General equilibrium models for energy policy analysis

Transcription

1 General equilibrium models for energy olicy analysis by HORACE W.BROCK SRI International Menlo Park, California INTRODUCTION In this aer we shall rovide an elementary overview of the concet of general economic equilibrium in the concrete context of the U.S. energy market. * With this aim in mind, we shall introduce and discuss several imortant, large-scale energy models which embody the assumtions of the methodology of economic equilibrium. The models which will be discussed were all develoed since the OPEC embargo of 1973-an event which has rovided the imetus for develoment of sohisticated comuter models useful in energy lanning and olicy-making. In the first section, the models of Hudson and Jorgenson! and Hnyilicza 2 are introduced. The discussion here will hoefully rovide the reader with a clear diagrammatic exosition of the concet of general economic equilibrium. ~y "economic equilibrium" we mean a state of the economy In which rices are such as to equate the suly and demand for all commodities under consideration. These two articular models rovide a good starting oint for our discussion since they are very broad in scoe, encomassing both the energy and the non-energy sectors of the U.S. economy. In doing so they take account of the imortant linkages which exist between the energy and non-energy sectors. Then in the second section, we introduce the SRI National energy model, sometimes referred to as the SRI-Gulf model since it was originally develoed with the collaboration of the Gulf Oil Cororation. OUf focus in this section is on the algorithm through which economic equilibrium is determined in a dynamic economic context. An understanding of the algorithm not only sonsors an in-deth understanding of the SRI model and "how it works," but ermits an areciation of the imortant role of comutation in largescale models. Finally, in the last section, we conclude with some remarks on the role of economic models in energy olicy analysis. * The research discussed in this aer was sonsored by the Office of Policy Research and Analysis of the U.S. National Science Foundation. The reort3 on which this aer is based was co-authored by the resent author, and by Dr. Dale M. Nesbitt of Decision Focus, Inc. of Palo Alto, California. THE HUDSON-JORGENSON/HNYILICZA MODELS AGGREGATE MODELS OF ENERGY AND ECONOMIC GROWTH Background In 1974, Edward Hudson and Dale Jorgenson! introduced a model of energy and economic growth. The Hudson-Jorgenson model consisted of two somewhat searate submodels: a macro-economic model of economic growth, and a multi-sector interindustry model. The model was the first to make use of a new and advanced methodology for econometric estimation in a general economic equilibrium context. This methodology is known as "translog economic modeling" in the technical literature. An ostensible roblem with the Hudson-Jorgenson model was its failure to integrate its two submodels in a comletely satisfactory way. It was not clear that the inuts and oututs of the two submodels were comatible. This difficulty rovided the motivation for Esteban Hnyilicza 2 to develo a model which, while very similar to the Hudson-Jorgenson model differed from it in its treatment of economic growth. Secifically, Hnyilicza has attemted to build a model in which the multi-sector inter-industry model and the macroeconomic growth model are satisfactorily integrated. The Hnyilicza model also differs from the Hudson-Jo~genson model in being much more highly aggregated. SecIfically, it consists of only two sectors, namely the energy and nonenergy sectors of the economy. In other imortant resects, such as use of the "translog" methodology, the two models are much the same. In this section, we are going to discuss the Hnyilicza model at some length. The urose of discussing this model rather than the Hudson-Jorgenson model is that our diagrammatic mode of exosition of the methodology used in both models requires that we limit ourselves to a simle model with very few sectors. Introduction Hnyilicza has constructed an integrated model for t~e urose of analyzing the relationshi between economic 11

