interesting of

they share other

productive activities

technological

provides

of market prices

should not be taken to imply that market prices as well.

approach

equi librium relationships

share the marginality conditions

thus,

the

as objective

prices and for those inputs where the fi:xed

positive

certain

we interpret

the complementary

any losses at the optimum must actually

all

if

the R vector

W, as

and

ex.ceeds demand, 7)

dual

the elements of matrix. A as input

per unit output

vector

further,

inputs,

slackness conditions naturally

equations

strictly

a zero value,

B vector as fixed supplies of

multipliers,

either

then the corresponding

To carry the analysis a little

requirements

is

They are,

f or the state-capital

agents independently

i st try

to

max:imize their an

own well-being

environment regulated

degrees.

In

determine

certain

this

to a budget constraint

by the government

environment,

The planner

the productive activities

can be affected

at varying

only indirectly

does not have real

independent

in

agents taken together

of the economy,

many other

bureaucracy

individual

outcomes that

by the planner.

decisions of

subject

command on all

but relies

"optimizers",

on the each exerting

an influence on the specific development path of the economy. The remedy to this

observation

is,

of course,

to construct

a

model where endogenous prices and quantities are allowed to transmit market

information

through different sectors of the

economy, thereby simulating the workings of and

intervened,

by a

social

yet absolutely

planner)

endogeneity

cannot

programming

models.

difficulty

lies

in

markets.

Yet,

this

To cite the fact

that

economic

in

result

program cannot

as a by-product

allocation

and production program is

result

from its

impact

on the structure

dual

in

general structure

consistent solution. of

"shadow"

expect

and saving factor

constraint

that

the resource by the solution of

factor

the quantities

solution

6

if

will

in

that

to put it

with the incomes and Indeed,

and

equations

prices

Or,

determined

demand,

are the outcome of the primal

and relations

functions,

of the maximization.

one cannot

linear

behavior

primal

include th'e

the linear

"the crucial

current endogenous

But the standard

differently,

a

-level of price

the main problem,

functions must be expressed

a linear

not commanded

be designed within the realm of

consumption

of

(i.e.

decentralized

such as budget constraints,

commodity prices.

a perhaps regulated

budgets that

prices have any supplied

general

that

not equal

the sol

demanded

quant.tites

general,

the one hand,

implied

those models which

and

linkages between the resulting General model

incorporate

by

the

dual

Equilibrium

prices,

models.

finds the market become te

solves for clearing

so:urces o)f

groups and determine

investment patterns

income generation

is

and sectoral

sectors. model

updates the initial

until

tatonnement

convergence It

paper

only

solve of

variables feed

exogenous

a

as the

set

of

in

and

turn

OQuantities imported

domestic production elasticities. through

of differential

The the saving which,

profit

demands in

algorithm and

iterates

in

rates

this

turn

across

manner,

the

prices through

a

the whole process

achieved.

for the

however, the

The rule

that

relative

economy.

normalization

practice.

demand.

function of

excess

su.ch

across sectors These

guess of do.mestic

should be noted,

can

has to

is

about one

investment share parameters,

After calculating

Walrasian

is

for various household

also endogenized

as a function

brium

groups and

economy as well

rates.

rule

the model prices

to

Yet into most

and

model,

commonly

designed

resorted

in

this

the

this,

achieve the

on

are termed Computable

levels

prices and relevant

behavior

are determined

the output

the pattern of

international

equii

Given an arbitrary

wage/rental

exported are solved as a

costs,

This paper

into the analysis.

the model

general

on the other,

inc:orp'orates the :international

that

price endogeneity

various worker--consumer

of demand (CGE)

enable this

the fundiamental

the incomes of

patterns

domestic markets

real..L

are

i on 1". •

ut

In

and

that

a

the

planner

completely to

and

which

will also be used here is to employ a no-inflation benchmark by level

defining a constant

of the price index,

which

prices and real

only relative

concern devoted

without much

phenomena as well very short-run,

to monetary problems.

stabilization

economic theory; superstructure

is still

a

interwoven with the microeconomic simple behavioral

general

for focusing on a vast array

These arguments should not be taken,

general

equations

Further,

tool.

