Journal of Applied Input-Output Analysis, Vol. 13 & 14, 2008

Price-endogenized Inter-industry Approach with Goods and Bads1

byPongsun BUNDITSAKULCHAI\ Hajime INAMURA1 andShigemi KAGAWA*

Abstract

Being used by local governments in many regions of Japan, the industrial waste-disposal
tax is thought to contribute a restraining effect in reducing the environmental burden. How
ever, whether this tax alone is effective and, if so, how much the tax rate should be areamong the controversial questions need to be solved. Based on the advancement in recycling technology and the importance of demand side management from a material-cycling
viewpoint, moreover, it is extremely important to introduce the appropriate methodology for
determining the optimal policy among the proposed alternatives. The present paper pro
poses a computable general equilibrium model emphasizing on the framework of the waste
input-output concept and thoroughly describes material and current flow among economic
sectors. Finally, we apply the proposed model to environmental scenario, accounting for
the waste disposal tax and its economic and environmental effects.

Keywords: Waste disposal tax, Industrial waste, Municipal solid waste, CGE model,
Policy implication

Correspondence Address:
Pongsun BunditsakulchaiSocio-Economic Research Center, Central Research Institute of Electric Power Industry, 2-11-1 Iwadokita, Komae-shi, Tokyo 201-8511 JAPANE-mail: pongsun@criepi.denken.or.jp

1 An early version of this paper was presented at the International Input-Output Meeting on Sustainability, Trade and Productivity from July 26th to 28th, 2006, Sendai, Japan. We gratefully acknowl
edge Masato Yamada and the Research Center for Material Cycles and Waste Management, National
Institute for Environmental Studies, Tsukuba, Japan for providing us the 1995 waste input-output

data. Despite this kind assistance from so many sources, any errors in the paper remain the sole responsibility of the authors. The opinions and conclusions expressed in this report are those of theauthors.

* Socio-economic Research Center, Central Research Institute of Electric Power Industry, Tokyo, Japant Graduate School of Information Sciences, Tohoku University, Sendai, Japan$ Graduate School of Economics, Kyushu University, Fukuoka, Japan

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Journal ofApplied Input-Output Analysis, Vol. 13 & 14, 2008

1 Introduction

In Japan, domestic recycling system has been increasingly promoted as a way to copewith the environmental problems involving energy consumption, global warming, andwaste disposal resulted from both consumption behavior of the household sector andproduction behavior of the industry sector. Such recycling system is based on a sce
nario in which new raw materials are saved by actively using recycled materials under

the recycling strategy, and thus eliminating energy consumption and carbon dioxide
emission that could have resulted from the production of those new raw materials.
In recent years, despite the growing consciousness in favor of waste reduction,
reuse and recycling, there is still no consensus as to what extent we should achievethese goals, who should implement the plan, and how they should be done. In this respect, we could therefore say that the waste management policy designed to achieve
the goal of a sound material-cycle society still remains in a state of trial and error.
In 2000, the total household waste emission2 in Japan amounted to 52.36 million
tons. That translates to waste emission per capita per day of about 1.132 kilograms.
Part of the refuse was sorted and then collected from all municipalities to be recycled.
Combined with the recyclable wastes that were processed through the intermediate
treatments, they amounted to 5.09 million tons. On the other hand, the recycling waste
called-back by registered resident groups under the subsidy from municipalities was
2.77 million tons. In total, the recycling waste of 7.86 million tons represents a recycling ratio3 of 14.3%. Summing together the direct land-filled wastes and the final dis
posed wastes after intermediate treatments yields the total land-filled wastes of 10.51
million tons. At the end of 2000, there were 2077 facilities used as dump yards for fi

nal disposal of general wastes. The remaining landfill capacity was 157.2 million m3,
which was estimated to last about 12.2 years4.
For the industrial wastes, the circumstances are more severe.

In 2000, the total

discharged wastes were 406 million tons. Among these, 184 million tons (45.3%)
were recycled and 45 million tons (11.1%) were land-filled. There was only 176.1
million m3 available as the remaining landfill capacity, giving an estimated 3.9 years ofindustrial waste landfill capacity5 (Ministry of the Environment of Japan, 2003a).
2 Total waste emission = Collected garbage + Directly brought-in garbage + Home-disposed garbage.
Base on the waste-disposal law, the amount of general waste-disposal is calculated by subtracting"Home-disposed garbage" from the total waste emission and adding "Recycling waste called-back byregistered resident groups".

Using this definition, the emission amount in 2000 is 54.83 million

tons.

3 r.

• „^

Total recycling waste irt^

3 Recycling ratio (%) = -—l*-r-.—xlOO =Total waste emission

4 „5.09+2.77 ,^CA 0„ xlOO = 14.3%

54.83

. .

Remaining landfill capacity up to the end of fiscal year-—
(Total general landfilled wastes/Relative density of landfilled wastes = 0.8163)
s ^Remaining landfill capacity up to the end of fiscal year
^ Remaining year =e——, . ,. ;, ,^„ ,~—.
Remaining year =Total industrial landfilled wastes

Consider the relative density =1.0

Price-endogenized Inter-industry Approach with Goods and Bads

95

As the increase tendency in quantity of discharged wastes could be expected fromthe rapid growth ofinternational trade and world economics, the capacity offinal waste

disposal will be tightly pressed. Various kinds of environmental issues will certainly
arise. Consequently, it is essential to construct an efficient system ofproduct recycling
circulation in Japan.

In order to reduce environmental externalities from industrial activities and ourconsumption lifestyles in a community, appropriate policy instruments aiming at mini
mizing emission and closing material cycles are necessary. In Japan, the industrial
waste disposal tax is the first environment tax enforced under the anticipation that it
help, to some extent, control the environmental burden released from industrial wastes.

Moreover, considerable attention has been centered recently on the hypothesis thattaxes imposed on polluting activities yield a double-dividend in that it helps not only
to protect the environment but also to raise revenue that can be used to reduce otherdistorting taxes (Bovenberg and de Mooji, 1994; Goulder, 1994).
However, whether this tax alone is effective and, if so, how much the appropriate
tax rate should be are among the controversial questions need to be solved. Moreover,based upon the advancement in recycling technology and the importance of demandand supply side management from a material cycling viewpoint, it is important to introduce an appropriate method for determining the optimal policy among the proposed
alternatives.

Even though there is an evident chain consisting of production, consumption,
waste generation, and waste disposal (or recycling), the decision making at each link
along the path is performed in isolation from the other. This mechanism impedes theconscientious recycling of potential resources contained in wastes. For this reason, it isessential to establish cooperation in forms of social systems that regulate the flow ofgoods and bads from an environmental viewpoint through the processes of manufactur
ing, consumption, waste generation, and final waste disposal or recycling. Economic
instruments for restraining final waste disposal and promoting recycling are some of
the tools to attain such formation of social systems.

In this paper, we develop a computable general equilibrium model so that it can
explicate the transaction between the entire production activities of goods and waste
disposal services and the corresponding household consumption behavior. The mathe
matical model and database developed in this research make it possible to examine theproposed environmental scenarios in order to accomplish a material cycle sustainable
society.

We start from a general idea concerning the overview of economic structure anddata structure of the production sector, emphasizing on the basic framework with thewaste input-output concept describing a fundamental material and current circular flow
among economic sectors. This is followed by mathematical expression of model's
structure to give more details about the production and demand specification, and also
how equilibrium conditions are characterized. Finally, we apply the model to the pro
posed scenario, particularly accounting for the waste disposal tax and its economic andenvironmental effects.

We draw several important originalities from this CGE model. Firstly, it takes
into account the waste generated from virtually any waste source in the economy, including municipal solid wastes (MSW) from final demand sectors, industrial and com-

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Journal of Applied Input-Output Analysis, Vol. 13 & 14, 2008

mercial waste from the goods- and services-producing sectors, and treatment residues
from waste treatment sectors. It also encompasses the entire life-cycle of each productfrom the production to consumption, disposal, and recovery and captures each pricepaid along the way, so taxes or other policy instruments imposed at one stage havetheir equivalent counterpart at another stage. Secondly, in a case where industries use
the available production technologies and jointly generate the waste, a product-mix
structure within the activity framework needs to be introduced. Based upon the
MAKE-USE framework, the model captures the facts that goods and services industries

produces not only ordinary goods and services but also waste treatment services, while
waste treatment service industries dispose of wastes and then recycles them into prod
ucts. Thirdly, the model expresses the correspondence between the waste treatment

technologies and the intermediate waste inputs taking into account the dynamics ofwaste management, by incorporating an engineering process of waste treatment throughthe allocation matrix.