2 12 National Comuter Conference, 1978 growth, and the (equilibrium) rices and quantities of both energy and non-energy goods. His model rovides the basis for comuting a trajectory of future market clearing (i.e., "equilibrium") rices and quantities of the following commodities: 1. consumtion goods 2. Non-energy consumtion goods 3. intermediate goods 4. Non-energy intermediate goods 5. Caital services to the energy sector 6. Caital services to the non-energy sector 7. Labor services 8. imorts 9. Non-energy imorts These oututs are generated on a eriod-by-eriod basis as the solution to a model consisting of fifty-five (nonlinear) simultaneous equations. By analyzing time-series rojections of the rices and quantities of these goods, Hnyilicza can diagnose the relationshi between economic growth on the one hand, and the relative rices of energy and nonenergy goods on the other hand. It is also ossible to study the rate of substitution of caital and labor for energy, as well as the economic imact of alternative tax and conservation olicies. Overview oj the model Figure 1 dislays the overall structure of the Hnyilicza model. There are three basic model sectors: industrial roduction, consumtion, and investment. * The fact that these sectors are enclosed by solid as oosed to dashed lines is suosed to describe the fact that the oututs of these sectors are determined endogenously within the model. This is not the case with the government sector and the foreign sector. The latter two (which are enclosed by dashed lines) are largely exogenous to the modeu Before delving into the details of the three sectors, let us briefly summarize what takes lace in the model in hoes of better motivating Figure 1 and in hoes of roviding the reader with a guide to the model. One reliminary word of warning is in order. It is extremely difficult to describe what "goes on" in any general equilibrium economic model on a sector-by-sector basis. The reason for this is simly that what haens in anyone sector affects every other sector. Nonetheless, we have tried to motivate the model by means of a sector-by-sector discussion since there seems to be no satisfactory exository alternative. Two things haen in the consumtion sector. First, the * It is erhas a bit artificial and unnecessary to identify an "investment sector" which is distinct from the consumtion and roduction sectors. We have only done so in order to facilitate a descrition of what goes on in a "growth" model. t Secifically, the behavior of the government sector is almost comletely exogenous. In the imort markets, whereas the suly curve for imorted goods is exogenous, the demand curve for imorts (energy and non-energy) is endogenous. "national household's" inter-temoral utility function determines the slit between resent consumtion andjuture consumtion (Le., savings). More secifically, the household is assumed to determine a utility-maximizing slit between consumtion and savings as an (econometrically estimated) funct~on of wealth, the wage rate, and government transfer ayment levels. Second, the consumer decides uon an intra-eriod slit between leisure, energy consumtion goods, non-energy consumtion goods, and caital services. The otimal slit is that which is utility-maximizing, subject to the consumer's budget constraint. This slit will of course be a function of the relative rices of the various consumtion goods, and the wage rate, among other things. The two industrial roduction sectors-energy and nonenergy-determine an otimal (rofit-maximizing) level of oututs, and an otimal (rofit-maximizing) configuration of inuts used in roducing the equilibrium outut levels. Finally, the investment sector determines the level of caital services which will be available in any given eriod. As we shall see, this level deends on both the efficiency of caital, and on the level of caital stocks in the receding eriod. The investment sector also determines the overall level of gross investment in any given eriod, as well as the fractions of gross investment going to the energy sector, the non-energy sector and the household. A diagrammatic exosition An imortant question arises concerning the best way in which to exlain and motivate a model which is as general as the Hnyilicza model. Two aroaches seem to be ossible: a mathematical aroach and a diagrammatic aroach. We have settled uon a diagrammatic exosition of the model. More secifically, we shall motivate the model by discussing each of the three sectors (roduction, consumtion, and investment) from the standoint of the demand curves and the