will

of development however,

have

such

and cumbersome

may turn out to be too general

model

in

ad hoc macro-monetary

own drawbacks as an analytical

useful

of monetary

a very difficult branch of

and building an

equilibrium system through

an exercise

using

analyses.

monetary spheres of the economy

and

Thus,

incorporation of the interactions between

equilibrium framework

its

variables would matter,

as the possibility of using such models for

On the one hand, the real

set

Equilibrium Models,

rule precludes the treatment

such a normalization

is

quite consistent

Walrasian General

with the early treatment of in

is

This choice

by the modeller.

exogenously

which

to be a issues.

to imply that

planning monetary phenomena is not possible or ill-advised all together. Depending on the question in hand and the time horizon to be analyzed, the monetary sphere of the economy can be incorporated into the CGE framework in various ways. elegant model

that

tackled

by Adelman and Robinson income distribution strategies Thus,

in

in

this

For example, a very

task quite effectively 1978 work,

their

of different

consequences

which

is

provided

focuses on the

development

South Korea.

to recapilulate,

the reader has to appreciate

8

the fact

that

in

applied

policy analyses much depends

on the specific

purpose of the model-building effort and the access to realistic data supplies, which

is

a major restraint on students of

still

Development Economi cs. constructed in

The Model

Dervis et.

from the works of

(1978); Lewis and Urata Lundborg

(1984).

this paper is al.

(1982);

Its distinguishing features are:

(2)

recognition of

product markets;

(3) recognition of

the sectoral

incentive-pack:ages The Model stages.

granted

is

construction which is static

(1) expliicit

and

(4)

wage

endogenous

subsidies arising from export-

by the government.

is constructed

The first stage

and designed to be run in

a within-period general in

parameters, the Stage 1 Model,

equilibrium

as will

and other

be called hereafter, finds

the relative prices and solves for all real/structural

the overall

In

two

its equations and variables.

Given certain exogenous government policy variables

of the economy.

and

in certain

inter-sectoral

labor;

expor't

(1978)

as distinct from private

monopoly power

differences for the same type of calculation of

Dervis and Robinson

(1983); Adelman and Robinson

specification of the public enterprises enterprises;

adapted and updated

other words, it

variables

comprises the core system of

Model.

The second stage, on the other hand, is designed to up-date the

exogenous variables of

system and

the

basically used for the

Armed with this background model.

I

first stage.

first

purpose of

we can begin

introduce the system of

9

It

is a dynamic

"aging" the

Model.

constructing

ncotation that

will

our be

used throughout

the entire

Model.

adhered to the following (1)

Endogenous any bar

are denoted

on them.

lower case letters

All

which

(2)

All

Greek

(3)

Letters

(4)

involved.

i

The subscripts

(e.g.

a:j,

of d. in

and rm)

and are

the Stage 1 stage.

variables.

are policy variables to be set

are omitted for all

all

range from

(..)

with a bar,

the second

not

without

by the government.

Time subscripts

explicitly,

in

are parameters

letters

letters

fixed parameters

with a circumflex

are time lags

(5)

capital

needs to be updated

letters

exogenously

by capital

(with the exception

exogenous variables or Model

I

legend of principles:

variables

(-)

Unless otherwise specified,

Thus,

unless otherwise specified

variables refer

to the current period.

and j

1 to n. or bj.),

sector of origin

variables unless there

are used for

sectors.

They always

When these two are used together the first

subscript

and the second

always refers

to the

to the sector of

destination. (6)

The subscript ranges from

(7)

Subscript

s

refers

to different

skill

types of

labor and

1 to m.

f is

the public firm

used to distinguish (p:

private;

10

g:

between the private and

public).

II - THE OPEN CGE MODEL:

STAGE 1

The core equations of

in

forms are constructed

functional with

the Stage

of

the presentation

in

1 Model this

their

expilicit We first

section.

begin

the price system.

