Modeling Interacting Resource-Economy Systems

NOT FOR QUOTATION WITHOUT PERMISSION OF THE AUTHOR

MODELING INEXACTING

RESOURCE-ECONOMY

S Y S E M S

Anatoli Propoi

Enstitute f o r S y s t e m s S u d i e s , 29 R y l e y e v S t r e e t , Moscow 1 1 9034, USSR

May 1984 CP-84- 17

C o l l a b o r a t i v e P a p e r s report work which has not been performed solely a t the International Institute for Applied Systems Analysis and which has received only limited review. Views or opinions expressed herein d.o not necessarily represent those of the Institute, i t s National Member Organizations, or other organizations supporting t h e work.

INTERNATIONAL INSTITUTE FOR APPLIED SYSTEMS ANALYSIS 2361 Laxenburg, Austria

PREFACE

Many of today's most significant socioeconomic problems, such as slower economic growth, t h e decline of some established industries, a n d shifts in pat- t e r n s of foreign trade, a r e international or transnational in nature. But these problems manifest themselves in a variety of ways; both the intensities a n d t h e perceptions of t h e problems differ from one country to another, so t h a t inter- country comparative analyses of r e c e n t historical developments a r e necessary.

Through t h e s e analyses we a t t e m p t t o identify t h e underlying processes of economic s t r u c t u r a l change and formulate useful hypotheses concerning future developments. The understanding of t h e s e processes a n d future pros- pects provides t h e focus for IIASA's project on Comparative Analysis of Economic S t r u c t u r e and Growth.

Our research concentrates primarily on t h e empirical analysis of interre- gional a n d intertemporal economic structural change, on t h e sources of and constraints on economic growth, on problems of adaptation t o sudden changes, a n d especially on problems arising from changing patterns of international trade, resource availability, a n d technology. The project relies on IIASA's accu- mulated expertise in related fields and, in particular, on the data bases a n d sys- t e m s of models t h a t have been developed in t h e r e c e n t past.

In this paper, Anatoli Propoi examines the interactions between economic systems and those sectors of the economy that produce resources, broadly defined. He presents a general scheme for modeling these interacting systems t h a t can be used to analyze both the structural dynamics of the sector con- cerned and i t s interrelations with the overall development of t h e economy. The method links a process model of the sector of interest with other economic models within an optimization framework, although t h e optimization i s an analytical means rather than an end in itself. The approach is flexible and has the advantage that the individual models can be built and used separately, whilst a t t h e same time making the fullest possible use of information (particu- larly subsystem shadow prices) derived from individual runs.

Anatoli Smyshlyaev Project Leader Comparative Analysis of Economic Structure and Growth

The a u t h o r wishes t o t h a n k Ingrid Teply-Baubinder and Julie Troutwine for t h e i r a c c u r a t e and patient typing a n d Tim Devenport for his careful editorial assistance.

CONTENTS

Introduction

1. A System of Resource-Economy Models 2. The Resource-Supply Model

3. Bibliographic Notes

4. The Cost-Assessment Model 5. The Demand Model

6. The Economy Model 7. Linking the Models

8. The Integrated Resource-Economy Model 9. Discussion: Methodological Aspects 10. Conclusions

References

-

vii

-

MODELING INTWACTING RESOURCE-ECONOMY SYSl'EMS

Anatoli Propoi

INTRODUCTION

Among t h e m o s t i m p o r t a n t problems of modern economic growth is t h a t of s t r u c t u r a l change in resource production and consumption patterns. Here t h e t e r m "resource" is u s e d in a somewhat broader sense t h a n usual, t o imply n o t only energy o r mineral resources, b u t skilled labor, food, water, fertilizers, etc., as well.

Two basic processes underly the problem. On t h e one hand, t h e r e h a s been some depletion of various kinds of resource. More precisely, economies c a n be said t o be shifting from a situation of "unlimited" resources (where t h e prob- l e m of substitution m a y not need t o be taken into account) t o one of limited r e s o u r c e s (where substitution assumes a crucial role). On t h e other hand, new, nonconventional technologies a r e being introduced into resource production a n d usage. Examples include solar and synfuel energy, biotechnology, robots a n d computer-based production, etc.

