The Dynamic Optimal Policy to Improve the

Water Quality of Kasumigaura•õ

Yoshiro HIGANO* and Takayuki SAWADA**

1. Introduction The in has been deteriorating since 1970's [15, 22]. The local government has constructed the sewerage system, and enacted the ordinance to prevent the deterioration of water quality. As a result, the water quality has been improved, but is still being deteriorated. The average depth of Lake Kasumigaura is only 4 meters and 56 rivers in total flow into the Lake. This is the root cause for the rapid deterioration of water quality. Furthermore, both the rapid population and economic growth in the catchment area due to the suburbaniza tion of the Metropolitan Area in 1980's have made the deterioration more serious. The deterioration has had the following negative impacts on the living and the produc tion environment around the lake: a) impacts on the living: stink of the water bloom, decrease in the quality of the drinking water; b) impacts on the production: death of a large number of bred carp, decrease in the catch of fish; c) impacts on the sight-seeing resource: closure of swimming place, injury of the beauty of the lake. The study concerning Lake Kasumigaura has increased in number as the water quality deteriorated. The subjects of the studies are confined to the ecosystem of the lake (Goda, et al. [6]), the relation between the load of the pollutant which leads the deterioration of the water quality and the economic activities in the catchment area (Hosomi, et al. [9]), the technology of water purification, or the evaluation of the water quality (Aoki [1], Naito [24]). Each study analyses its own subject from each view point. But, the analysis is not sufficient for a substantial improvement of the water quality since they consider neither the total system including both the socio-economic system in the catchment area and the ecosystem of the lake and rivers nor the changes that would occur in a long range of the time

•õ This is a revision of the paper presented at the 32nd Annual Meeting of the Section of the Regional Science Association International (Nihon Chiiki Gakkai) held on Oct., 1995, in Rissho University, Tokyo. The authors are grateful to the official chairmen and discussants of the day who were so kind as to make valuable comments on an earlier draft of this paper. They also appreciate minute and helpful comments by anonymous referees. * University of Tsukuba ** SAP Japan

75 76 Y. HIGANO ano T. SAWADA horizon. The deterioration of the water quality will still continue in future because the catchment area which is a part of the Tokyo Metropolitan Area will be urbanized more rapidly, and the level of socio-economic activities will grow up. There are many studies focusing on the close linkage between the products and the pollutants based on the expanded (inter-regional) I/O analysis (e.g., [14], [20], [231), all of which take account of the Principle of Materials Balance (Ayres, et al. [2]). Namely, the environment is the source of the inputs of natural resources or energies into the production process of the human beings and it is also the destination of the wastes which are residuals of the production and the consumption (eg. Owen [26], Nijkamp [25], Fukuoka [5], Smil [28], ect.). The series of inter-related production processes make difference between the values of input and output of each process (Kohno and Higano [18], Higano [8]). On the other hand, the materials are conserved through the production and consumption processes and the same amount of wastes are discharged into the environment . It must be noted that the deterioration of the Lake will follow the Principle of Materials Balance, too. Pullutants once discharged by the production and consumption activities in the catchment area will flow into the lake finally. Therefore, they will be accumulated (though few will be resolved naturally), and will deteriorate the water quality of the lake unless the (accumulated) pollutants in the lake will be ever removed by the amount which surpasses the amount of the pollutants ever flowing into the lake. In this study, we analyse the dynamic coptimal policy to improve the water quality of the lake considering both the total ecological system in and around the lake and the situational changes over a long period of time. The point of the analysis is that not only the capital accumulation in the region but also the accumulation of pollutants in the lake are optimally controlled so as to maximize the value of the products and the water quality of the lake.

2. The framework of the model

We specify two sub models and one function in order to analyse the optimal policy to improve the water quality of Lake Kasumigaura. Figure 1 shows the skeleton of the model

Fig. 1 The skeleton of the model. Dynamic Optimal Policy to Improve the Water Quality of Lake Kasumigaura 77