PR ICES

model

To begin

invokiing

restrictions, tradables modelled

the absence of

the neo-classical

too small

to affect

is

these should be fed in

in

especially

practice,

the perfect

exaggerates

fixed

The applied macro models,

aggregation

the

quite

misleading Another

sectoral perfect

and

activities,

of

the domestic

involve a at

such

levels

assumption

substitubility

fair

may

the

price

due to the understable etc.,

data limitations,

greatly

price system and

system.

of

of the productive

assumption

substitubility

trade policy over determination

aggregation

variables.

when we are trying to build

the role of the international

computation,

and

markets

as given,

domestic

of

price

The prices for the open

models with limited degrees of disaggregation sectors,

price

or endogenous,

the international

into the model

the

implies that

by the given world

to solve at all.

are determined

that

the country being

there remains no independent,

system for the model economy model

assumptions,

the world prices,

prices are set

relative

any trade

and that

substitutes

Thus,

However,

in

are perfect

the domestic ratios.

with,

to the applied model

problems

presents some interesting

builder.

an open economy

of the price system in

The specification

reasons

amount

of

of lead

to

results. difficulty,

as

illustrated

11

by

Dervis et.

al.

( 1982,

Chapter 3)

is

that

assuming

hypotheses

along with

the above mentioned neo-classical

the specification of the productive

technology as one of constant

returns to scale,

result

in

extreme specialization in the sectors that the domestic economy has comparative advantage, with no home production ever sectors that it doesn't have.

not supported by empirical

trade is

is a very crude

of the way economies engage into international trad.e

portrayal and is

Obviously, this

on the

abound,

Two-way sectoral

evidence.

especially at high

levels of

aggregation.

A formulation to handle these problems has been proposed in a 1969 paper

by Armington which distinguishes

only by their kind place of

machinery,chemical -

e.g.

production.

In

commodities not but

also by their

Armington's commodity system, not

only

is each good different from any other good, but also each good is assumed to be differentiated by the country of origin of

supply. Following Armington's hypothesis, domestically produced

goods and

imports are assumed to be imperfect substitutes.

To

reflect this, we define a tradable composite commodity CCI,

which

is a CES aggregation of the domestic commodity DC:t, and the imported

foreign good,

CES function, ai,

M±.

The elasticity

of

the difference between

substitute them with agriculture, food

of the

reflects the differences between the domestic

and imported good from the buyer's viewpoint the greater

substitution

each other).

processing

whereas for 'the capital

DC±

and M1

and

Plausibly in

or textiles,

goods sectors it

12

(the smaller the as ,

aC

the harder

to

sectors such as

is fairly large,

is quite low.

The ex.plicit .formulation of i-th

= B I.

where BS ,

":i.

M,.

S.

the

( -8,.)

o•

DC

(II-

. are parameters;

good in

substitution,

(

-I/P/

-P

+

and p

the imported

CCI

and p:.i

is

by the expression

The consumers are then

with

just like

related to the elasticity ao

=

Accordingly

the aggregate output CC±..

of

1 /+pi.

hypothesized as mi.nimizing a co(st "technoology"

a firm trying to produce a specified level

mini mum cost.

)

giving the share of

G S

function subject to the CES composite commodity

PC-.,

in

sector is: ---

CC:

the composite commodity

M 1

and DC,. are like

of output at

"inputs"

producing

"Therefore, the composite good price,

can be exipressed u.sing the cost function of the CES

I: gy < > te hnol. ff± .

PC . = 1 / B

where PM.i is wh:i ch will tariff

( i-C :k) PM .

(1 - 6

rate tm±.,

= PFWM

(1+tm,.)

"- EPCj

is

1 I-( I:-2)

ER

usually dollar).

(I I-3)

the specification of

ac1

the ad valorem

(defined as units of

unit of foreign currency,

their- product ti on pl an s.

where tni

1

price F'WM:.,

and the ex-change rate ER

also introduce the net price,

= PD.

( l-cr,.) F D,.

be determined by the world

To complete

P N.:i

)

the domestic c.urrency price of the imported good,

domestic currency per

FPM :

Cy±. +

PN-=.,

the price system I will

upon which the producers make

Thus;

-

tn.

PD,. + sn-c

the indirect tax

PDF).

rate and sn.i:

(11 -4)

is

the net production

versus public

the granted

enterprises,

of one unit

input

of intermediate

stands for the amount

production

subsidy rate

j

Further,

used for the

gives the value of

Hence EPCjaj.

i.

of

is

as across sectors.

among firms as well

differentiated aji

towards private

Depending on the government's attitude

subsidy.