In short, we a r e now witnessing the transition from old or conventional s t r u c t u r e s of resource production and consumption (which we consider were

"optimal" or "equilibrium" in t h e past) to new, nonconventional structures, which will be "optimal" in the future (Koopmans 1981).

In t u r n , t h e transition period can be analyzed on t h e basis of two main characteristics. First, there is the influence of many interdependent factors on t h e process. When we speak, for example, of the sufficiency of a certain kind of m k e r a l resource in a region, it would be wrong to assess only t h e reserves of this resource: its availability and transportation costs, a s well a s ecological constraints, t h e possib'ility of substitution, and the world market situation must also be taken into consideratioi. Thus, a local problem formulated for a partic- ular region a n d a specific kind of resource very quickly t u r n s into a global prob- lem. Second, we need t o consider t h e dynamics of t h e process. The transition t o t h e new s t r u c t u r e of resource production and consumption requires research a n d development for the new technologies involved, t h e modification or replacement of capital stock, and retraining of t h e labor force. All of these stages need time, s o we a r e clearly dealing with a long-term problem.

For these reasons conventional economic models a r e not appropriate for analyzing transition periods in an economy. For example, t h e production func- tions in econometric models are explicitly based on statistics of past trends and therefore cannot detect or project future structural changes.

This paper describes the approach and corresponding system of models t h a t a r e being developed a t the Institute for Systems Studies in Moscow t o study these +roblems. The approach i s oriented toward analysis of t h e transition period in a particular sector of t h e economy (which produces a certain kind of resource) of a region or country and its interrelations with the r e s t of t h e econ- omy (which consumes the resource). We refer t o the entire interacting struc- t u r e a s a "resource-economy system". Examples of such systems include energy supply-economy, mineral resources-economy, skilled labor supply- industrial production, water supply-agriculture, forage supply-livestock breed- ing. and so on (Carter e t al. 1977; Propoi 1978. 1979; Kallio e t al. 1980; Dantzig

e t al. 1981; Propoi and Zimin 1981; Csaki and Propoi 1982).

This paper considers a system of models of resource-economy interactions.

First, we describe a general resource-supply model and then we discuss its link- age to a model of economic development. The linkage can be performed through a specially built, integrated resource-economy model or by iterative linking of t h e separate models. For the l a t t e r case two special "interface"

models are often needed: t h e first model projects demand for t h e resource and the second model assesses the total costs of developing t h e resource-supply system.

I t

should be noted t h a t such an approach has already been used in one way or another for a number of specific resource-development studies (primarily in t h e analysis of energy-economy interactions).' Nevertheless, much work remains t o be done t o unify this approach, develop t h e corresponding software, and make it available for routine applications.

1. A !3YSIZH

OF

RESOURCE-ECONOMY MODElS

We shall single o u t t h e following stages of resource-economy modeling:

R € ? S O U T C ~ - % ~ ~ ~ ~ Model. Let us consider the problem of the transition of a sector (resource subsystem) of a given economy t o a new production structure;

we may be dealing h e r e with a regional or a national economy.

For this, we normally s t a r t with t h e exogenously given demand for this resource (or for the final product) during t h e whole period considered. Note that t h e demand is usually given in generalized t e r m s t h a t somehow character- ize t h e usefulness of t h e product (e.g., i t might be units of electrical or nonelectrical energy, carbohydrates or protein), rather t h a n in straightforward units of final product output.

Usually, t h e r e exists a number of alternative technologies t h a t can, in principle, satisfy t h e given demand and there are initial production capacities associated with each of these technologies (for new technologies these are zero a t the starting point of t h e analysis). Each alternative technology h a s its own advantages and drawbacks, concerning its input and output characteristics, impact on t h e environment, etc. Therefore, an optimal mix of the technologies

'see the bibliographic notes in Section 3.

phased over time m u s t be found t h a t satisfies the given constraints on demand a n d on t h e availability of external products and factors (which a r e needed for operating and developing t h e resource system) and minimizes some chosen cri- teria. One criterion frequently chosen for minimization is t h e total cost over t h e period considered; and i t can be argued t h a t this type of o p t i m i z a t i o n m o d e l simulates a possible transition from t h e mix of technologies currently used ( t h e initial s t a t e of t h e system) to a more progressive and, in a sense, optimal future mix of technologies.