The present paper is organized as follows. First, as a basis for comparison, we review the related literatures in the next section. In section 3, a mathematical model isformulated, followed by a discussion of the Walras's law and equilibrium conditions in
section 4. Section 5 describes the economic accounts and a basic structure appropriate
for computable general equilibrium analysis and a micro-consistent benchmark data set.
We show the results from model simulation under the proposed scenarios in section 6.
Finally, section 7 concludes the paper.

2

Literature Review

To evaluate the merit of the system of product recycling circulation society, it is necessary to make clear the demand-supply balancing structure accompanied by the ability
to estimate the waste quantity excreted by each industry and household. The crucial

starting point aim at waste disposal policy analysis is the development of the Waste
Input-Output (WIO) model (see Nakamura, 1999; Nakamura and Kondo, 2002; Kondo

and Nakamura, 2004). The WIO model describes how different types of waste are
generated and treated by different technologies in a research framework that is widely
acknowledged among the industrial ecologists. Kondo and Nakamura (2005) present a
decision analytic extension of the WIO model. The model is extended in several direc

tions and the authors present another extension using Linear Programming (LP) to
identify the waste management and recycling strategy that maximizes 'eco-efficiency'
potentials subjected to technological and resource constraints.
Kagawa (2005) explores another extension of the WIO model and introduces theextended input-output framework by Miyazawa and Masegi (1963) to WIO model
where income distribution, household consumption and household waste production are
explicitly accounted for. The study by Miyazawa and Masegi (1963) interconnects
household sectors with inter-industry accounts, opening a variety of new possibilities ofaddressing the effect of demographic changes, the rebound effect, income inequalities

and household consumption patterns that are of great interest in industrial ecology.
Kagawa (2005) not only presents a thorough theoretical basis for the household endo-

Price-endogenized Inter-industry Approach with Goods and Bads

97

genized WIO model but also demonstrates the applicability and the usefulness of themodel with a case study.

Takase et al. (2005) introduce the augmented framework with the structural relationship representing the dependence between household consumptions and household
waste generations. This framework is every useful in analyzing the consumption rebound effects. Takase et al. (2005) also estimates C02 emission and landfill consump
tion induced by household consumption. They empirically evaluated sustainable con
sumption scenarios, such as shifting transportation mode from a private car to public
transportation and the longer use of household electric appliances.
In the environmental taxation aspect, Pigou (1920) first suggests a direct tax on
waste, at a rate equal to marginal external damages, as an efficient method of control

ling pollution. As a practical matter, however, enforcement of this tax may not be fea
sible, for example, due to the possibility of inducing illegal dumping or burning. Re
search by Russell, et al (1986), also indicates that the U.S. government monitoring andenforcement activity is quite low.
Fortunately, alternative incentive-based methods that retain many of the propertiesof a direct tax while minimizing the need for monitoring and enforcement. A practicalexample is a deposit-refund system (Fullerton and Kinnaman, 1995, 1996; Kinnaman
and Fullerton, 2000) on items such as glass bottles and aluminum cans. The two-part
instrument (2PI) is a generalization of a deposit-refund system, however, because it canbe used to address other types of pollution. The tax and subsidy do not have to apply
at the same rate, to the same commodity, or even to the same economic agent (Fullerton and Wolverton, 2005). Palmer and Walls (1997) also discuss combination of instruments, and Walls and Palmer (2001) provide the closed-form solutions for the first-

best two-part instrument that exactly matches the incentive effects of a direct tax onpollution or waste. If taxing the upstream pollutants is feasible, for example, then
Pigovian emissions taxes along with a combined output tax and recycling subsidy will
generate the social optimum.

Regarding CGE-based models for environmental analysis, Masai et al. (2000) con
struct a dynamic model in which the economic activities and their related environment
burden are integrated and evaluate the economic impact of imposing the constraint on
carbon emission and final waste disposal. However, their model does not explicitly
formulate the government sector's behavior. Tax system analyses, therefore, cannot be

implemented effectively due to the lack of macro-level I-S balance constraint. In thismodel, moreover, the production technology of the pollution abatement inputs is notavailable. This implies no price-responding interaction to the supply-side behavior canefficiently be analyzed. Finally, although household wastes are handled, no disposal
service is required under the budget constraint causing a free disposal propensity.
Kawase et al. (2003) extend the pioneering model of Hashimoto and Uemura(1997) and Hashimoto and Oh (2002) to study the possibility of achieving double divi
dend by applying a carbon tax together with a reduction in other taxes to Japanese
economy through several scenario analyses. A similar static CGE study is presented
by Felder and van Nieuwkoop (1996) as well as Felder and Schleiniger (2002). How
ever, these models do not take the disutility of environment externality, i.e. carbon
emission level, into account.

Their results regarding the double dividend are hence

more or less over- or underestimated.

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Journal of Applied Input-Output Analysis, Vol. 13 & 14, 2008

Okushima (2004) proposed two independent models to study the economic im

pacts of global warming policy and waste-recycling policy. His models are aimed toanalyze the change in not only the effectiveness but also the equity of implementing
environmental tax policy to each sector of the economy. However, the assumptions
used in each model are unconnected. The C02 cut-back effect and the final waste dis

posal reduction effect of each production sector are thus not able to be integrated. To
evaluate these effects in more efficient way, it is essential to incorporate both schemes
into one consistent model. With regard to the waste disposal tax imposition, Okushima

put this tax not only on the final disposal but on all kinds of wastes, including recycled
ones. This obstructs the study on waste recycling promotion effect and should betreated separately instead.

Being the first environment tax actually put into practice in Japan, the waste dis
posal tax and its contribution to waste recycling encouragement are thoroughly studied
using a coherent CGE model in Washida (2004). The possibility of evading the utility
loss due to tax imposing through a tax revenue neutralization scheme is also verified.
However, some theoretical problems associated with his model can be noted. Firstly,
despite the natural difference in treatment methods among 18 types of industrial andhousehold wastes presented in this model, there exists only one waste disposal sector
responsible for all recycling services and final disposal service without intermediate
treatments. Secondly, all recycling services and final disposal service have a constantprice with no explicit production technology. Thirdly, the ratio of waste to be recycled
and final disposal waste to the total production of any industry are fixed, not allowing
producer to choose how much he/she is willing to recycle the total waste emission cor
responding to the market service prices. Fourthly, unlike Masai et al. (2000) andOkushima (2004), Washida's model treats recycled goods as prefect substitutable to pri
mary/ordinary inputs. Finally, the product mix nature of production technology consid
ering by-product and recycled goods as secondary products is ignored.
Centered around these range of existent works, this paper try to develop an elabo
rate environment-integrated CGE model using the 1995 WIO database as a reference
point. Our model contains many points that cannot be tackled using pre-existing models.

First, based on the MAKE-USE framework, secondary products such as byproducts from goods and services industries and recycled goods from waste treatment
service industries can efficiently be handled with price-responsive production technology. Second, the model allows the intermediate waste treatments through the allocation matrix expressing the correspondence between the waste treatment technologies
and the intermediate waste inputs. Third, we incorporate the substitution between theordinary and recycled intermediate inputs/energy inputs into the model with explicit
demand-supply market clearing conditions to study the recycle-inducement effect oftaxes or other policy instruments. Fourth, the model can be furthered modified to copewith a deposit-refund system or a two-part instrument designed to avoid the possibilityof household illegal dumping. This is done by setting all waste disposal prices to be
zero and taxing commodity consumption with the appropriate consumption tax rate.
The effectiveness of implementing a deposit-refund system in the real economy withdisaggregate consumption goods, pre-existing distortionary taxes, and substitution behaviors between recycled and virgin materials or energy inputs is also verified. Readers should refer to Bunditsakulchai (2006) for further mathematical details.