suly curves which are imlicit in the equations which characterize economic behavior in each sector. This strikes us as a comact and intelligible mode of exosition. Furthermore it ermits us to conclude our discussion with what we hoe to be a highly aealing summary of the model: namely, a icture (Figure 5) in which we suerimose the various suly and demand curves which we "extract" from each of the three sectors. The ricequantity airs of all of the oints of intersection of these suly and demand curves will clearly constitute a general economic equilibrium. And these equilibrium rices and quantities coincide with the values of the endogenous variables which are determined when the model is solved. In light of our decision to exlicate the model in terms of the suly and demand relationshis that are imlicit in the equilibrium equations of the model, a caveat must be issued from the outset. Whenever the reader sees a icture of a suly curve or a demand curve, he should realize that he is beholding an illusion. For in oint of fact, there are no such things as suly and demand curves er se. There are only conditional suly and demand curves. Let us illustrate this oint since it often engenders confusion. Consider a two

3 General Equilibrium Models for Policy Analysis 13 r HOUSEHOLD SECTOR Final Demand Emloyen J ' INDUSTRIAL PRODUCTION SECTOR ENERGY NONENERGY INPUT OUTPUT INPUT OUnUT Labor Labor N'ln Services Consumtion Services Con umtion Caital Caital Guods Servrces Seovices Nonenergy Nunenergy Imorts Intermediate Imorli Intelillediate Gauds Intermediate Intermedilte Investment No.lentrgy Intermedi~te Nonenelgy Consumtion IrlVESTMENT SECTOR r-- L -, SAViNGS INVESTMENT I Foreign I I L Sectol -1 I WEALT.. CAPITAL STOCK I ~ ----' ' Figure I-The Hnyilicza model structure Wages commodity world consisting of coffee and sugar. In general, the reader would be hard ressed to sell out his ricedemand relationshi for coffee. He would only be able to do so if he knew how much sugar he would be allotted. Thus we can seak of a demand curve for coffee conditional uon a articular consumtion level of sugar. For this reason, it is somewhat artificial to characterize market equilibrium below in terms of a set of suly curves and demand curves.:j: Methodology of the model Industrial roduction sector The function of the roduction sector in the context of the larger model is twofold: a. to determine an equilibrium factor inut mix which is otimal (rofit maximizing) for each industry in roducing its total outut; b. to determine the total (equilibrium) outut levels that meet the demands of the intermediate market and of the final goods market. As we saw in Figure 1 and as we see in more detail in Figure 2 on the next age, we can think of the roduction sector as an inut-outut structure. We summarize this inut-outut structure in Table I. * Nonetheless, it will be true that if we somehow knew the equilibrium quantities of all commodities, then we could sketch a set of conditional suly and demand curves whose oints of intersection do constitute the market equilibrium. The roblem of course is that one does not know the equilibrium in advance. It is imortant to realize that even though we are seaking of roduction in "inut-outut" terms, the Hnyilicza model is not an inut-outut model in the classical sense of that term. Rather, it is a generalized inut-outut model. In such models the inut-outut (transactions) coefficients, rather than being given exogenously (as would be the case in the economy whose technologies ermitted no substitutability among inuts), are functions of the rices of all inuts and the configuration of final demand. Secifically, we can write a ij =f(w,,y,x) where: w is the vector of inut factor rices is the vector of outut rices y is the vector of final demands x is the vector of gross oututs. The equilibrium coefficients {aij*} that are imlicitly solved for by the model designate the rofit-maximizing I Industry Oututs Consumer Intermediate TABLE I Inuts Labor Services Cai tal Services* Imorts Intermediate Intermediate Industry Oututs Consumer Intermediate Investment _I *Caital services are the annual services generated by existing stocks of caital goods. These services are rovided to the roductive rocess. "Caital goods" have a life exceeding one year, by definition, whereas "intermediate goods" are consumed by the roduction rocess within a year.