These kind of models a r e also often called p r o c e s s m o d e l s (Ayres 1978;

Manne e t a l , 1979; Koopmans 1981) because 'they describe t h e process of transformation of a primary resource to a final product (or secondary resource). We use t h e t e r m s resource-supply model or simply resource model t o emphasize t h e role t h a t t h e system modeled plays in the economy.

~ o r ' m a l l ~ speaking, resource-supply models a r e dynamic optimization models a n d in most practical cases they can be formulated in a dynamic linear programming framework (Propoi 1979, 1980). They a r e usually large-scale models because many factors and constraints need to be taken into account. 2 Another feature is t h a t such models a r e typically formulated in real (quantity) t e r m s because t h e associated price relations a r e only starting to be established during t h e transition period.

Note t h a t t h e r e a r e two main groups of exogenous variables t h a t influence t h e behavior of t h e model:

(i) demand for the output of t h e resource-supply system;

(ii) external factor requirements (labor, capital) t h a t a r e needed for operating and developing t h e resource-supply system (see Figure 1).

For t h i s reason, an isolated resource model is limited in its possibilities a n d linkage of t h e resource-supply model to a model of economic development i s in order.

'see the references cited in Section 3,

Figure 1. The general scheme of resource-economy models.

L

Economy Model. This represents the more inertial (or more conservative) part of the economy (in comparison with the resource subsystem). Hence this model can be described in a more conventional way.

I t

can, for instance, be an input-output model or a macroeconometric model. Linking the resource model t o an economy model in principle allows us to analyze t h e process of substitu- tion, not only from t h e supply side but also from t h e demand side. For this rea- son it is expedient t o formalize t h e economy model as a multisectoral optimiza- tion model. Therefore it becomes again a dynamic linear programming or, in other words, a dynamic optimization input-output model.

Economy model

I t

is necessary, however, t o underline t h e principal difference between t h e two models discussed above. The resource-supply model is a detailed optimiza- tion model in real terms: the use ol value terms is inappropriate t h e r e because t h e production relations and consequently the values of t h e various production factors are only starting t o be established in t h e transition period. In com- parison with the resource model, t h e economy model may be more aggregated

v

Requirements from the economy

Demand for the resource A

Resource-supply model

and may be written in value t e r m s (see also t h e discussion of this issue in Ayres (1978)).

There a r e two alternative ways of linking the resource and economy models. First, we could build an integrated model of t h e resource-economy sys- tem; this might be a dynamic linear programming model with a detailed resource sector, such as t h e PILOT model of energy-economy interaction (Dantzig 1976) or a nonlinear optimization model with an aggregated macroeconomic model, like the ETA-MACRO model (Manne et al. 1979). The second approach is to link existing models of resource supply and economic development: one example is t h e IIASA system of energy models (Hafele e t ^al.

198 1).

Both approaches have their own advantages and disadvantages, which will be discussed later. We will now t u r n to a more formal description of the models.

2.

THE

RESDURCE-SUPPLY MODEL

The verbal description of the resource-supply model given in the preceding section implies in a quite straightforward way its formal structure.

Let us consider t h e production of a resource (a final product) by

K~

alter- native technologies. The s t a t e of t h e system in each period t is described by t h e values of production capacities a t t h e beginning of the period for each of t h e k technologies.

The s t a t e equations define t h e change of s t r u c t u r e of the production capa- cities in relation t o investments, which a r e considered as t h e control elements in t h e system. These equations are of t h e form

(k

=

1,2 ,..., K R ; t

=

0.1 ,...,

T

- 1)

where

?/# ) is t h e production capacity of the k-th technology in period t ; v P ( t ) is t h e increase in production capacity of the k - t h technology over

period t ;

do

⁾ is t h e depreciation factor of the k-th technology during period t ; KR is t h e total number of alternative technologies for resource pro-

duction t o be considered in t h e model;

T

is t h e time horizon; and the superscript

R

refers t o t h e resource'system.

An alternative description of the dynamics of production capacities involves t h e assumption t h a t t h e capacities are constant during their lifetime T k . and t h a t thereafter they a r e zero. In this case

The initial s t a t e of t h e production capacities is given by

?/:(o)

=

y i R (k

=

1.2

...