Price-endogenized Inter-industry Approach with Goods andBads

99

3 The Model

In what follows, we describe the large-scale CGE model emphasizing linkages among
sectors and consumer of the national economy. The model provides a comprehensive
framework to analyze the structural effects of federal environment policies. Figure 1
shows an overview of the economy6. Based on the commodity technology assumptionthat there exists an industry mainly producing the concerned commodity by means of awell-defined production technology, all production technologies are separated into m
goods and services technologies, n energy-related producing technologies and waste
Figure 1: The structure of economy
Use Matrix

Waste Disposal Service

Industrial Waste

Industries

Generation

Make Matrix+
Energy Requirement

Substitution

Thermal Recycled
Energy Sources

EffectIntenndustry Portion

Final Demands(By-product Matrix),.

¥>

ofUsc Matrix

Recycled Goods(Technological
Coefficient Matrix)= §Ordinary Commodities

Value added(Primary Factors)

Commodity Output(Supply)

Industry Output

Taxes on Labor Use

HouseholdTaxes on Capital Use—'

Capital Use by Industry—

Disposable Income

Labor Use by Industry

To simplify the diagram, taxes levied on emission and/or discharge from the production process andthe household consumption, taxes levied on the energy input and taxes or subsidies on the virgin andrecycled material inputs.

We assume that, in this model, there are q types of industrial and household municipal solid wastes

need to be disposed of by p waste treatment technologies. The share of industrial waste k disposedof by the waste treatment technology /, s,*, is represented by the industrial allocation matrix
5i=(5ik)fei P,*=i ,. The household allocation matrix S2 =(S(*),=, p:M , shows the share of household
waste k that is treated by treatment method. See also Nakamura, S. and Kondo, Y. (2002) for thefurther detail about this concept.

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Journal of Applied Input-Output Analysis, Vol. 13 & 14, 2008

treatment technologies7. This model also introduces a product-mix structure within theactivity framework where industries use the available production technologies andjointly generate commodity outputs and wastes. All industries are categorized into m
goods and service industries, energy-related industries and p waste treatment service
industries. Furthermore, this procedure implicitly presumes that any waste treatment

service industry mainly uses one of the available waste treatment technologies. Practically, the main waste treatment service can be identified from the waste treatment ac
tivities levels in physical and monetary base.
3,1 Production sectors

3.1.1 NCES (Nested Constant Elasticity of Substitution) system of the production
function

Industrial technology production function is represented by a multi-level production
process as shown in Figure 2. The top level process consists of a Leontief production
function in which intermediate input is combined in fixed proportions with other intermediate inputs and extended value-added. At the intermediate level, industries substi
tute among a primary factor value-added input — capital and labor, a total energy requirement input and a total waste disposal service input. At the bottom level, we also
allow for the substitution between the virgin and the recycled materials or by-products
within the intermediate input components and between the original energy sources andthe recycled ones.

The activity level of /* (j=l,..., m+n+p) production sector expressed in a monetary
value,
gj,
is
given
by
the
Leontief-typed
production
function
gj = min (U\jlb\j,...,Uijlbij, ...,Umjlbmj,VfxlbT) with the intermediate inputs of commodity
from industry j, Uy, the aggregated input other than intermediate input, Vf*, involving a
primary factor value-added input, a composite energy input and a composite waste dis

posal service input, the fixed coefficient of aggregated other inputs, bf, and the intermediate input fixed coefficient, by, which is the element in the use matrix8:)1jn+n+p

B =s m+n+p, 1

Om+n+p,m+n+pbm

Underlying this function is the assumption that intermediate inputs and an aggregatedother inputs are weakly separable. The assumption of such separability permits the op
timal combination of components in an aggregated other inputs to be determined apartfrom the intermediate inputs decision.

The aggregated other inputs function is represented by the CES technological relationship combining primary factor inputs, Vf, a composite energy input, Vf, and a corn-

Here, the intermediate input fixed coefficient derived under the mixed technology assumption andwaste treatment technology assumption is completely different from the input coefficient ais of ordi

nary IO model calculated by simply dividing the monetary value of flow from sector / to j by total
production of sector j, XJXh Please refer to Kagawa et al. (2003) for more information about the as

sumptions used in this model. The derivation of bi} is presented in detail by Bunditsakulchai (2006).

Price-endogenized Inter-industry Approach with Goods and Bads

101

Figure 2: Production function and substitution elasticity{1^

vir8in Amm
Material,^j^piMaterial Substitution Effec&^:&^pmm^9 Vf j I Waste^flisypsal Service , F/ jM^m^^B^n *¥*jPetroleum and ] [ Electricity,{ Coal, Eij J I
f Natural Energy

1^

E2j

Recycled Energy |~§4 ^ Sources, £/ J

Sources,£j y

Energy Substitution EffectIndustrial Waste : Wij, W2j

W4

posite waste disposal service input9, Vf, with a scale parameter df, the elasticity of sub
stitution of and the share parameter af, afe, afw for primary factor inputs, a compos
ite energy input and a composite waste disposal service input, respectively.
V? = Oraf(Vf) <* +a?e(Vje) <r +ar(V?) «"; aYJ+aY'e+aer - 1

The demand function for a composite energy input, a composite waste disposal service

9 In Washida (2004), only a final waste disposal is taken into account here. We, however, allow pro
ducers to choose among various alternatives of disposal technology what suits their wastes with regards to the market price of each choice.

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Journal of Applied Input-Output Analysis, Vol. 13 & 14, 2008

input and primary factor inputs per unit of aggregated other inputs, VT, are determinedby min PfVfx = P^Vf+PlVf+PfV? subjected to the above production technology con\vf,vf,v;\

straint, giving:
Vs

+af

or

+af

OTPj

af-'PJ

l-of

I—

I-of'

(1)

which applies for s =/, e and w.

Capital Kj and labor Lj inputs together form a primary factor value-added that is
produced subject to the CES technology with a scale parameter dj, the elasticity of
substitution between capital and labor inputs of and the share parameter aj. By taking
into account the industry output tax and the appropriate markup rewarding the true costof commodities absent from the model for a given price elasticity of primary input demand, the cost minimization min
PjVf =(\+zf)(\+mf)((\+Zj)rK}+(\+zlj)wLj)
is per\K„Lt\
X
formed so as to determine the factor demand of capital and labor as:of

afj{\+t'j)w
aiHl-a'j)(l-atf)(l+tf)rlj Vf 6j\(*1(\-gj)(\+zf)r
afj(l+vl)w

\-a{

(2)

+(l-arf)(3)

Here, zf is an industry output tax rate imposed on the monetary value, z) is a capitaltax rate, z) is a labor tax rate, is a nominal rental rate, and is a nominal wage rate. my is
the markup ratio expressed as a percentage of unit primary factor cost.
The production technology of the composite energy input and the composite waste
disposal service input are also expressed as the CES functions. As a result, an energy

input coefficient, ey, and the waste disposal service input coefficient, a)y, are derived by
the cost minimization behavior as follows.
\-oj

2 a*

Vf

I-of

ahPii

for /=!,...,n',j=l,...,m+n+p,

(4)

a;

CO'u =

wi

l

vr

ej

2 a*
*= i

\-a;

az(pr+zr)

for i=l,...,p;j=l,...,m+n+p(5)

Here, Ey is the energy input i=\,...,n (for example, petroleum, coal, electricity, andgas, etc.) of industry j, dj is a scale parameter, of is the elasticity of substitution
among energy source inputs, and aey is the share parameter of each energy input. Py is
the price of energy input accounting for the carbon dioxide emission level and the carbon tax. The ordinary input-output model usually treats these energy source input coefficients as fixed. In this model, however, they could be changed in accordance withthe variation in their relative prices and imposed tax rates. This will be explained indetail later. For the waste disposal service demand function, Wy is a waste disposal
service input i=l,...,p (for instance, incineration, waste shredding, waste composting,dehydration, reclamation, etc.) of industry j, 6j is a scale parameter, of is the elasticity

Price-endogenized Inter-industry Approach with Goods and Bads

103

of substitution among waste disposal service inputs, and #J- is the share parameter of
each waste disposal service input. z-'s stands for the waste disposal tax (or subsidy) rate
imposed on each waste disposal service input on physical based unit (such as yen perton) and is the price of waste disposal service input.
3.1.2 Substitution effect

One of the main purposes in performing this analysis is to clarify the behavior of pro
duction sectors with respect to the substitution effect between virgin and recycled ma
terial inputs, such as virgin steel and a recovered steel scrap, in the intermediate input
technology for any industry10. For this reason, while keeping by constant, let us state
the interconnection between virgin material input and waste-recycled input coefficients.
First, the intermediate input requirement of any commodity from an industry j, Uy, isexpressed as a function of a virgin material input, Uy, and a waste-recycled input, Uy',by the following CES function with a scale parameter 6y, the elasticity of substitution
Py and the share parameter @y.
Pf-l

pi,-

Uy=&!j- ffyWQ « +(l-0$)(Uy") *for i=l,...,m,j=l,...,m+n+p

Then, the substitutable intermediate input demands, determined by minimizing the costof producing a given level of intermediate input, are determined by&(l+r,")fl""" Uu dl 'i-ti$+(!-$) Ul-$)(l+r,')/r )

and

(6)

.