J-t

inputs used in

intermediate i-th

of

the production

one unit of

the

good. The two other prices used in

PWEI

and the export price,

PKý

capital,

at a later point of the Stage 1 Model. however,

will

be introduced

below,

At this juncture, of

I will turn to the specification

technology of

the price of

the Model,

the production

the economy.

PRODUCTION TECHNOLOGY AND FACTOR MARKETS

The crucial

assumption

CGE Model

of the Open

a single commodity the Hicksian

sense).

is

in

that

models, as entries

envisaged

to produce

(may be thought as an aggregate-commodity Conversely,

very much

in

sector

the tradition

input-output

in

each such commodity is

enables us to continue to define of an

is

each sector

associated with a single production specification,

the productive sphere

constructing

of the economy. of

This

early economy-wide

the productive

sectors

table.

As hinted in the net-price equation

(II-4),

the intermediate

input demands has been assumed to constitute a linear system with fixed-coefficient production technology for such input-usage.. The retention of this specification is not necessary for the nonlinear CGE Model

and extensions of this technology have been

14

in

t ried

Lewis and Urata

(1983)

and also in

Ahluwalia and

For purposes of realism we may need to separate

(1979).

the technol]ogy of

intermediate

technol.ogy for primary specification is

inputs from the production

inp.uts -

capital and labor,

the production technology available to a

firm can be thought to be given by either a oneCobb-.Dougl as funrction of f:

r

(-^" :I.

= A.r

Our

perhaps the simplest way to achieve this.

particular,

In

X.f±i

Lysy

l)

capital

and labor

in

or

a two-]evel

each sector

L+ : -a

Tr LI.U±

K.i

i,

(11-5)

or

X f'-.

i Kf

= A

where L.:

I.... L.

is

.~.

( II-6)

further formulated

di ff:erent skill

levels

as a CES aggregation of

below).

(11-7

The modeller can choo)se either

of

the spec if icat ion for

produc.tion technology for a particular firm or sector, the two,-level Cobb-Douglas because it between all

is

labor

is

labor types on the one hand, assumed in Then, for

the

the

I will

Model.

f i. xed-coeff is

formulation

i ci ents, amount

be used to

of

of substitution

the same and equal and to capital

to that between

on the other,

as was

(II-5).

retain For

However,

technology seems to be more realistiic

very unlikely that the elasticity

types of

the

the two-level

such technology, composite

c api tal

make up one unit

good of

good

Cobb-Douglas technology

capital

with

originating real

15

is

thought

elements

b.j•

,

from sector capital

in

sector

as a

where i j.

that

b.i j will

Further, capital

stock is assumed to be fixed

period modelling

of the first

combine machines

This assumption tries

stage.

capture the fact that capital

in the within-

i.e. that

is not "malleable", cannot

once installed

to

be converted

into trucks

easily. Li±,

The labor parameter,

of the Cobb-Douglas production

technology is

given by a further

skill

Thus;

types.

CES aggregation of m different

( II-7)

,... , L. i m)

I,,. = L- .i (L»'n

where L.F:R.o- " R-, is

m skill

distinguish between More detailed

levels

However,

reportedly

world applications

Cobb-Douglas functional

degree

of parameter

yielded quite realistic

II

N

technology

of our model,

N

X .

estimation

results

properties

in

real

-- X:.

Eaj a-

X €.:.}

4

16

of the

we should first

the gross production possibility set Xf

",CX . :i. I

forms

(see References).

from the nDt. production possibility set,

X÷.

that need to be

and parameter

to turn to the mathematical

production between

"moderate"

of

specifications

always faces the trade off

specification

The CES and two-level

used here require a

Now,

the production technology

functions mean more parameters

between vigorous functional estimation.

the Model.

more detailed

and the applied modeller

estimated,

and have,

in

specifications of

are of course possible. the production

So we

a CES function of skill categories.

distinguish

= {Xf

which is:

,..

,X, n

N

The desirab.le property. of course strictly convex. convex

is that the set X.- be

this is ac hieved if thnd

A

t he set

X+ is stri c•tl y

and the Hawk ns--Si mon cond i t ions are sat i s i ed.

basically

achieve convexity by assuming capital

fix ed.