K R ) ( 2 )

In t h e case of ( l a ) i t is also assumed t h a t t h e increases in capacities dur- ing the period preceding t h e time horizon ( t

<

0) a r e given a s well

v ; ( T ~ )

= vi

R ( - ~ k ) ;

By choosing different controls { v ; ( t ) j in (1) or ( l a ) one can calculate t h e corresponding trajectories t V f ( t ) j of the production capacities of t h e resource system. However, not all of these trajectories will be admissible because of t h e constraints on t h e process. We can identify a number of groups of constraints.

First, we consider constraints on output.

Constraints o n the Utilization of the Production Capacities. Let $ ( t ) be t h e output of t h e production capacity for the k-th technology a t time t . E,vi- dently, for each t

Demand Consfraints. We consider JR components by which t h e output of t h e resource system is measured (for example, these might be units of electri- cal or nonelectrical energy; calories or units of protein or amino acids, etc.). I t is assumed t h a t t h e demand for the final product d:(t)

(j =

1.2

...

J R ) is given in these t e r m s for t h e whole period t

=

0,1,

.... ^T -

1. Total production should satisfy t h e demand

where d$(t) is t h e output of final product j per unit intensity of technology k . R e q u i ~ e m e n t s Const~aints. For operating and developing t h e resource- supply system, external factors (capital, labor, raw materials) a r e required. Let f F ( t ) be t h e available amount of factor s , s

=

1,2,

..., sR,

in period t . Then t h e constraints can be written as follows

Here t h e coefficients fAR(t) and f s K ( t ) denote, respectively, t h e amounts of external factors required for t h e operation a n d construction of one unit of pro- duction capacity of technology k

.

Constraints on primary raw materials (for example oil, coal, gas, uranium, in energy systems) are frequently singled out from (5):

where ~ ~ ( t ) is t h e available amount of t h e i - t h category of t h e raw material (primary resource) at time t .

Usually, cumulative consum.ption is bounded by available reserves. So, instead of ( 6 ) , we write

fi(0)

=

5; (the given initial reserves of primary resource i)

for all t

.

Ecological Constraints. Let pg(t ) be the admissible level of t h e g -th pollu- t a n t a n d p q k ( t ) the amount of t h i s pollutant emitted per unit intensity of t h e k -th technology. Then

for each

t =

0,1,

.... T -

^1.

For some types of pollutant it is necessary t o limit cumulative pollution.

In t h i s case

where jiq(0) is given.

Objectwe nLnction. The constraints (1)-(9) determine t h e s e t of feasible strategies for t h e development of t h e resource system. This s e t may still be r a t h e r broad and in order t o formulate a strategy i t is necessary t o specify an objective function for t h e system. The most frequently used objective function for these models involves minimization of the total cost discounted over time

where ~ : ~ ( t ) represents operating and maintenance costs for technology

k

a t time t , cZR(t) is t h e investment required for constructing one unit of produc- tion capacity of the k-th technology, and @ ( t ) is t h e discount rate.

An alternative objective might be maximization of t h e system output

where t h e a,(t) a r e weight coefficients.

It m u s t be stressed t h a t the optimization procedure should not be viewed as t h e final stage of the modeling activity (yielding a unique, "optimal" solu- tion) but r a t h e r as a tool for analyzing t h e interdependence of different policy alternatives and system performance.

Thus the problem is to find controls tvE(t)j ( t h e strategies for resource system development) and corresponding s t a t e trajectories tyE(t)j ( t h e dynam- ics of production capacities) t h a t satisfy all t h e constraints on t h e system (for example, (1)-(9)) and that, for t h e given initial s t a t e t g R ( t ) j ( t h e initial s t r u c - t u r e of production capacities), optimize t h e chosen objective function ((10) or (lOa>>-

The model is particularly oriented toward analyzing s t r u c t u r a l changes in production capacities for a given resource.

Viewed in another way, t h e model describes the process of transformation of a primary resource into a final product. For this reason i t is often con- venient to present this process as a material flow with several stages of transformation.

Let N be the total number of stages of the process a n d let z&)(t) be t h e volume of flow a t time t of product io,which is used a t stage EN for t h e production of an (intermediate) product j d n ) using technology

k d n ) .