(7)

P'h

(l-&)(l+r,')/rA$a+r,")/r j

l-/o;,

\-Ph

+0-$)

Here, by is the intermediate input coefficient of virgin material, by" is the intermediate
input coefficient of recycled material. z\ and t" are the virgin material input tax rate
and the recycled material input tax (or subsidy) rate, respectively. Pi' is the price of vir
gin material (ordinary goods), and P" is the price of recycled material input.
According to the energy input demand, the production sectors also perform thesubstitution behavior like the intermediate input requirement explained above. Let P'e

and P''e be the price of primary and thermal recycled energy source input, respectively.
Then, each industry's energy input price accounting for the carbon dioxide emission
level and tax, Pye and B"e, could be expressed as:/f = P'e+f(J)y' for i=l,...,n-J=l,...,m+n+p,
Pj'e = Pi"e+f(J)iJ' for i=l,...,n',j=l,...,m+n+p,

10 Virgin and recycled material inputs are perfectly substitutable in Washida's model. Masuda et al.
(2000) use the Cobb-Douglas type production function implying that virgin materials and waste ma
terials are substitutable in a symmetric fashion. To avoid the strange behavior against the well observed fact that one can use the latter in place of the former only to a limited extent, an extraneous

elasticity value can be set to any proper low level. Furthermore, the optional constraint can be added
to set the upper limit of recycled material usage for any industry, i.e. to define the model as a com
plimentary problem. For further details, see Ferris, M. C. and Pang J. S. (1997).

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Journal of Applied Input-Output Analysis, Vol. 13 & 14, 2008

where and (fry are (J)" respectively a Carbon dioxide emission level (in Ton Carbon) per

unit primary energy source input and per unit thermal recycled energy source input ofindustry j. f is a Carbon emission tax levied per unit Ton Carbon. By adopting theminimization behavior, the primary and thermal recycled energy source input coeffi
cients, eli and elf, are determined as:
e!j--

E!j

Oep'ie

1

i

e!l--

' Ev~

y-P'i j i-p5•K'-WlcHOif1 I •<8)«lil^:J +d-«)(9)

3.1.3 Price system
Due to the homogeneous of degree one property of the CES functions and under thecompetitive market assumption, each firm exposes to the zero profit condition. Ac

cording to this assumption, it is beneficial to derive the price system of producers forthe purpose of capturing the market clearance conditions later.

Firstly, the price of aggregated other inputs establishes the balance with the priceof primary factor input, the composite energy input, and the composite waste disposal
service input.

PT = Pttj+Plxtj+PW(10)

Next, each price component in equation (10) could also be further formulated using thebalance condition as shown in equation (11)-(13):pf =(i+zna+m^i+zfykj+a+z^wi),

a i)

pJ=tP^>(12)^ =E(pr+rrx

d3)

To account for the substitution effect, each energy input price must again be related to its substitutable primary and thermal recycled energy source input price as:
y= Py ey+Py dj.

Q4)

The price of composite intermediate input, Py, describing the relationship between theprice of a virgin material input, and the price of a recycled material and the composite
price of all intermediate inputs, , are presented in equation (15).

Py = (l +z!)P!by+(l +Zr)Prby'(15)

Finally, combining the composite price of all intermediate inputs with the price of ag
gregated other inputs comprises the composite output price, Pj, as follows.
m

D=PTbT^Ilby(16)

3.1.4 The output of goods and services

To explain the structure of the economy's supply side, we need to apply a make matrix

Price-endogenized Inter-industry Approach with Goods and Bads

105

as a tool to convert the activity level of each industry gj into the output levels ofgoods
and services. We assume that the production levels of primary and secondary products
within industries are technologically constrained, and that the market shares of the byproducts from the industries are temporally stable. The important point is that there
exist no scraps/wastes without the joint- production of primary and secondary products.
This is called the mixed technology assumption. Using this concept, we propose thefollowing two matrices11. The first matrix is called the primary and secondary product-mix (ps) make matrix:
1,1
cfi

C" =

C \,m

%(m+n)xp
rPs

i^m+m.l...

^^ m+n,m+n"px(m+n)

A/;x/jwhere the element (df)iJ=] m+n represents the output of goods / per unit activity level ofgoods, services and energy-related industries j. The elements along the diagonal of a(pxp) identity matrix represents the output of waste disposal services solely producedby types of waste treatment service industries.
The second one is the marketable by-products (mb) market shear matrix:

Cmb =

mb

mb

Cl,l

Cl.nH

mb

mb
C m+n,m+n

C/n+n,lS*mb

Cl,/n+H+lmb
L-m+n,m+n+\

...

rmb

. . .

mb
C m+n,m+n+p

L|,m+n+/)where the element (cyb)iJ=l m+n represents the market share of by-product / of goods,

services and energy-related industries j, and (cTfn+n+j) ±\ m+nj=i,..,P represents the market
share of by-products or recycled products of waste treatment service).
This make structure implies that the outputs of the by-products and recycled prod

ucts depend not only on the goods, services and energy-related industries' activity levelbut also on that of waste treatment service producing industry, while the output of eachwaste treatment service depend only upon its corresponding waste treatment service industry's activity level. Hence, the domestic supply level of each product can be deter
mined as follows.

Primary and secondary ordinary goods, ql = 2dlfgj for i=\,...,>m
m+n+p

By-products and recycled goods, ql' = 2 cfgj for /=!,...,mj=\Primary energy outputs, q'm+i = Sc^g, for i=l,...,n
;'=i
m+n+p

Thermal recycled energy outputs, q'm+i = 2 cT+ugj for /=!,...,nThese two matrices are in fact interrelated through the two-layer input-output structure. Again, see

Bunditsakulchai (2006) for the detail of underlying assumptions and methodology. Even though the

product mix structure is presented in other models like Masui et al. (2000) and Kawase et al (2003),
by-products are not clearly concerned.

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Waste disposal service outputs, qm+n+> = gm+n+j^j=D for i-l,...,pThese complete the main structure of the production side's behavior.
3.2 Representative Households

Now, let us explore the demand side of the model. The production process creates aflow of income to the owners of primary factors that consist of capital and labor as areceipt in the budgets of households and as factor-tax revenues in the budgets of a gov
ernment. Out of their income, households purchase commodities, energy, and waste
treatment services.