4 14 National Comuter Conference, 1978 CAPITAL SF.RVICE.::l t:::-lergy ~t31 E~ IMPORTS '" a:lii'., QUA~'Tl1Y -----_.- -j t-- INPUT ENERGY OUTlllff r LAUOR ENERGY --- SERVICES CONSUMPTION CAI'ITAL SERVICES v. { UII'OIITS t D ENERGY nrreilmediatk NON -f:nergy U : INTEIUtU:PIA1'E GOOlJS r.~ ENERGY GOODS GOODS ENEIIGY I NTl::IIt.'.!;: DlA'rE lioijds - D INPUT SERVICES CAPITAL SERVICES NON-ENl::RGY IMPORTS ENERGY INTEIUIEIIUTE GOOIIS HON-I::lft.RGY INTI::IGUm I ATE GOODS f;on...enellg't OUTPUT NON-ENERGY CONSUMPTION GOODS NON-I::NERGY UITERMEU I ATE GOODS INVESTMENT GOODS S NON-ENERGY f7 QUAl:TI1'Y ~'!IE!\GY CONSUMPTION 0.1\ GOODS / ~~_'S_ ~UANTITY '----ts: E;iGs:27]~ HON-ENEIIGY ntports CAPITAL SERVICES ><: NON -ENERGY f It INTERMEDIATE GOODS D D ~ I,,'-TY Qu_.n D g~iio'-ejlergy ~~ QUANTITY QUANTITY Figure 2-Industrial roduction sector number of units of commodity i which are utilized in the roduction of each unit of commodity j. Let us now ress towards a deeer understanding of what is going on in the roduction sector. A result of this will be an enhanced understanding of the equilibrium coefficients {aij*}. The most straightforward way in which to characterize what goes on in the roduction sector of the model is to deict the various suly curves and demand curves which are imlicit in the equilibrium equations which characterize rational economic behavior on the art of the two industries: energy and non-energy. The entrereneur must make essentially two different tyes of decisions. He must decide uon a rofit maximizing level of outut of the commodities he manufactures; and he must decide uon a rofit maximizing mix of inuts to be used in meeting his (otimal) roduction schedule. Clearly his otimal choice of outut levels and inut mixes will be a function of the relative rices of oututs and inuts. Indeed, it is customary to seak of the relationshi between the rice of a given inut and the quantity demanded by the entrereneur at that rice as the derived factor demand curve of the inut (or "factor") in question. And the relationshi between the' otimal outut level of a given outut and the rice of the outut is summarized by the suly curve of the outut. With this in mind the reader is referred to Figure 2, where we identify the various derived demand curves and suly curves that are generated within the roduction sector. Let us summarize the information contained in the figure. The derived factor demand curves and the suly curves There is one derived factor demand curve for each inut. Since both the energy and the non-energy sector use five inuts, there are therefore ten derived demand curves in all: Demands.' Labor Services Caital Services Intermediate Intermediate Imorts Labor Services Caital Services Intermediate Intermediate Imorts The derived demand curves associated with these inut demands are illustrated in Figure 2. With resect to suly, the energy sector roduces only two goods whereas the non-energy sector roduces three

5 General Equilibrium Models for Policy Analysis 15 goods: Suly: Consumtion Intermediate Consumtion Intermediate Gods Investment The associated suly curves are indicated in Figure 2. An inut-outut interretation We are now in a osition to give an interretation to the equilibrium Inut-Outut coefficients {aij*}. Note in Figure 2 that in two (and only in two) of the markets ictured there do we have well-defined suly and demand curves. This is the case in the markets for energy intermediate goods and non-energy intermediate goods. Suose now that we could "comlete" our descrition of the remaining eight markets by obtaining the missing suly and demand curves. (As will be seen, these missing curves are generated in the other two sectors of the model to which we shall turn shortly.) Suose finally that we were to take note of the equilibrium oint in these ten markets, that is, the equilibrium rices and quantities of the ten commodities. It would then be straightforward to comute the equilibrium inut-outut coefficients either in dollar terms or in hysical terms-using simle arithmetic. The collection of coefficients so obtained would coincide with the collection {aij*}. That is, these are the equilibrium inut-outut coefficients associated with rofit-maximizing behavior on the art of the industries with resect to the choice of inut mix and the choice of outut level. The consumtion sector Figure 3 ortrays the consumtion sector in some level of detail. Looking at the to art of the figure it is clear that two things take lace in the consumtion sector model. First, an "intertemoral" ~tility function determines a utility-maximizing slit between resent and future consumtion. This utility function is an econometrically estimated function of: Time Interest rate Existing wealth Wage rate Government ayments to household (e.g., welfare) Consumtion Budget Inter Temoral Utility Factor Consumtion Caital Services Savings Labor Services Caital Services Consum ~s Consumtive ~d q '-----q q Figure 3-The household sector