And l e t @ ) ( t ) be the volume of intermediate product i input t o stage n , with zi(n+l)(t) as the volume of output of the same stage.

Then t h e following balance equations hold:

Here u p ) ( t ) is the intensity of t h e k -th techno!ogy in stage n a t time t ; t h e summations in (11)-(13) a r e taken over all possible flows in t h e system; and t h e technical coefficients a,@, and

y

show t h e efficiency of the transformation pro-

C

cess.

For t h e initial stage

where t h e r i ( t ) have the same meanings as in (7).

For t h e final stage

where t h e

4 ( t )

were introduced in (4).

For the intensities we have

where yJn)(t) is the production capacity k of stage n a t time t This constraint is similar t o (3) above.

The flow representation is very convenient because i t clearly shows all t h e intgrconnections in the systerr~ for a given t (say, for t h e years 1980, 1990, 2000). This type of representation h a s been used in energy models (the so- called Reference Energy System (Markuse 1976)), a n d other examples can be found in Ayres (1978).

3.

BIBLlOGRAPHlC NOTES

This section does not pretend t o give a full o r comprehensive list of refer- ences on resource-supply models; r a t h e r , i t attempts to provide a few examples of real-life models t h a t can be formulated within t h e framework outlined above.

The most representative type a r e probably the energy-supply models, some of which a r e reviewed in Manne et al. (1979) and Propoi and Zimin (1981). Mineral resource models a r e described in Manne et al. (1979), Hibbard e t al. (1979), and Golobin e t a,. (1979). Manpower a n d educational models have been studied fairly extensively (Grihold and Marshall 1977; Propoi 1978), and t h e r e is a good deal of l i t e r a t u r e devoted t o models of agriculture and food supply (Carter e t al.

1977; Il'ushnok 1980; Csaki and Propoi 1982) a n d t h e forest sector (Kallio e t al.

1980). Even health-care systems (Propoi 1977) may be thought of a s resource- supply systems producing a special type of "resource"--the health of t h e popula- tion.

4.

THE

COST-ASSE- MODEL

Suppose we have performed a r u n of t h e resource-supply model, and hence have arrived a t a strategy for t h e development of t h e resource system. (At first. this is usually done without the direct requirements constraints (5).) In order t o assess this strategy i t is necessary t o know t h e direct and indirect requirements from t h e economy a s a whole t h a t a r e needed for t h e implemen- tation of t h e strategy.

The direct requirements q R ( t ) can be calculated using the left-hand side of inequality ( 5 ) , t h a t is

where tz[(t)j a n d {v[(t)j are obtained from the resource model r u n .

However, in many cases i t is very important t o know t h e indirect require- m e n t s from o t h e r sectors of t h e economy t h a t support t h e resource-supply sys- tem: we shall refer t o these formally as "supporting" sectors. Let s

=

1,2.

...,SO

be t h e number of supporting sectors and l e t y,O(t) be the capital stock or pro- duction capacity of t h e j - t h sector a t time t . Then

where v p ( t ) is t h e increase in capital stock j during period t .

The bill-of-goods equation for t h e supporting sectors can be written in t h e form

where ~:(t) is calculated from (17), c ( t ) is t h e remainder of t h e final demand, a n d e,O is t h e net export.

Evidently

Indirect requirements a r e defined by t h e outputs z,O(t) of t h e correspond- ing supporting sectors. In order t o calculate the values of z,O(t) one can pro- cede in two ways.

First, i t is possible t o define t h e increase v,O(t) in productibn capacities for t h e supporting industries using t h e following nonlinear equation

which simply means t h a t investments a r e made only if a consequent increase in output is expected. This approach and a corresponding model ( t h e IMPACT model) were developed by Kononov and Por (1979) t o assess t h e direct and indirect requirements of t h e energy-supply system. To r u n t h e model i t is necessary t o solve a nonlinear system of equations a t each iteration.

The second approach h a s been developed a t the Institute for Systems Stu- dies. In this case a linear programming (LP) problem is solved a t each itera- tion. That is, instead of (21) we introduce an objective function

T-1 9

J

= 2 C

c,"<t)vSQ(t) -, min

subject t o constraints (18)-(20). The solution of this LP problem means t h a t only the minimum a m o u n t of new production capacity needs t o be constructed in order t o m e e t t h e required demands ~:(t) of t h e resource-supply system.