Table 1. Kinds of the sources of the pollutants and the policy instruments

([8] [18] [21] [25]), The ecosystem model describes how the pollutants are changed and moved in the lake and the rivers. The socio-economic model describes the social and economic activities in the catchment area and the relationship between the activities and the emission of pollutants. Table 1 shows kinds of the sources of the pollutants and the policy instruments. We assume two types of control-indirect or direct control-of the water quality of the lake. The indirect control is made by reducing either the pollutants emitted or the activity causing the pollutants, i.e., it means control of the sources of the pollutants. On the other hand, the direct control is made by reducing the pollutants in the lake directly. Both types of control are implemented by the local government. The sources of the pollutants have two types, too. One is called-pointed source of the pollutants, e. g. households, factories, etc. The other is called-nonpointed source of the pollutants, e.g., forest, farm land, etc. The latter has the following characteristics ([31]): 1) it covers wide area; 2) the pollutants emitted are moved by the natural forces, e. g., by rain, wind, etc; and 3) we cannot identify who emits the pollutants. So, it is difficult to control the emission by the nonpointed sources of the pollutants indirectly ([7], [27]). Land use planning is effective to control the land use causing the pollutants, and converts it into another land use emitting less pollutants. The valuation function describes how the inhabitants in the catchment area make a trade-off between the benefits of the improvement of the water quality of the lake and the increase in the value added. The optimal policies are derived so as to maximize the valuation function subject to the structural equations which describe both the ecosystem and socio-economic system.

3. The specified model 3.1 Ecosystem model We divide the lake into 4 sections ([6]). The total mass of pollutants in section i in period t is defined as the net stock of the pollutants in section i in period t -1 plus emission by the social activities plus the net inflow of the pollutants from the other sections minus the direct improvement of dredging of bottom sludge or collecting water bloom by the local government: 78 Y. HIGANO ano T . SAWADA

αit=(1-x)αit-1+rit+Σj∈iQji・Cjt-1-Σ j∈iQij・Cit-1-R・kGAt, (1)

in whichƒ¿i

t: total mass of the pollutants in section i in period t,

ri t: total load of the pollutants emitted by the social activities in period t,

cit: density of the pollutants in section i in period t,

kCAt: capital of the local government used for the direct abatement of the pollutants in

period t, x: coefficient of the natural decay of the lake,

Qij: total mass of water moving from section i to section j, R: abatement coefficient.

3.2 Socio-Economic Model The mass of the pollutants which are loaded in the lake through the rivers is defined as the gross pollutants emitted from the pointed and nonpointed sources minus the pollutants removed at the sources of the pollutants by the indirect controls such as sewerage system , combined treatment septic tank, treatment facilities, etc:

pt+l=Pxt+Ez1t+Fz2t+Gz3t+Hz4t+Bnt-DkAt, (2) in which Pt: total mass of the pollutant emitted by the socio-economic activities in period t, xt: production in period t, z1t: population using sewerage system in period t, z2t: population using combined treatment septic tank in period t, z3t: population using septic tank in period t, z4t: population using human waste treatment facilities in period t, nt: area of nonpointed sources in period t, kAt: stock of the purifying plant available in period t, P, B, E, F, G, H: coefficient of the pollutant emission, D: coefficient of purification.

Taking account of both the natural dissolution in the rivers and soil and the effect of the subsidy for using foods less polluting the water quality of the lake, we define the total mass of the pollutants which finally flows into the lake as follows: rt=(1-a)pt-f-IkFPt-JkFAt-Kt3t, (3) in which a: coefficient of the natural decay of the rivers, kFPt: production of cultivating fishery in period t, kFAt: stock of the pollution abatement plant of the cultivating fishery in period t, t3t: subsidy for the cultivating fishery which uses food containing lower nitrogen and phosphorus in period t.

The equations (2) and (3) describe the accumulation of pollutants in the lake . The dynamic equations of the capital accumulation are given as follows: Dynamic Optimal Policy to Improve the Water Quality of Lake Kasumigaura 79

kPt+1=(I-dP)kPt+iPt, (4) kAt+1=(I-dA)kAt+iAt, (5) kGAAt+1=(I-dGA)kGAt+iGAt, (6) in which kPt: stock of the productive capital in period t (including kFPt), kAt: stock of abatement capital in period t (including kFAt), iPt: productive investment in period t (including investment of the cultivating fishery), iAt: abatement investment in period t (including abatement investment of the cultivating fishery), iGAt: abatement investment of the local government in period t,d P,A, GA: depreciation rate .