Mathematically, the household's net disposable income, Y, can be expressed as
m+n+p

,

"»+/»

m+n

Y„ = (wL+rK+
2j=\ mi(wLJ+rKj)h-T>-xs)+bRg-'^P,i;',-2lP',irh.
\
'
i'=l
/-l

(17)

Here, Z and K are labor and capital endowment of consumer, respectively. These areshown in the data set as total wage and salary and total operating surplus deducted bya capital tax. The markup ratio m} represents the producer's revenue of other missing
commodities accrued to the consumer. zy and z5 are a household's income tax rate anda social security tax rate, b is the rate of a direct transfer from the government treatedas a fixed proportion of total tax revenue accrued to the government, Rg. Ilh and I"h are
the exogenously given investments in the private sector for the ordinary commodity
and recycled product i, respectively.
To take into account the environmental externalities in the society, we use the con

cept of damage function. The environmental damage function D = D (Qn,Q„ W) is associated with total amount of landfill consumption for household municipal solid
wastes, Qh, and industrial wastes, Dh expressed in Ton, and total carbon dioxide emis

sion level, W, expressed in Ton-carbon. The marginal damage functions with respect toeach variable are assumed to be positive and increasing — i.e. the first and second partial derivatives are positive. From the model structure, we could not express this function in the explicit form due to the lack of the function that clarifies the relationshipbetween the consumption level and the amount of discharged wastes or pollutants. As
a result, the social optimal consumption bundle could not be directly derived from themodel simulation process. The best that we can do is carrying out the comparative
static to examine how the physical amount of each environment quality in damage
function change under policy changes, and then comparing the after shock values withthe base-run benchmark levels. Moreover, these externalities are modeled by the addi
tive type in the utility function and do not influence household's marginal utility (thefirst order condition). Then, this problem could be disregard in our model.
Encountering many policy alternatives, the social planner maximizes net social
surplus — household consumption utility less the above social environmental damage
function. We use our model to test for the proposed tax policy by checking the trade
off between decreasing in the utility level and the environment quality improvement.
Note that an integrated approach is necessary for identifying the most efficient policy
instruments and for setting those instruments at the right levels especially in a world
with multiple externalities like our model.

According to the consumption bundles, a weak separability assumption amongPrice-endogenized Inter-industry Approach with Goods and Bads

107

composite goods and services, energy, and waste treatment services is introduced into
the following CES utility function12.
-1

max

77 -

5-1

5-1

-D(Oh,nhW)', yg+ye+yw = l,

TgCg 6 +TeCe * +TwCw

lcf,c„cj u ~where U is a household's utility level, Cg, Ce and C are a composite goods and serv
ices consumption, a composite energy consumption and a composite waste disposal
service consumption of a household, respectively. ys, ye and yw are share parametersand 5 is the elasticity of substitution.
For the case of private markets, individuals ignore the effect of their own activities
on the total externality. Namely, individual household consumption choices do nothave any effect to the changes in the aggregated landfill consumption level and the ag
gregated carbon dioxide emission level. Therefore, the differentiation of damage function with respect to each consumption choice becomes zero.
In this decentralized economy, the utility maximization is performed under house

hold's budget constraint, Y=PgCg+PeCe+PwCw, with the goods and services composite
price, Pg, energy consumption composite price, Pe, and waste disposal service consump
tion composite price, Pw. Then, the following composite demands could be achieved.
y.op-oy^h*s J-

C* ~ ^<5pl-5, v5pl-5
lgrE

i/eJTe/io\

5pl-5 »V10^

T j w-l w

which applies for s = g, e and w.
Next, maximizing the utility of consuming good or service i, Cgi,
(m

6*

5H Wl

EtvQs.

max;Er*=i,subjected to the budget constraint with goods and services price, P'h and consumptionm

tax rate, z\, i.e. PgCg = T>B'(l+zf)Cgi, each commodity's demand is then solved as:
»=i

C, =

r^

(Pl(\+z^\±y%(P;(\+mrfor(=l,...,m.

(19)

Substituting these demands into the above utility function, the composite price ofgoods and services could be solved as shown in equation (20).
ip^grft/ra+tO)1-*)1"*(2°)

As for the utility maximization behavior in the energy consumption and the waste

disposal service consumption, the household performs exactly the same behavior as in
the case of goods and services consumption. As a result, the optimal energy consump-

Another version of household consumption model is designed to verify the effect of proposed waste

disposal taxes under the condition that household waste disposal prices are kept constant. The utilityof household in this system is no longer depended on the waste disposal service consumption. See
Bunditsakulchai (2006) for further details.

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Journal ofApplied Input-Output Analysis, Vol. 13 & 14, 2008

tion demand, G„ and waste disposal service demand, Cw„ is derived as in equation (21)and (22), respectively.

a =(fl"+i*0»)4(srS(fl"+t*^)'t^"77ifor*) «=i.-.»(21)

C- =(pr+o6-(2r^(Pr+rr)'-&j^^TV f«r '=1.-^<22)

Here, </>, is a Carbon dioxide emission level per unit energy consumption of household,Ci. The energy consumption composite price, Pe, and the waste disposal service com

posite price, P„, could also be achieved in the same manner as'3£=(2r^r+rW-&)'~5'

(23)

l

pw = [i:y%(P7s+zry- ^(24)

As the composite prices are included in each demand function, it may be difficult
in comprehending the demand mechanism. For this reason, let us explain again in
more detail about the process the consumers use to make their choices. Firstly, assume
that consumers take the prices of goods and services, energy and waste disposal serv
ices as given. Then, according to equation (20), (23) and (24), the composite prices
could be calculated. Given the household's disposable income, each composite com
modity's demand could then be calculated. Finally, the demands for each goods andservices, energy and waste disposal services are derived from equation (19), (21) and(22), respectively.

3.3 Government and Exogenous Demands
In order to reflect the influence of commodity prices, this model presumes a CEStyped function for an exogenous demand. To capture the effect of proposed environ
mental policy options, such as carbon tax, land-fill tax (or waste disposal tax), we also
make the assumption that there is no need for any waste disposal service demand in
the government consumption bundle. As a result, the government uses the collected
taxes revenue deducted by the direct transfer to a household and the public investment
to consume ordinary commodities and energies as shown in the following disposable
income balance, Yg:
m+n

m+n

Yg = (l-b) R-11B' ir-ll P" I,-.

(25)

I!8 and I"8 are the exogenously given public investment (or increase in stock demand)for the ordinary commodity and recycled product /, respectively. Regarding the con
sumption bundles, a weak separability assumption among ordinary goods and energies

13 Note that the composite prices in household consumption behavior, Pg, Pe and Pw, are not the same as
the composite prices in the production sector's cost minimization behavior, Pj, Pj and Pf.

Price-endogenized Inter-industry Approach with Goods and Bads

109

is presumed. Then, the demands for composite commodities could be derived as fol
lows:

C

=

A'FY,

j^ and C =Xpg^+a-Aype{\-XfP?Yn(26)

where Cg and C are the composite goods and services consumption and the composite
energy consumption of government, respectively. Pg and Pe are the corresponding com
posite prices. Xis the share parameter, and £ is the elasticity of substitution.
»'nUnder the budget constraints, PgCg = HP'Cgi and PeCe = 2/TC, the goods and
1=1

/=i

services demand, Cgi, and the energy consumption of government, G„ are solved as:Cg; —(Bf(±AgHRy-")

and Cd =" m'(±M(R'y*)'(27)

Finally, we could determine the composite price for commodity and energy in term ofeach commodity's price as:/J =(±AgHPy-"YCf and R=(±AHP'T^\(28)

3.4 Rest of the world

To deal with the transaction against the foreign sector, we firstly make the assumptions
that any export-import commodity has the same quality as the domestic one, and there
is no import and export for waste treatment services. We utilize the function form thatshow the response from domestic prices and the exchange rate toward the import andexport demands. Moreover, the import demand is also affected by the income effect,
which is in proportion to the corresponding commodity's total domestic output value.

Ignoring this income effect could lead to an unrealistic reaction in the case that demands for commodities depend heavily on foreign imports rather than domestically
produced ones. Then, under the premise that there is no import and export tariff, we
propose the following functions.
\5«ex; = cor

- |and EX/' = cor'fl-XB for /=!,...,m+n

(29)

x

tp,V~
+Zl(fc!d!f)gj andmi = (ory=i(30)
mr = corP"+ S (Krc't)gj for i=l,...,m+n;'=i

EXi and IMf are the exported value and the imported value of commodity /. o)T and co""are the scale parameter representing the relative price effect of exported goods and im

ported goods, respectively. £„ is the relative price elasticity in the export function. £,,„ isthe relative price elasticity in the import function, x is the exchange rate, and at, is the

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Journal of Applied Input-Output Analysis, Vol. 13 & 14, 2008

income effect coefficient of imported goods. The single dash superscript (for example,
EX!) distinguishes the ordinary goods from the recycled ones having the double dashsuperscript (for example, EX!').