Clearly, the s e t of feasible strategies tv,O(t ) j for t h e supporting sectors pro- duced by optimization model (18)-(20), (22), also includes t h e strategy t h a t is obtained from (21). However, t h e optimization version of t h e model seems t o be more flexible. In particular, if we have some upper constraints ori t h e increase of the capacities

then t h e optimization model may still have a solution (which means t h a t t h e required increase can be achieved for several periods, none of which violate (23)), but eqn. (21) may give values of v,O(t) t h a t a r e inconsistent with (23).

Note t h a t to ensure t h a t investments a r e not made earlier than necessary, i t should be assumed t h a t

c,(t

+

¹⁾

<

c,(t)

Note also t h a t t h e real-life model differs from t h e above description in cer- tain iietails; in particular, it can include delays in construction, assessment of envirchmental constraints, etc. (Kononov and Por 1979).

5. THE DEMAND MODEL

The other link between t h e resource-supply system and t h e economy is t h e demand for the resource from t h e economy. There a r e two basic approaches for long-term resource demand evaluation.

The first approach u s e s direct calculation of t h e demand for t h e resource from each sector of t h e economy. Formally, this approach is based on t h e rela- tion

where t h e a,,(t) a r e the intermediate requirements for t h e j - t h component of t h e resource per unit intensity of t h e i - t h sector of t h e economy, t h e b,,(t) are t h e corresponding requirements for construction in the i - t h sector. $(t ) is t h e f i n d demand, and e t ( t ) is t h e n e t export.

However, implementation of t h e model based on direct calculation runs into several difficulties. F'irst, t h e level of detail of t h e sectoral outputs on t h e right-hand side of (24) needs t o be r a t h e r high in order t o take into accbunt all t h e resource users. Second, there might be alternative ways of using t h e resource. Therefore, expert selection or some other form of optimization of these alternatives is afso necessary. Third, in addition to t h e model structure, other factors influencing demand exist, which in most cases a r e difficult to for- malize but which a r e still too important to neglect.

The second approach evaluates the behavior of resource consumers and is based on t h e econometric technique. However, because econometric methods rely upon historical statistics and t h u s on past trends and phenomena, it is dif- ficult t o use this approach straightforwardly t o detect structural changes in t h e future demand pattern.

An example of a model for t h e long-term evaluation of t h e demand for energy is

MEDEE

(Lapillone 1978), which was used in the Energy Systems Pro- gram a t the International Institute for Applied Systems Analysis (IIASA) (Hafele ef al. 1981).

6. l'HE ECONOMYMODEL

For t h e reasons discussed above. it is most appropriate to link t h e resource model with a dynamic input-output model of economic development. We describe here very briefly an optimization version of such a model.

The state equations of t h e model are

where y ( t ) is t h e vector of capital stock or production capacities a t time t , v ( t ) is the increase in these capacities between times

t

and

t +

1, p ( t ) is the depre- ciation diagonal matrix, and I is the identity matrix.

The bill-of-goods equations are of the form

where C ( t ) is t h e vector of final demand and e ( t ) is t h e vector of n e t export.

The basic constraints on \he variables a r e

where matrix ~ ( t ) shows t h e requirement for a certain type of labor per unit activity in each sector of t h e economy and l ( t ) is t h e vector of the available labor force.

In order t o specify t h e solutions of t h e system (25)-(28) i t is necessary either t o s e t an investment function or t o introduce an objective function, which may take a number of different forms. For example, i t may be maximiza- tion of a function of final consumption

or minimization of the difference between the given behavior of certain vari- ables, for example macrovariables (scenario assumptions), and their model values.

7. LTNKING THE MODELS

Four basic models have been considered above. Each of these models can be used individually; b u t carrying out separate r u n s of each model has, how- ever, only limited usefulness because many important features of t h e system as a whole a r e neglected by such an analysis. Therefore we need t o build a con- nected system of models in order t o analyze interactions between the resource

a n d economic systems. This can be done either iteratively or by building a new, integrated model.