6 16 National Comuter Conference, 1978 Second, an "intratemoral" utility function determines the slit within a given eriod of household exenditures between the four consumtion goods, namely energy consumtion goods, non-energy consumtion goods, caital services, and leisure. By caital services we mean the annualized value of the services which flow from consumer durables or residential stock. The intratemoral utility function which erforms this slit is an econometrically estimated function of rice, the level of consumtion of each good, and time. A suly and demand curve interretation A deeer understanding of the consumtion sector can be obtained by considering the suly and demand curves which are imlicit in the equilibrium equations characterizing utility-maximizing behavior on the art of the household. These rice-quantity relations are shown in the lower ortion of Figure 3. Interretation of all of these curves is straightforward with the excetion of the suly curve of labor services. This curve is in fact the inverse of the demand curve for leisure services. As the wage rate increases, leisure becomes more exensive. Work is substituted for leisure, which increases the suly of labor. Investment and caital accumulation Formally seaking, the investment sector is art of the roduction sector. Nonetheless, it is useful to isolate it as a searate sector for the uroses of enhancing an understanding of caital accumulation in the Hnyilicza model. The situation is ictured in Figure 4. Consider the uer art of the figure. The suly of new investment goods that come on stream in a given year t aears on the left. Next, the suly of new investment goods is slit three ways into the shares of investment goods going to the energy, nonenergy, and domestic sectors. This slit is realized by the use of a multilier which reflects historical ratios in the aortionment of investment goods. Moving further to the right, we add in the dereciated value of caital stock for the resective sectors. These are the values of stocks at the end of the revious year. The result of this addition is the current level of caital stock. Moving yet further to the right in Figure 4, the values of the current level of caital stock in the two industrial sectors are multilied by the efficiency of caital. The result of this oeration is defined to be the level of caital services in eriod t. We exhibit the current suly of caital services generated in this fashion within each of the two industries as two suly curves. The reader will note that these suly curves are erfectly inelastic. The reason for this is that the level of caital services is not a function of any current rices. One might think that this level would be a function of the current rice of new investment goods. This is not the case, for in this model there is a one eriod lag between the time when caital goods are roduced and the time when they begin to generate caital services. The investment goods which come "on stream" in year k and which aear in the uer left of Figure 4 were actually roduced in year (k-l). Suly of New Inyestment.. slit Coming On-Stream Gros~ Investment Section Gross Investment Section IInvestment I IGoing to Householcll, DE!reciated Cc:ital Stock From Past Years I Suly of,.. Caital Services of ll Savings Cai.tal Services Caital Se;:vices PL= Investment Figure 4-Investment sector

7 General Equilibrium Models for Policy Analysis 17 Two other rice-quantity curves aear in the figure. First, there is a demand curve for investments goods. This demand curve is seen to be erfectly elastic. Moreover, it aears as a dashed line. Why? We have used a dashed line to indicate that this demand curve is an artificial construct. For in the Hnyilicza 2 model, the (equilibrium) level of investment goods is, in fact, "suly-determined." Whatever quantity of investments goods is sulied is assumed to be absorbed-irresective of own rice. It is for this latter reason that the curve aears as erfectly elastic. In oint of fact, it is ossible to introduce a demand function for investment goods in the Hnyilicza model. For one of the basic equilibrium conditions of the model is that investment equals income minus consumtion. [This equilibrium condition is imosed on the model] Consumtion, in turn, is a function of income and of the rice of labor, caital, etc. Thus, the demand for investment goods is indeed a function of "rices" in the Hnyilicza model. Our oint above is simly that it is not helful to characterize a market of investment goods er se, and to lot the demand for investment goods as a function of the rice for investment goods. For, as we said above, whatever quantity of investment goods is roduced is assumed to be demanded. Last of all, there is a demand curve for savings. This aears as a dashed vertical line. Why? The reason for this is that there is no "demand curve" for savings er se in the model. Rather, savings is assumed to equal investment. Once again, just as in the case of the demand for investment goods above, it is ossible to assert that there is a demand function for savings embedded in the Hnyilicza model. For the so-called "static equilibrium condition" of this tye of growth model is that savings equals income minus "desired" consumtion. This relationshi is imosed on the model, and serves to relate industry demand for savings to consumtion and hence to relative rices, since consumtion deends in art on rices. The reader who finds the rather arbitrary treatment of investment and savings erlexing should be aware of the