4 Equilibrium Conditions
We first present private market equilibria — ignoring the effect of each sector's activity
on the environmental externalities — and then show how the Walras's law could be

proved from this model. On the production side, the budget balance of each production sector is obtained by substituting equation (10), (11), (12) and (13) into (16) andthen multiplying both sides by the activity level gj.
m

Vgj = PTbfgr+llPTMj=(l+TfXl+m^a+TfykMl+rtwk^gj
n

p

(31)

m

+Z Pljb^jgj+Z (Pr+TDK^jgj+Z PTib„gj

where,

bm+Uj = ~'77Z*77f = bfveeiey for i=l,...,n
§j

Vj

Vfx
vJ

1

Vj

Vw Ws
vJvr'Ji ex w s j?
• ibm+n+i,j = — ~ ~ = bfvljOfy
for i=l,...,p* ij — Jij ey-ritj dj

PI = (l+Z!)B'by+(l+Z!')B"by"

No industry anywhere in the perfect competition world may make above-normal prof
its. In equilibrium, the total value of sales for any industry exactly covers its cost of
production. Were this not the case, industries making losses would cease the opera
tion. Equally, if positive profit were possible, given the constant returns to scale as
sumption used in this model, industries would make attempt to produce large amountsof output and equilibrium could not prevail.

For the private markets, the household budget balance is presented as follows.
m+n+p

m+n

m+n

wL+rK+ S mj(wLi+rKj))(l-z>-Ts)+bR-'Ep'ir-'^P"Ii"h= PgCe+RCe+P„Cw
m

(32)
n

p

=2/?'(l+r0Cs,+2(/?"+^(/>1)C,+E(/>r+rr)C„,
«-l

/'=!

/=1

For the exogenous demand, its budget balance could be drawn as,
m+n

m+n

m

n

(l-b)R-S/?y,'s-2/?7,."g =p,Cg+RC. =I]P'Csl+^P"a,(33)

To close the model with respect to the trade balance in the external-sector transactions,credits must equal debits in the external account, i.e. exports of commodities (received
from abroad) must equal imports (paid abroad).
n\+n

m+n

m+n

m+n

^P'EX!+Zp"EXr = 2/?7M/+2/?7M,".
i=l

/=!

i=i

,=i

(34)

W^7

Price-endogenized Inter-industry Approach with Goods and Bads

111

The equilibrium condition according to the commodity balance states that demands must equals supplies for all commodities and factors. Market demands forgoods include the household demand, the production sector intermediate input demand,and the government demands, along with the export demand for the foreigners. Mar
ket supplies of commodities reflect total production, together with the import demand
component in the final demand. Market demands for factors reflect industry uses in
production; factor supplies reflect the endowments of the factor owners.
Mathematically, let us define the excess demand function for primary factor — labor, di, and capital, dk — as:m+n+pd,= T, IjtfagrL,

(35)

7=1
m+n+p

dk = 2 kjVejbygrK.

(36)

The ordinary goods and recycled goods excess demand need to be separately treated as
the different functions as shown in the equation (37) and (38).
m+n+p

I m+n

\

d'gi = 2 blMig&C.&C.r+If+ir+EXl- Hdfgj+IM; for i=\,...,mm+n+p

I m+n+p\d8r =2 bifbygj+ir'+ir+Exr- 2 dtgj+Mr jfor i=\,...,m

(37)

(38)

Like the consumption goods, the energy consumptions could also be drawn from bothprimary and thermal recycled sources. Therefore, we adopt the following two excess
demand functions.
m+n+p

I ™+n

\

<£= Se,;L,*+C,+C»+t+L+ffi- T,dUjg,+ML,• fori=l,...,nm+n+p

I «+"+/»\

di' =2 ey-bm+ijgj+Im'^a+EX^ 2 Cm+ugj+IM^i jfor i=1,...,/i

(39)

(40)

As the waste disposal service could not be recovered, it has only one excess demand.
m+n+p

dwi = 2 bm+n+i,jg}+Cw-gm+n+j^j=i) for 1=1,...,/>

I4!)

y=i

Finally, we define the government excess proceeds function (the budget imbalance), Dg,
in correspondence with the taxes revenue, as follows.
(m+n+p\wL+rK+T> mj(wLj+rKj)
m

n

f>

+2/rtfc8,+2 ^c,+2 tra,
m+n+p

I

\

+2 x\wligl+tkkig1+xf{\+mJ){{\+x'r)wli+{^yki)gi+f 2

2 ((J}!ieljbm+,j+(l)if'eif'bm+i,j) \gfift I£f tf"2w;.; Igj

(42)

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Journal of Applied Input-Output Analysis, Vol. 13 & 14, 2008

m+n+p Im\

+ 2 2 (z!B'by+z!'B"by")by gj-Rg
Under the above budget balance constraints together with the excess demand functions,
the Walras's law could be established.

First, assume that the exchange rate is given

and all the budget balance constraints are satisfied. Then, the summation of all excess
demand values must equal to zero, i.e.
m

m

n

n

p

wdffnfc+2/Td^^^

=0.

(43)

This model has total of 2m+2n+p+4 unknown variables, i.e. m ordinary goods
prices B', m recycled products prices /?", n primary energy source input prices B'% nthermal recycled energy source input prices B"e, p waste disposal service prices PF, 2
primary factors prices w and r, total government's income Rg, and the exchange rate x.
This equals to the total number of equation (35)-(42) plus the equilibrium trade bal
ance condition (34).

5 Micro-consistent Data for Equilibrium Analysis
We describe here the economic accounts appropriate for computable general equilib
rium analysis and present a micro-consistent, benchmark data set. The economic ac
counts provide an explicit and rigorous data framework that focuses on the interactionsof economic agents. In the collection and refinement of the numerical data base forthis study, the accounts identified variables for which data were required and indicateddesirable levels of aggregation.

5.1 Commodity, industry and waste classifications
The data set on which the accounts are based provides statistical information used inthree distinct phases of the study: (1) in calibration of structural parameters of the CGE

model, (2) in testing the logical consistency of the model, and most importantly, (3) incounterfactual policy experiments.
Three objectives were considered in the selection of data accounts. First, the accounts must explicitly identify flows of products, factors, and income; second, the accounts must correspond to basic variables of the general equilibrium model; third, thenumber of accounts should be as small as possible without relinquishing the first two
objectives.

The following six 1995 Japanese input-output tables estimated by Kagawa et al.
(2003) representing economy-wide transaction were chosen: (1) Input-output techno
logical table (X), (2) Input-output product mixed table (V), (3) Waste Input-output(WIO) table, (4) Physical unit input-output table, (5) By-products and scraps inputoutput table, and (6) Environmental emission coefficient table (See also Ministry of theEnvironmental of Japan, 2003b; Ministry of the Health and Welfare of Japan, 1995).
These six tables are adjusted and rearranged with regard to the industrial types andtheir behaviors of waste generation and waste recycling. The table 1 shows the indus-

Price-endogenized Inter-industry Approach with Goods and Bads

113

Table 1: Commodity (Industry) classification
No.

Commodity (Industry) Sectors (1-21)

Commodity (Industry) Sectors (22-42)

No.

1.

Agriculture

22.

2.

Mining23.

Other transportation equipment

3.

Food and tobacco products

24.

Precision instrument

4.

Apparel and textile products

25.

Other manufacturing

5.

Lumber and wood products

26.

Construction

6.

Furniture and fixtures

27.

Wholesale and retail

7.

Pulp, paper and paper products

28.

Financial service and insurance

8.

Printing and publishing

29.

Real estate

Automobile

9.

Chemical and allied products

30.

Transportation service

10.

Plastic products

31.

Communication and broadcasting

11.

Rubber products

32.

Public administration

12.

Leather and leather products

33.

Education and research

13.

Stone, clay and glass products

34.

Medical service and social insurance

14.

Pig iron and steel products

35.

Other public service

15.

Nonferrous metal products

36.

Service for business16.

Metal products

37.

Service for person

17.

Industrial machinery and equipment

38.

Others18.

Office machines and machinery for service
industry

39.

Water supply
Gas and heat supply

19.

Household electric appliance

40.

20.

Electric and communication equipment

41.

Petroleum and coal products

21.

Heavy electrical equipment and other elec

42.