Consider t h e first approach. The iterative linking of the resource and economy models might be done as follows.

At the beginning we define some initial estimate of t h e resource demand dk

(t

) for a given time horizon

t =

0.1,

...,

T

-

1 a n d for given scenario assump- tions on the development of the economy. By running t h e resource-supply model (Section 3) we can find the optimal mix of resource-supply technologies t o meet this demand. Then t h e cost-assessment model (Section 4) gives t h e requirements Z R ( t ) t h a t t h e resource system places on the r e s t of the econ- omy. Now we can run t h e economy model (Section 5) with fixed requirements (ZR(t)) for t h e resource system. If this run of the economy model is satisfac- tory (and t h e r e may be many different criteria for such an evaluation), but in particular if t h e model giv4s a demand for the resource t h a t is consistent with t h e initial estimates, t h e n t h e linkage procedure is terminated. If not, t h e demand value should be updated a n d the iterations repeated.

The advantage of t h e iterative approach is t h e possibility of experts con- structively "interfering" a t different stages of the linking process.

At

t h e same time i t may still be unclear whether the solution obtained is optimal from t h e point of view of criteria by which t h e performance of the system is evaluated.

Or, in other words, have all t h e possibilities of interactions between t h e resource and economic systems been used?

8.

THE

INTEGRATE3

RESOURCE-ECONOMY

MODEL

The type of optimum or equilibrium described above can also be identified by using an integrated resource-economy model. Once again, it is however advisable to build t h e model in such a way t h a t experts can play some role in t h e linking process (Kallio e t a l . 1979).

Let us begin by partitioning the economy model (Section 6) into four parts (see Figure 2):

--

t h e resource-supply model (denoted by superscript RR);

--

t h e economy model, which represents t h e r e s t of t h e economy (super- script EE);

--

t h e demand model, showing t h e demand for resource R by t h e econ- omy E (superscript RE);

--

^the cost-assessment model, evaluating the requirements of t h e resource-supply system R from the economy E (superscript ER).

Figure 2. Decomposition of the economy model.

According t o this decomposition, t h e s t a t e equation (25) may be rewritten a s

vR(t

+

¹⁾

=

(1

-

^,.LR(t ) ) y R ( t )

+

v R ( t ) ; yR(0)

=

y0R

and

# ( t

+

1 )

=

( 1

-

p E ( t ) ) y E ( t )

+

v E ( t ) ; y E(0)

=

yoE The bill-of-goods equations now become:

s v

( I -

A R R ( t ) ) z R ( t )

=

~ ~ ~ ( t ) z ~ ( t )

+

B R E v E ( t )

+

B R R v R ( t )

+

k R ( t )

+

e R ( t ) (31)

for the resource outputs, and

( I -

Am(t

))z E ( t

)

=

BEE(t ) v E ( t )

+

A E R ( t ) z R ( t )

+

for the outputs of the economy. The meaning of eqns. ( 3 1 ) and ( 3 2 ) should be quite evident and needs no further explanation.

Let us denote by d R ( t ) t h e economy's demand for resource

R.

Frorn ( 3 2 ) we obtain (cf. eqn. ( 2 4 ) )

Note t h a t the last t e r m on the right-hand side of eqn. ( 3 3 ) is usually small and can be neglected. In this case, eqns. ( 2 4 ) and ( 3 3 ) become identical.

Also, l e t us denote by

zER(t)

t h e requirements of t h e resource-supply sys- t e m for products of t h e economy. From ( 3 2 )

Again, apart from differences of notation, eqn. ( 3 4 ) coincides with eqn.

( 1 7 ) .

Using ( 3 3 ) and ( 3 4 ) , the balance equations ( 3 1 ) and ( 3 2 ) can be rewritten a s

and

Equations ( 3 5 ) and ( 3 6 ) a r e analogues t o (4) and ( 1 9 ) . Partitipning constraints ( 2 7 ) and ( 2 8 ) gives

Thus we have obtained equations t h a t represent explicitly, and t o a certain degree independently, four submodels (see Figure 3 ) :

--

t h e resource model

RR -

eqns. ( 2 9 ) , ( 3 5 ) . ( 3 7 ) , ( 3 9 ) ;

--

t h e economy model

EE -

^eqns. ( 3 0 ) , ( 3 6 ) , ( 3 8 ) , ( 4 0 ) ;

--

t h e demand model

RE -

^eqn. ( 3 3 ) ;

--

t h e direct requirements model

ER -

eqn. ( 3 4 ) .