)

We

stocks to be

conve:xity is to be increased with

Further, the degree of

the number of fix.ed factors of production in

each firm,

this implies the well-celebrated hypothesis of:

since

diminishing

returns to scale to the variable factors. In contrast to retaining

the neo-classical

properties in its

productio.n technology, the Model recognizes two ki:nds of imperfections for the portrayal one is the ex.plicit

allowance

of market behavior.

The first

of monopoly power in certain is the recognition of

productiv e sectors; the other

intersectoral

wage differences for the same category of labor. Incorporation of

mono(poly power into CGE type policy models

has not been a common practice Robinson

1978 study).

Yet,

(with the e.xception of Adelman &. in a recent p)aper

Per Lundb(:rg

provides evidence from the Malaysian tin market showing that the frequent procedur-e of m:isleading results

assuming comp1etitive markets may lead to

(see Lundborg,

Especial.ly, when

effects of different policy

analyzing the distributional packages,

1984).

existance of monopoly power may have important

consequences which the competitive markets cannot generate.

The

income flows arising from the monopoly profits may be substantial

,

and may further result

in biased

innovations

(of the

Binswanger -..Hayami - Ruttan type) affecting the i ntertemporal grow':.t h I:)ath ( of the ec on omy. p 1 a

-3 . .' ) N .

) >~:,

on the other hand, its

3

/ Wp

suffers from

decisions,

labor-hire

associated with the

1 / Lp, AL 3

and from

"politicization"

of

incentives. In

particular,

distorted by an is

interference factor,

INT±

(0
,j. c i nsc E

r=

Sectoral

"umJ

1 / 1 NT]

1

i'

[I

'WI,.,)

>s , .-M,,) Ri,

Xr
/ ( I NT'. 'W: : ,.) ]3

1/ (,..k

tun

Total

XS,.

= XS,.

sector i

output in

(I

+ XS,

Given labor demands in

= E

each sector,

category s can be calculated.

each skill

DL,

then becomes:

(Lp

,

total

-17)

labor demand

for

Thus,

(11-18)

+ L.i,.)

i

In fixed

at

natural

Stage SLi,,:. growth

I,

l.abor

These, rate

for

supplies by skill however, l.abor

wi:ll. be and

21

type are endogenized

assumed to

be

by assuming

recoglnizing the possibi.lity

a o.f

migratiU.on from agricultural

to urban

sectors in the second,

dynamic stage of the CGE Model. Given *fixed labor supplies for each market clearing nominal

wage rate,

W.,

skill

category, the

can be found via iteration

on

DL

- SSL

= O

(11-19)

Note that,

for certain

skill categories

the nominal

wage

rate can be taken as given or having a lower bound, reflecting,

for instance,

becomes a fixed variable and the level determined by the level The model factor

The'n W.fi,

government's policies on minimum wages. of employment is

of demand.

can further be enriched by specifying monopolistic

markets reflecting

flow of the core model, Having derived

labor unions' power and so on.

however, will

the wage bill,

The

remain the same.

the profits of the enterprises

can easily be calculated as residuals in the sectoral

value added,

Thus, the private enterprise profits become:

RPF'

=

PF'Nr,

XSp:,i

-

E

WpA ,,,:,L LF) ,,J

and the public enterprise profits

R C3.

PNg±

'

XSj.

Ez

(II

-2"0)

(losses if negative) are:

(II-21) (11-21

FOREIGN

TRADE

Now we can construc:t the trade equations of the import side, problem

recall

domestic: In

good,

that the marginal to their

function

with imported

good,

M:,.

a

and the

the buyer's problem

demand

ratio

is

which satisfies

simply to find the condition

rate of substitution between Mi

and DC.

be

respective price ratios.

convenience,

I

repeat here the composite commodity

(II -1)

-

CCI,. :=

CC.,

Economics jargon,

For

"cost

IDC. , taken as "inputs".

the import-domestic

equal

where the relevant

was one of a CES formulation used to "p3roduce"

composite commodity,

On

that we have specifi ed the buyer's

as one of cost minimization,

function"

our model.

B.:L .I:

M..

I.

-

+

::.

-"1/p

(II - 1)

( - E. ) DC

The Lagrangean of the buyer's problem is:

S = PMi.

MI. + PD.

* DCi

+ > LCC

- BBi ( 8M-.

-'.:.