The flow condition in the product markets is given as follows:

xt_??_AXt+ct+iPt+iAt+BgiGAt+ġWiĢzi

t+ġġS1kĢLkl(t)+ġġS2kDLkl(t)+ăWzt+mt, (7)

zt+1=(1+ng)zt, (8)

zt=z1t+z2t+z3t+z4t, (9)

zit+1=zit+Ģzit-dzit, (10)

in which

A: inputoutput coefficient matrix,

Ct: consumption (including durable goods such as housing) in period t,

mt: net export in period t,

Wi: formation coefficient vector of each system,Ģ

zit: increase in the population covered by each system,

S1k: land use k formation coefficient vector,

S2k: land use k demolition coefficient vector,

Ģ Lkl(t): formation are of land use k in zone 1,

DLkI(t): demolition area of land use k in zone l,

W: social overhead capital formation coefficient vector,

zt: total population in the catchment area,

ă: coefficient of per capita public expenditure for the social overhead investment other

than those for purifying pollutants,

dzit: decrease in the population covered by each system,

ng: rate of population growth (exogenous).

The socio-economic model of this study only covers a regional economy of Japan. We may assume the regional economy is small relative to the whole national economy and it is open system in that products are traded in the open competitive markets. So, we only specify the following constraints on the sum of net exports over the simulation period:

ƒÀ1_??_ƒ° mt+ƒ°(1-M3)•tt+r•EM1ƒ°ƒ¢z1t_??_ƒÀ2, (11)

in which 80 Y. HIGANO ano T. SAWADA

M3: rate of the subsidy for the local government from the central government in period t

(exogenous), tt: total revenue of taxes of the local government,

M1: rate of the subsidy by the central government to the construction cost of the sewerage

system,r

: per capita construction cost of the sewerage system,ƒÀ1

: upper limit of the accumulated net exports (ƒÀ1<0),ƒÀ

2: lower limit of the accumulated net exports (ƒÀ2>0).

Parameters ƒÀi are exogenously gived based on the data for Ibaraki prefectural economy .

We categorize industries into two groups: those industries in which the production

linearly depends on the input of land and the input of capital .

(12)

I nt=ƒ°k•¸ƒÕƒ°lLkl(t), (13)

in which

1nt: cultivated acreage in period t,

Lkl(t): area of the land used for land use k in zone 1,ƒÕ

: set of indices of land use in the agricultural industry,ƒ¿

, ƒÀ: positive parameters.

The construction cost of the sewerage system is financed by the local government bonds and the construction is subsidized by the central government. We assume that it takes 4 years to be able to supply sewerage services since the construction has begun.

(14)

tƒ°r=1 dbt_??_ƒÅ•Ett, (15) in which

dbt: amount of the local government bonds issued in period t,ƒ¡

, ƒÃ: positive parameters, Parameter ƒÅ is exogenously given by trend.

The maintenance cost of the sewerage system is covered by the user charge and the annual expenditure of the local government. mct=t1t+Nz1t, (16) in which mct: maintenance cost of the sewerage system in period t, t1t: appropriation for making up shortage of met in period t, N: per capita user charge (exogenous).

The construction cost of the combined treatment septic tank is paid by the user and the Dynamic Optimal Policy to Improve the Water Quality of Lake Kasumigaura 81

construction is subsidized by the local government.

• ƒ¢z2t=(1/M2)•Et2t , (17)

In which

t2t: subsidy by the local government on the construction of the combined treatment septic

tank in period t,

M2: rate of the subsidy to the construction cost of the combined treatment septic tank,ƒÂ

: construction cost of the combined treatment septic tank (exogenous).

The total revenue of taxes is defined as follow:

(1-M3)•Ett=ƒÃzt, (18)

in whichƒÃ

: positive parameter.

Constraint on the annual expenditure for purifying the pollutants is defined as follows:

t1t+t2t+t3t+giAt_??_ƒÖtt (19)

In whichƒÖ

: rate of public expenditure for purifying the pollutants.

The conversion of land use in the catchment area controlled by the land use planning is specified as follows:

(20)

(21) Lkl(t+1)=Lkl(t)+ĢLkI(t)-DLkI(t),

in which L: total catchment area.