motivation for the static equilibrium conditions such as "Savings=Investment" that are imosed on the model. The rationale for these assumtions is simly to insure consistency between the aggregate savings decisions by individuals on the one hand, and the aggregate investment decisions of roducers on the other hand. There would be no need, in rincile, for imosing static equilibrium conditions if the model included a full set of futures markets, and if an equilibrium set of rices and quantities across time were comuted simultaneously, as is the case in the SRI model. Of course, to oint this out is not to make a value judgment about the quality of the SRI model versus the Hnyilicza model, since the emhases of the two models are different. General equilibrium in the Hnyilicza model Figure 5 shows the result of collecting together the various suly and demand curves that we have extracted from the roduction sector, the consumtion sector, and the investment sector. The oint of intersection of all of these curves coincides with the equilibrium rices and quantities that Hnyilicza's fifty-five simultaneous equations are solved for. We can thus interret equilibrium in terms of suly-demand balance in the following markets: 1. Caital Services to the Industry 2. Caital Services to the Non-energy Industry 3. Labor Services 4. Imorts 5. Non-energy Imorts 6. Consumtion 7. Non-energy Consumtion 8. Intermediate 9. Non-energy Intermediate 10. [Investment ] 11. [Savings] Time-series rojections of these equilibrium rices and quantities are the rincial oututs of the Hnyilicza model. The following variables are exogenous to the model and are required as inuts: Inventory investment Labor force Tax rates Government exenditures Exorts International financial claims Government transfer ayments (e.g., welfare) Rate of unemloyment Imort rices Rate of relacement of caital stock Initial year rivate national wealth Initial year caital stock Quality of caital (a constant, multilied by caital stock to give caital services) A note on the new version of the Hudson-Jorgenson model* Hudson and Jorgenson have recently reworked their original model. Their new model is very similar to the Hnyilicza model, esecially as regards the use of the variable coefficient inut-outut methodology in an economic equilibrium context. Where the two models differ is in the degree of disaggregation of the roduction sector. As we saw, the Hnyilicza model's roduction sub model consisted of two sectors: energy and non-energy. The Hudson-Jorgenson roduction sub model consists of six sectors: Coal Crude etroleum Refined etroleum roducts Electricity Natural gas ( crude) Delivered gas * The author is grateful to Dr. Edward Hudson for a helful discussion.

8 18 National Comuter Conference, 1978 Savings y I q Cait3l Services to the Industry I,,~ s ~"d q --- Caital Services to the Ind \ s I\d / q Labor S crvices Imorts Imorts --q bd ---~d q q i \ "- _. ya Consumtion Consumtion Enel'gy Ivef:tment Inter- Investment medicte X X \/S ~-)~ d d d d \ q q q q q Figure 5-Summary of markets in the Hnyilicza model THE SRI NATIONAL ENERGY MODEL Introduction The SRI National Model is an economic equilibrium model of the U.S. energy system covering all major fuels from rimary resources to end use energy consumtion (Le., energy service demands) over the eriod 1977 to The model is regionally disaggregated with nine demand regions (such as New England), twenty rimary resource suly regions (such as Alaska North Sloe), and 600 transortation and distribution links. Conversion technologies such as coal gasification, crude oil refining, and electric ower generation by tye of fuel are exlicitly modeled. The model comutes regional rices and quantities of all energy forms, as well as energy technology requirements over the eriod of 1977 to 2025 by balancing suly and demand. The SRI model differs in several imortant resects from the models considered in the revious section. To begin with, the Hudson-Jorgenson and Hnyilicza models are highly aggregated models of the overall economy. In contrast to this, the SRI model is a very disaggregated and detailed model of the energy sector of the U.S. economy. All this detail can be reresented grahically by means of a "satial network." We shall discuss this network just below. Above and beyond this, the SRI model makes use of a different methodology. While the model is an economic equilibrium model in the sense that it determines rices and quantities which are in suly-demand balance,-just as the other models do-it does not make use of the "translog" methodology. There are no variable inut-outut coefficients. Rather, economic equilibrium is characterized in a much more direct manner. One solves directly for rices and quantities which are in balance. Moreover, we can visualize "equilibrium" in this model in terms of a sulydemand balance at each oint in the satial network referred to above. Partly for this reason, we shall start off by discussing the satial energy network which lies at the heart of the model. Next we shall describe what is meant by "equilibrium" in this context. Finally, we shall gain a dee understanding of the model by analyzing the algorithm used to achieve a suly-demand balance throughout the network.