+

where CCi is order

(l-&:L)

a pre-specified

conditions of this

mi

Recall

M/./DCt

that

DC±

=

1/

:'

]

level

(11-22)

of

"output"

of CC:.

The first

problem yield:

( 1/ 1-

(PD.i/PM.t )

.'i = 1/l+p:.'.,

-

)

is

the elasticity

Import demand for commodity i

.. )

(II-23)

of

substitution.

can be found easily from

(II-23):

Mi.

calculated and be fed into

(II-24)

DC,.

point DC, is

at this

However,

.)

(C/l-

(PD.i/PMi.)

=

Yet,

(II-24).

without

import-quantities domestic production/consumption cannot be realized and there is and M±

A simple trick

simultaneously.

market,

DS.,

decisions

solving for

both DC±

solves the problem,

domestic supply minus exports.

given by total

is

knowing the

that domestic supply for domestic

by using the identity

however,

no way of

needs to be

It

not yet known.

We

get, DS. = XSi

Further,

in

DCs

Hence,

=

(11-26)

DSi

using

Mi

(II-25)

E,

product market equilibrium we must have

=

commodity

-

i

(11-26)

we can derive the import demand

for

as:

(

(PD' /PMi )

/l-i)

DS,.

(11-27)

which is a workable relation for the Model. On the export side, price for each commodity. prices as in

equation

we first

need to formulate the export

Similar

(11-3),

to the treatment

of import

the export price relations can be

formulated as follows:

PEj. = PWE±

where PEI.

is

from sector

*

(II--28)

(1 + SE±.)ER

the domestic currency receipts per unit exported i;

SE.

is

the rate of export subsidy for the product

24

of

sector i.;

CU.r rr e n i

and PWE:,. is the -fixed world price in foreign

,,

Further, there are certain have to impose on

constraints that

(11-28) to guarantee meaningful

price of

, the domestic

commodity i,

then

the Model

instruct the productive enterprises to export all output

leaving

nothing for domestic consumption.

situation should, of

commodity i d omest i cal

than

will

of the domestic Such a

course exert upward pressure on PD.. until

both prices are equalized. possibility that

we

results in the

Note that if PE.,. happens to be greater

rest of our model. FPD

behavioral

Thus, although there is

PE:. > PDi. and that

all

the logical

domestic demand for

mgight b:e satisified through imports, whhil.e all

that is

y produced be i n g sol d abroad, we will rule out. t hi s

extreme behavior by recognizing the following constraints on the ex:port side. PD.

!:PE.i. such that

if

PD., - PE. , E

if

PD> Yet,

!:0

PEi , Ei

= 0

another problem is the very hypothesis we have invoked

about the treatment of tradeables in general. distinguish products by country of origin

Accordingly, we

and hence, there is the

possibility that the export demand functions .for the home country's products may be less than infinitely elastic. The export then

be in

E.

demand functions for

the form:

E. (AWPF

, PWEI)

our country's products must

is an

where AWPi

world price for products in the

"aggregated"

all

aver.age of

trade policies

costs and

production

reflects a wei..ghted.

as well

s ector i 's out!:put category which,

of all

countries. In

special

sense that PWE:L

However,

the small

retain

we will

),

E.(

the specific form of the export

designing

AWP

PWE,

costs will

(II-29)

as we present them

increase in

the export

leads to a fall

to remain constant export demand market

there will

for product

i

the price of

and raise

In

be an

and

our our

Also an

or a devaluation

(an increase

the latter

if

case,

increase for our

hence,

an

increase

AWF'.

were

country's

in

our

world

share.

Following (1982)

FWE .

in

increase

into the world market.

subsidy rate in

an

deduce that

increase PDI

exportables

of ER)

sectoral

rate:

we can easily

(II-29)

production

Dervis and Robinson

one can make the assumption

whole behave according generalized composite in

in

= PD./[ (l+SE.)ER3

From

by the

determined

as reflected

export policy

the exchange

and

in the

as fixed and given.

endogenous price,

now becomes an

domestic production costs, subsidy rates

country assumption

be treated

will

demand function

to the rules

CES function specifying

good.

(1978) that

and

also Dervis et.

the world consumers

of cost

minimization

form:

26

as a

with a

the world commodities as a

We can then specify the export

the single elasticity

al.

demand

functions

E . = E.,

(AW ./ PF'WE

(I -30)

)

where ':(.is the elasticity of export demand and EJ.i.is the normal trend level

PWE,.

of the home country exports when AWP:I.