Electricity supply

trical devices

Table 2: Waste disposal service industry classifications
No.
1.

Waste disposal service industry (1-6)
Incineration

2. Dehydration
3. Shredding
4. Waste-composting

5. Land-filling (Reclamation)
6. Other treatments

trial classification with 42 sectors roughly separated into 2 large groups as 39 ordinarycommodity sectors and 3 energy related sectors (G-industries).
Waste treatment service industries (W-industry) are classified into 6 sectors asshown in Table 2. Each sector has 4 major intermediate inputs for its waste disposal

activities, i.e. electricity, petroleum products, chemical products and transportation serv

ice, which represents the different waste treatment technology. There are 20 types ofindustrial and household wastes in this model (Table 3). The share of waste disposedof by the waste treatment technology is represented by the non-negative rectangular al-

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Journal of Applied Input-Output Analysis, Vol. 13 & 14, 2008

Table 3: Industrial and household waste classifications

No.
1.

Industrial waste (1-20)
Incineration ash

2. Sludge
3.

Waste Oil

4.

Acid waste fluid

5.

Alkaline waste fluid

6. Waste plastics
7. Waste papers

8. Wood chips
9.

Waste fiber

10. Waste residuals of animals and plants
11.

Waste rubber

12.

Waste metal

13. Waste glass and ceramics
14. Slag
15.

Construction wastes

16. General waste particles

17. Office machines and machinery for service industry
18.

Infectious medical wastes

19.

Cinders

20.

Otherslocation matrix Si = (,s,*)i=u,6;a=i 20 and S2 = Cs/*)/=i 6;*=i 20 for industrial and household

wastes, respectively. See Kagawa et al. (2003) for further details about the allocation
matrix used in this research.

5.2 Configuration of elasticity parameters
Elasticity of substitution is one of the most influential parameters in this model, because a lot of parameters and coefficients depend on its value. Consequently, the con
figuration of elasticity parameters has a much impact on the performance of an entire
model. At the same time, the value of this substitution elasticity fluctuates largely ac
cording to difference in the estimation methods and the data bases. Moreover, it is dif
ficult to catch the tendency of these parameters from previous literatures. As a result,in performing the simulations, we adjust these parameters little at a time by taking notice of the feedback from the model and finally we come up with a suitable configuration of elasticity parameters that make a good response of the model as shown in Table

414. Additionally, we also assume that common substitution elasticity applies to all theindustries, but different values apply to different levels of production technology. Notethat the substitution elasticity in the household consumption functions usually has ahigh value as compared to that in the production functions. The values of substitution
elasticity in the exogenous demands' consumption functions are suppressed at the lowlevel in order to keep the behavior close to the fixed coefficient type.

Price-endogenized Inter-industry Approach with Goods and Bads

115

Table 4: Configuration of elasticity parameters
Definition

SymbolValue

Elasticity of substitution in the aggregated other input function
Elasticity of substitution between the primary factor (labor and capital)

ofx

0.5

of

0.6

Elasticity of substitution in the energy input function

of

0.4

Elasticity of substitution in the waste disposal service input function

or

0.4

Elasticity of substitution between virgin and recycled material input

Pi

0.7

Pu

0.7

Elasticity of substitution between natural and thermal recycled energy input
Elasticity of substitution in the household main utility function

5

0.6

Elasticity of substitution in the household goods and services consumption

o8

0.7

Elasticity of substitution in the household energy consumption

de

0.4

ftr

0.4

Elasticity of substitution between the exogenous aggregated demandse0.3

Elasticity of substitution in the exogenous demands' energy consumption

&
le

0.3

t>

Relative price elasticity in the import function

0.3

t"

fcim, &im

-0.25
0.25

With regard to the relative price elasticity in the export and import demand func
tions, Washida (2004) states that it has a propensity to decrease gradually since 1970s
and this value fell down to about 0.2 in 1993 and moved up to about 0.4 in 1997 ac

cording to the Japanese white paper on international trade. Referring to this, we set
the absolute value of the relative price elasticity to be 0.25 in this model.

6 The Policy Implication and Major Findings
6.1 Model simulation scenario

A scenario is a specification of exogenous changes in selected variables of the model.
To conduct an experiment in the CGE model, a scenario is introduced into the benchmark economy. The scenario represents a shock to the initial comparative static equi
librium. AJl other exogenous variables besides those indicated in the scenario are held
constant. The equations of the model are then solved to obtain new equilibrium values
for each of the endogenous variables. The difference between the initial and derived
values of these variables is interpreted as the effect of the scenario.

The experiment is conducted to assess the economic and environmental effects of

it is a standard practice of CGE modeling that extraneous elasticity values are vastly specified on thecase-by-case basis depending on estimation method and available data, as noted in Shoven, J. andWhalley, J. (1992, pp. 118-123) and Washida, T. (2004, pp. 216-217). No econometric estimation by
the historical data is done here. The values are drawn from Washida (2004, Table 7.10 pp. 217) as a
guidance for the adjustment.

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Journal of Applied Input-Output Analysis, Vol. 13 & 14, 2008changes in waste disposal tax policy. This short-run tax policy changes is described bylevying a 1000 yen per ton of tax (effective rate of tax: 1995 price) to the disposal
service of industrial wastes and the household solid wastes by the reclamation (landfilling) method and keeping all other taxes constant.
The experiment is also designed for testing the possibility of alleviating the wel
fare lost as the result of imposing a waste disposal tax under the government revenue
neutralization scheme by keeping the total revenue from all taxes and saving of gov
ernment constant. The tax revenue from the waste disposal taxes can be used to decrease either the income tax rate or the capital tax rate.
Results of the experiment at a national level are reported in Table 5.
If 1000 yen per ton landfill tax is put into execution throughout Japan, the restraint effects to reduce the landfill consumption of industrial wastes and household
wastes are estimated to be about 57.0 (-20.79%) and 1.54 (-19.92%) million tons, respectively. It could be said from these figures that these effects are significant. Moreover, we should take the 8.3 (0.614%) billion yen of recycling facilitatory effect into

consideration. According to the carbon-dioxide emission reduction impact, although it
is seemed to be small, total carbon-dioxide emission is reduced by imposing 1000 yen
per ton of landfill tax. This could be said to be the double-dividend advantage of thewaste disposal tax15.
Next let us explain the influence of imposing 1000 yen per ton of landfill tax

from the welfare facet. In this model, total amount of labor and capital are completely
employed by the production sectors. This makes the nominal net domestic product determined only by the wage rate w and rental rate r. According to the counterfactual
policy experiment, the nominal net domestic product is decreased by 0.007% (19.2 bil-

Table 5: Overall effects of the proposed landfill tax (1000 yen/ton)
Variables

Base-run Value

EV for goods and services(Billion yen)

Total industrial landfill consumption(Million Tons)

0

-13.1

274*2

(-57.0)7Jl(-1.54)

Total household landfill consump-tion (Million Tons)

Total recycled products value(Billion yen)

Total carbon-dioxide emission(Million Ton-carbon)

Gross National Product (GNP) value(Trillion yen)

After-shock Value Percentage change

13482

217.2

6.17

1356 5(8.3)

312.98313'56(-0.57)^(_0 20)929 59-0.005%-20.79%-19.92%0-614%-0.183%-°022%

15 Note that the definition of double-dividend here is different from what defined in Goulder (1994)
and Kawase et al. (2003). Since using tax revenue from the waste disposal taxes to decrease either
the income tax rate or the capital tax rate is similar to those in Kawase et al. (2003), the doubledividend advantage of the waste disposal tax in the traditional fashion is also verified here.

Price-endogenized Inter-industry Approach with Goods and Bads

117

lion yen). This figure somehow indicates the lowering in welfare level. Nonetheless,in consideration of the change in relative prices, we are supposed to refer to theequivalent variation (EV) of income. The accurate decrease in consumer's welfare is
therefore estimated as -0.005% (13.1 billion yen).
By keeping the total revenue from all taxes Rg constant, the welfare lost effect canbe drastically improved by this government revenue neutralization scheme. The underlying reason is that the tax revenue from the waste disposal taxes can be used to decrease the income or capital tax rate. Therefore, the welfare loss is relieved due to theincrement in purchasing power of consumers.