3.3 Valuation Function We assume that the utility of the inhabitants in the catchment area in each period depends on the water quality of the lake and the value added. The utility function is specified as follows:

uit=ƒÊ(yit)ƒ¿-ƒÐ(ƒ¿it)ƒÀ, (22)

In which

uit: utility level of inhabitants in zone i in period t,

yit: total value added in the catchment area in period t,ƒÊ

, ƒÐ, ƒ¿, ƒÀ: positive parameters.

4. Simulation

4.1 The simulation model The model is applied to the catchment area including City and Ami Town. The pollutant analyzed in the simulation is only phosphorus, which has been affecting the

ƒÂ 82 Y. HIGANO ano T. SAWADA deterioration of the water quality in Lake Kasumigaura strongly ([30]). Due to the data limitation, it is assumed that the land use will be held constant over the time horizon . The initial period of the simulation is 1992 and the time horizon is 15 years. Namely we simulate the model from 1992 to 2006. Input-output coefficient matrix is quoted from "Input -output analysis of the economy of ([11]) (Table 2)." Table 3 shows the load of the pollutant by the each human waste treatment system ([19]). Industries are divided into three according to the load of the pollutant in the lake (Table 3) ([19]). The

Table 2. Input-output coefficient matrix

Table 3. The load of pollutant

Table 4. Numerical value of parameters Dynamic Optimal Policy to Improve the Water Quality of Lake Kasumigaura 83 theory of multiplicative utility function is applied to estimation of the valuation function ([16, 17]). We made the questionnaire and sent them for the inhabitants in Tsuchiura City. We obtained 15 answers to the questionnaire and among them 12 have shown consistency. The valuation function is estimated as follows:

ut=325•Ey0.5t-0.4• ƒ¿1.5t (23) yt is measured in million yen and at measured in kg. Table 4 shows other numerical values of each parameter.

4.2 Simulation results Figure 2 shows the total mass of the pollutant in the lake. The rate of accumulation of the pollutant at the period 3 to 8 is lower than at the period 1 to 3. The difference is due to the effect of the abatement capital of the local government which is used for direct purification of the water quality of the lake (Figure 3). The total mass of the pollutant rapidly decreases by period 10. This is the effect of the investment in the sewerage system (Figure 4). The ratio of the direct purification to the indirect is 2:3 and the people covered by the combined treatment septic tank is held constant (Figure 4).

Fig. 2 The total mass of the pollutant in the lake.

Fig. 3 The stock of the abatement capital of the local government. 84 Y. HIGANO ano T. SAWADA

Fig. 4 The population covered by each system (50% case).

Fig. 5 The population covered by each system (60% case).

We also simulated the model in which the cost of the combined treatment septic tank is lower or the purification capacity of the system is higher in order to examine the reason why the population covered by the combined treatment septic tank is held constant. In this simulation the people covered by the system is still held constant. Next, we have analysed the effect of a change in the rate of the subsidy by the central government on the construction path of the sewerage system. If the rate of the subsidization is increased from 50% into 60%, the decline of the total mass of the pollutant in the lake occurs earlier than 50% case (Figure 2). It is due to the earlier construction of the sewerage system than 50% case (Figure 5).

5. Conclusion and Further Development Analysing the simulation results, we conclude as follows: a) the local government should invest not only in facilities of the indirect control but also in the direct improvement. Dynamic Optimal Policy to Improve the Water Quality of Lake Kasumigaura 85

b) though the efficiency of purification by the combined treatment septic tank is high and it can be constructed in short periods than sewerage system, the population covered by the system is held constant. The sewerage system has an advantage over the combined treatment septic tank and the local government should more invest in the sewerage system than the other indirect control. c) the central government should vary the subsidy rate for the construction of the sewerage system depending on the deterioration of the water quality case by case. This study has presented an architecture in which both the ecological and socio-eco nomic activities are simulataneously taken into account in a spatial and dynamic context. However, the simulation depends on the simplifying assumptions and there is room for further development. Unresolved problems are as follows: 1) Data limitation: only old data of the load of the pollutants is available by each indusutry in the region. And, data on the cost of land use conversion are not available. If we could get those data, we could analyse the set of optimal policies including land use planning more precisely. 2) The dynamism of another pollutants in the region and in the lake have to be taken into account, and we could propose a set of optimal policies totally and more accurately. 3) Technical Progress: it is expected that a highly developed and efficient technology to reduce emission of the pollutants in future. So, the simulation have to be modified to take account of such a technical progress in the pollution abatement industries.

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