Having thus constructed the export demand equations, what

is

left for us is to find an endogenous expression for the export subsidy rate, SE,..

Many governments, instead of

granting a

single ad valorem subsidy rate to ex porters, provide a comp:lex set

of incentives for producers to encourage the ex.portation of

their products.

These incentives may range

neighbor mercantilist policies, to a tradables.

In this paper,

from beggar-thy-

laissez--faire treatment on•

a policy pacl.kage consisting of four

different ex.port incentive schemes is recognized modelled

These are:

son tn.:, (1) rebates on pr.).oduction taxes,

the products destined for exports; income tax

and explicitly

(2)

allowance on the corporate

at a certain percentage rate of export

earnings;

permission of

.dutyfree intermediate 'imports used for the

production of

exports;. and

valorem export subsidy paid out of

(tax

(4) if

(3)

a sectorally di.fferentiated ad negative)

rate which is directly

the government budget.

It w:i.ll further be assumed sets sectorally differentiated

in the Model

that the government

"eligibility criteria"

that may benefit from the above schemes,

on ex.ports

such as exports destined

for designated world markets, or export earnings exceeding some minimum value in foreign currency, etc.

Depending on the

st.r i ctness of these cond i t i ons it will b e assumed that the eli gi bility rate for exports in the pr'od.ucti on tax

r'ebate and

allowance on corporate income tax schemes is historically around

27

is

For the remaining

exports.

of total

ee. percent

two schemes ee

taken to be 100.O under

Therefore, sector

TSR±

i

will

= tn:.

be:

* ee:L

* FPWE

which corresponds

* ER

allowance

granted

TKA = kta

* Eee

* EE

income tax

TSA:.

* PFWEi

* eel

which corresponds

percent.. income tax

total

(II-32)

, E,

* ER

the granted corporate

kta

* ee± scheme,

allowance

income tax allowance rate.

(corporate)

PWE.

* ER

income tax rate,

scheme is:

subsidy on exports due to this

= tk

of tn.

is:

Letting tk denote the capitalist total

(II-31)

to subsidy equivalent

Under the corporate

where kta is

subsidy granted to

scheme total

the first

* E.

(II-33)

to an ad valorem subsidy of

tk ,

ee.

kta

percent. As for value of

the third

imported

scheme,

observe

intermediate

that

the domestic

inputs used for export

currency

production

is:

EMI.

= EPWMj

* ER * dj

, mj

* a.:

(II-34)



J

where d. is the domestic use ratio of the j-th composite good (see equation

11-57 below);

and mnj

ratio introduced in equation gives the amount of

imported

is the import-domestic good

II-23 above.

Thus d

intermediate good

good i produced and exported.

28

* mj

* 'a

j, per unit of

tax to be paid on such imports then becomes:

import

Total

=T Etmj. , PWM.. 1

T"EMI'

dj ,

ER R

,

m.J

a...j

)

(II--3

Ei

which gives rise to an ad valorem subsidy rate of *dj mj

Etm.j* FWM

) per unit of exports.

* (1/PWE.

aji

-i

Combining

=- (tn . + tk

SE:i.

export subsidy rate becomes:

the realized overall

on exports,

+ Etm.j

(II-36)

ee,.

* kta)

d..

* PWMI.

PWEi in

equation

above expression further entails solved by numerical Balance

* M:. -

EPWM ±

) + te,.

(I/PWE:

a.j. 2

m..

J

which appears in

subsidy/tax rate of te.

sectoral

with an explicit

Note that since the

(11-29). PWE. ,

it

needs to be

methods.

of Payments EquIilibrium is

E.

EF'WE:,.