We should also note that the capital uses are more sensitive to the waste disposal
tax than the labor uses. This implies that the economic sectors tend to shift toward thecapital-intensive technology as a result of the elevated rate of waste disposal cost. The
after-shock exchange rate is 0.0247% higher than the base-run value. Hence, the import demands go up while the export demands drop down, bringing about a small defi
cit in the foreign current account.

At the industrial level, the landfill tax has the comparatively greater effect on theenergy and service sector than on the relatively waste-producing sectors such as pulp,
paper and paper products or pig iron and steel products industry (manufacturing sector)
with respect to the percentage changes in the commodity prices, total industrial outputs
and household consumptions.
Incineration and energy producing sectors (Petroleum, Coal, Gas and Electricity)
could noticeably bring about the reduction in carbon dioxide emission, while agricul
ture and mining industry generated more air pollution as a result of imposing the land
fill taxes (see Figure 3).
Figure 4 explains that the recycling-oriented sectors like apparel and textile products, pulp, paper and paper products, and chemical and allied products industries are in

Figure 3: The reduction in carbon dioxide emission as a result of imposing thelandfill tax (%)

1.600

1.400

1.200

1.000

0.800

0.600

0.400

0.200

.

0.000

-0.200-0.400Incineration Petroleum and Gas and heat Transportationcoal products
supplyserviceElectricity
supplyOthersn

Manufacturing Construction.
Agriculturekiinin ?

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Journal of Applied Input-Output Analysis, Vol. 13 & 14, 2008

Figure 4: The increment in recycled product value by sectors (%)
1.000

0.900

0.800

0.700

0.600

0.500

0.400

0.300

0.200

0.100

0.000

Appareland Pulp,paperand Chemical andtextile products paperproducts alliedproducts

Agriculture

Pigironand
Nonferrous Petroleum andsteelproducts metalproducts coalproducts

Foodandtobaccoproducts

Electricity
supplyStone,clayand
glassproducts

the top rank of declination in recycled products due to the affirmative increasing in theprices of recycling waste plastics, construction wastes and waste glass and ceramics.

The thermal recycled products especially petroleum and coal products play a magnifi
cent role in controlling the carbon-dioxide emission through the relatively cheaper intheir prices with respect to those of ordinary energy sources.
6.2 Limitations, extensions, and discussion

Some authors have argued that a Pigovian tax on waste disposal is infeasible becauseof the potential for illicit dumping or burning and the monitoring or enforcement prob
lems (Dinan, 1993; Fullerton and Kinnaman, 1995; Eskeland and Devarajan, 1996;
Palmer and Walls, 1997). However, in general equilibrium, only the relative prices ofwaste disposal services matter, and the waste disposal tax can therefore be set equal tozero as long as taxes on all other relevant activities are adjusted so as to induce desired
relative prices.

To avoid the possibility of illegal dumping, the free collection of garbage is quitesensible with the subsidy on legal disposal close to the direct cost of garbage collec
tion. However, taxes on relevant private consumption are required to restore the proper
relative prices in general equilibrium. This consumption tax rate should reflect the ex
ternality such as aesthetic and health costs on those who live near the landfill area andthe possible externality from illicit dumping or burning. This is called a deposit-refund
system or a two-part instrument. In general case, the Pigovian tax would raise therelative price of polluting choice (such as reclamation) and induce producers to substi
tute for the other input (such as incineration or shredding) through the substitution ef
fect. It would also raise the price of output and thus reduce the equilibrium output
quantity through the output effect. The two-part instrument uses the subsidy to achieve
the desired substitution effect and uses the output tax to fix the output effect. This is
the intuition underlying the two-part instrument.

Price-endogenized Inter-industry Approach with Goods and Bads

119

The welfare lost effect in our model can be further improved by the government
revenue neutralization scheme. By keeping the total revenue from all taxes and saving
Rg constant.

Having industrial waste taxes be national taxes used for environmental
restoration, the problem is arisen in the light of how the revenue from these taxes canbe used.

Other than using the tax revenue from the waste disposal taxes to decrease the income or capital tax rate in relation to double taxation, municipalities have otherchoices such as to raise waste management funds, to put the collected revenue into afund for waste reduction and other purposes, and to use collected fees to fund measures for promoting recycling.
For example, Mie Prefecture levies a tax of 1,000 yen per ton (the same amountas levied in this paper) on businesses that annually generate 1,000 tons or more of in
dustrial waste that undergoes intermediate processing and final disposal in the prefec
ture.

This covers about 60% of industrial waste and the fee does not exceed the costof transport outside the prefecture. Uses for the revenues include subsidizing the costof developing technologies for decreasing business waste generation, infrastructure
preparation around final disposal sites with public-sector involvement, and beefed-up
monitoring of illegal dumping. Taxing industrial waste is an environmental good because it encourages, for example, waste reduction and recycling. There are also expec
tations that such taxes will discourage bringing waste from other prefectures,strengthen monitoring of illegal dumping, and provide funds for environmental restora
tion.

Three observations can be made on this trend.

1.

The Law on Legislation for Government Decentralization, which became effectivein April 2000,made it easy for municipalities to introduce non-statutory independ2.

Local governments are beginning to perceive the importance of economic instru
ments in environmental policy because they can see the limitations to using exist
ing regulatory instruments, as in the increases in carbon dioxide and waste emis

3.

The financial situations of municipalities are deteriorating. Local tax revenues areent taxes (non-statutory general and special purpose taxes).

sion.

slumping badly due to the recession, making it urgent to secure stable revenue
sources.

Although industrial waste taxes provide little revenue, their greatest significance isthat they are a form of taxation which substitutes for income and corporate taxes, andwhich reduces waste generation and the environmental burden. This created an open

ing for environmental taxes, which are used for environmental conservation. The exclusive use of administrative guidance and regulations until now did not offer enoughincentive, but the exemption from this tax for businesses generating under 1,000 tons
offers them an incentive to lower their tax liability by generating less waste. Up to

May 2005, 23 prefectures have already introduced industrial waste taxes.

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Journal of Applied Input-Output Analysis, Vol. 13 & 14, 2008

Conclusion

The present paper contributes to developing the CGE-based model designed for the en
vironmental policy appraisal program. Framework focuses on the entire life-cycle ofeach product and waste generated from virtually any source in the economy. The pro
posed model demonstrates how industrial, household, and waste disposal service (or recycling) sectors are connected each other. In addition, it shows how wastes are gener
ated from these sectors. Calibrated with the 1995 Japanese input-output data set, theproposed model is applied to evaluate the environmental and economic consequencesof the landfill tax by running the simulation in which the benchmark equilibrium of the
CGE model is perturbed by the imposed tax policy.
Some of the results are specified here. By imposing 1000 yen per ton of landfill
tax to the whole economy, the industrial and household wastes are estimated to be reduced by about 57.0 (-20.79%) and 1.54 (-19.92%) million tons, respectively. Accom
panied by the carbon emission suppression about 574.3 thousand tons-Carbon, the pro
posed tax policy could manifestly bring about the total environmental burdens restrain
effect under the relatively slight declination in the welfare level.
This model has some points to be further improved. First, the paper does notconsider the possibility of illegal waste disposal. However, this could be easily doneby setting an appropriate two-part instrument scheme to the model, for example bylevying the output taxes on the dirty goods and followed by subsidizing for clean tech
nology used in production, or for recycling the final good. The point is also to avoid

the enforceability or measurement problems of a tax on pollution by applying the tax
to observable market transactions such as the purchase of an output by consumer andsimultaneously to subsidize other market transactions such as the purchase of clean inputs by the polluting firm.

Second, in many recycling markets, the government orders the producers to recycle their products. Thus, recycling is not voluntary. The government often specifies
the recycling rate of a weight base. Unfortunately, under the strong assumption thatthe technology of each firm remains constant in this static model make us unable tohandle with this aspect. Some adaptation should be implemented to make this model
become more realistic under the economic systems with goods and bads.
Third, considering the recycling promotion aspect, the thermal recycling is much
more feasible to implement than the recycled raw materials because of the inefficiencyof material recycling method. Promoting thermal recycling also contribute to the reduction in carbon-dioxide emission resulting from fossil fuel refinery process.
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