Now we will make some concluding remarks. The decomposition of t h e economic system described above is only t h e first stage in building t h e resource-economy model. To analyze structural changes in t h e resource sys- tem, t h e corresponding blocks of t h e economic system should be disaggregated (see Figure 3 ) . Moreover, t o make i t possible to investigate t h e process of sub- stitution between different technologies, the corresponding parts of t h e matrices

~ ( t )

^and B ( t ) should be made rectangular (see Figure 3 ) and t h e vari- ables related t o t h e resource parts of t h e model measured in real terms. (This is not apparent in the matrix notations ( 2 9 ) - ( 4 1 ) . )

This decomposition, together w t h the disaggregation, also makes i t possi- ble to introduce into each submodel nonlinearities and scenario assumptions (as in t h e demand model

RE

of Section 4 ) or to take into consideration t h e indirect requirements of t h e resource subsystem in an explicit form (as in t h e model in Section 5 ) .

Figure 3. The resource-economy model with a detailed resource submodel.

From a formal standpoint the model described above constitutes a linear or nonlinear programming problem of block structure. The problem has cou- pling variables d R ( t ) and z E R ( t ) and coupling constraints (41) (Figure 4). A special algorithm has been developed t h a t is suitable for this particular model s t r u c t u r e (Kallio e t al. 1979).

9. DISCUSSION: hfEL'HODOLOGICAL

ASPECTS

This paper has shown how to link a process model of a certain sector of t h e economy (the resource model) with other models in order to analyze t h e struc- tural dynamics of the sector and its interrelations with t h e development of t h e economy a s a whole. The approach is flexible and makes i t possible t o investi- gate many different aspects of these interactions.

Figure 4. Interrelations between t h e resource-supply a n d economy submodels.

I t

can be seen t h a t t h r e e of the four models are written in a unified optimi- zation framework. (Even t h e demand model can be reduced to an optimization problem if substitution of resource uses is allowed.) However, t h e optimization procedure serves h e r e not t o obtain a single, "optimal" solution but r a t h e r for distinct modeling purposes, namely exposing the most important interrelations

*

a n d connections between separate factors and blocks of t h e system. Therefore a flexible optimization modeling system is required. Generally, s u c h a system should comprise subsystems for data management, model generation, optimiza- tion, and postmodeling analysis. The modeling system can also include subsys- t e m s for aggregation and parameter identification; it also makes it possible t o extend the research beyond running a single model so t h a t different problem- oriented models can be built, based on the same common data base (Propoi e t al. 1982).

A major advantage of t h e approach described is t h a t indiiridual models can be separately built and used (even on different computers), whilst a t t h e same t i m e utilizing the information obtained from these separate r u n s t o t h e fullest extent. In particular, it allows very effective use of the shadow prices obtained from each subsystem. For example, if the marginal o r "local shadow price" of a factor (say, labor) has been obtained from running t h e resource model then t h i s value c a n be taken into account when running the economy model, and vice versa.

Simultaneous r u n s of several large-scale models can be r a t h e r trouble- some and expensive in computer time. Therefore, in some cases it is more expediept t o link t h e resource model with a macroeconometric model, as was done in the ETA-MACRO model for energy-economy interactions (Manne e t al.

1979). On t h e other hand, when running a "conventional" input-output model of t h e whole economy, s t r u c t u r a l changes in the different sectors can be taken i n t o account from preceding runs of the corresponding sectoral or resource models. The data obtained from such r u n s can be used for evaluating t h e future dynamics of the technical coefficients of the input-output rpodel o; t h e parameters of t h e production function.

10. CONCLUSIONS

A general scheme for modeling resource-economy interactions has been presented and discussed. Modeling s u c h complex, large-scale systems requires thorough research into many methodological questions, some of which have been raised here (see also Thrall e t ^al. 1963). The work certainly appears t o be worthwhile, because incorporating resource process models into t h e framework of economic modeling will improve t h e flexibility and predictive power of t h e modeling effort.

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