FF -

then achieved when,

C 0

WR

(I1-37)

.

where F and WR starnd for resource

the ex:ogenous value remittances,

inflow and workers'

of the net

foreign

respectively. (which

is

the

If

as well a

exchange rate is

allowed to adjust freely

policy decision,

hence we continue to use a circumflex. on ER),

will if

(I1-37)

need to be iterated until the government chooses to fix

is

satisfied.

at some value,

ER

guarantee that Balance of Payments Equilibrium would (a to

surprise to no one!); imports

ration

resources. abound

and

works cited

or

try

hence, to

Such commercial the :i.n

interested

reader

the References

there is

no

be satisfied

or get

more

foreign

analyses using CGE Models may wish

to this

29

Per contra,

the government would need either

increase exports, policy

ER

to

paper.

consult

with

the

are

INCOMES GENERATION,

CONSUMER DEMANDS

The functional Model

AND SAVINGS

incomes of different consumer

are generated using the results derived in

groups of the the factor

markets and the derivations are quite straight forward. For labor- skill-type total

YL.

s,

assuming that the tax

rate is

ts

disposable income can be written as:

=

where w group

E

(1-ts)

is

',Lp,.

(WI

+

S..Lg.±.)

the share of workers'

)

4

*WR'ER

remittances

(II-38)

captured by labor

s.

Capitalists'

disposable income becomes:

ERP,

YK =: (l-tk)

(I 1-39)

Fublic enterprises'

YK3 =

+ W

(1-tk)

aggregate after-tax

income is:

ERG.

(II-40)

Government's total

income

is: (II-41)

YG = Ets E(WpisLpi,

+ tk E(RF'.

+ RG± -

+ ECtm ,*PWM.t

-

kta'eei*PWE. sEREi±)

ER,'M-EtmAjPWM.,

+ Etni :F'PDXSI-ee: .

+ W,.iL,,,)

'*PWE± 'EREi]

ERd-j *mj

-

Yte

a.1 ,E±3

*PFWEi *ER E,

sn

1 [sn±

,PD'D.

,XSp,.

+ sn.,

(

,-.O,

(B-4)

C.K:

CL..

where of

I

and

.,

type-s,

are

income

and of

of

elasticities

the capital

ists,

consumption

respectively.

clemand Note that

the system of

is

consumption demands

function of PC~'s

specified as a

originally

(the composite good prices); of

need to have an expression for the elasticity price. demand with respect to the dom.estic ...

( CL.

t.i . =

) * (FPC./F'PD.

) * (PCi../CL.B

/F'PC

which explains the presence of tFOD,±

)

i

(B-5)

(F'PD./PC,. )

(the elasticity

of composite

(B-3) and

(8-4).

Thus:

F:'C

(-I)

(B-6)

F-DI

In order to find the elasticity of first begin by writing the components of

Z.

we use

government consumption demands are given by the

fixed share-coefficients. 0 Mt-

we

consumption

Thus,

price with respect to the domestic price) in The sectoral

and yet,

investment demand we Z±

more clearly:

E (HjTFPS + HGj ,( IF)/PKj]3

= Ebij -i

(Hj*TPS + HGj*'GIF)/( Eb

SEb,. j

..,*PCJ

(-7)

*I.,

j

Thus: 9Z./aPC,

= -Eb... -

CH..jTPS + HG.j, GIF3/(Eb,: , FPC .)

j

I*:

which yields z

s..ZC == (Za./PCFC

=

-E Cbi. .j = -E

) * (PC./Za)

(Hj'*TPS+HGj *,GIF)(PCF:',/Z.)/(bUi

The latter

component

/ d W ....,. * d W .. ,,,/ld D ) :i

(dL...j,,/dW..i,,; dW.js,/dPD:s.)

is

embedded

in

solution algorithm for clearing the labor markets and yet observable

in

a functional

formm.

able to make use of the functional

(1)

I am indebted to Prof• point.

T".

In

what

follows,

relationship

the is

we are

(B-11 ).

Roe f:or his comments on this

67

1)

not

not

intermediate demand

of

The assumption that the elasticity

is XT)

zero,

Yet,

clearly puts a downward

as we argued,

bias on the aggregate value of

.

due to the fixed-coefficients technology, of

overall price sensitivity

the

intermediate demands have to be very

low and the incurred bias shouldnot be substantial. P'C;

Our final

task is

to derive an expression for

to,-

.

Since, aT

FPC

(l-a.-

= 1/B.tE6:.

i.A

)

+

PMi

( -a•

1/I

)

-a.,

J

PD,.

(1-$.)

(B-12)

we have a 9aPCC /sPD

=

(PC:. /PD

a i.t

)

(l/B.)

(PD

/PCF . )