9 General Equilibrium Models for Policy Analysis 19 A satial network reresentation of the energy market The essence of the SRI model is a satial network reresentation of the energy system. In the network, the major elements of the U.S. energy system-from the rimary resource sulies through the end use energy demands-are described in relationshi with each other. A samle energy network is shown in Figure 6. In this figure, the resource suly curves are at the bottom; the usable energy demand curves are at the to. Between these curves is the network describing the entire energy system. The 'current network has about 2400 materials, rocesses, and transortation links. A material is a rimary resource roduct, or usable energy form at a secific location. A material is reresented by a node in Figure 6. A rocess reresents a sector of the energy industry such as coal mining or gasification at a secific location or a class of consumers using a articular energy-consuming device. A transortation link reresents the rocess of moving a material from one location to another. To get a sense of the many aths in the network, consider first the ath where coal is mined, converted into synthetic (high Btu) gas, ied to a demand center in a demand region, distributed to industrial users, and consumed as boiler fuel to roduce steam. The same end use market could be sulied by coal transorted by unit train, distributed to the same industrial users, and used in a coal boiler to roduce steam. These two aths can be traced in Figure 6. In the SRI National Model, there are 24 end uses (such as industrial steam) in each of the nine demand regions, and thirty rimary resource sulies (such as coal) in the various resource basins. The alternative conversion technologies in the model include all imortant tyes of electric ower generation (in base, intermediate, and eak load alications), crude oil refining, coal gasification, methanol from coal, hydrogen roduction from coal, transortation, distribution, and end use conversion. The model exlicitly considers the evolution of the energy system through time-it calculates rices and quantities in a number of time eriods. It is imortant to recognize that the solution to this "dynamic" model is not equivalent to using a "static" model in each of the time eriods. Rather, ~ INDUSTRIAL STEAM RIC RESISTANCE HEATER R/t;.'. ElECTRICITV ~ Y we ElECTRICITY ~~ 0lS1 RIBUTIUN RIC DISTILLATE L~ DISTRIBUTION ElECTRICITY DISTIllATE (REGION GATE) ~ m[gion GATE) POWlR LDAntNG - PEAK LOAD POWER 1- INTERM[DIATE LOAD POWER CONVENTIONAL f 1'. NUCLEAR PLANT ) DISTILLATE (COAL REGION) ~AL li0uefaction Irw. HBlu GAS BOILER,L,...-IND. )/ HBtu GAS IND. HBlu GAS DISTRIBUTION IND. UIGH SULFUR COAL BOILER l HIGH-SUU UH COAL IND. COAL 11 DISTRIBUTION HIGH-SUlFUH ), :r COAL (REGION GATE) UNIT TRAIN NUCLEAR FUEl U/lANItlM MINING I }!,NO ENRICHMENT --_.- L/ () Millclials HIGU-SUl.fUR [ [] ProCI!SSC~ --J CUAl MINE [\ Tlall~IIUllaliuli Llllks l--- Figure 6-Examle of elements of the energy model NATURAL GAS WELL 1I_

10 20 National Comuter Conference, 1978 the rices and quantities in each eriod are described by equations interrelating both ast and future rices and quantities. On the meaning of economic equilibrium in the SRI model P k + 1 D ' ) ( k+1 DEMAND FUNCTION CD qk+l In their earlier research, Brock and Nesbitt 3 have drawn uon economic theory to establish the following results concerning economic equilibrium in satial networks: 1. There exists an aggregate demand curve and an aggregate suly curve at every material node (circle) in the network; 2. There exists a suly curve and a demand curve on every link in the network. Any such air characterizes the suly/demand conditions governing the behavior of the (unique) conversion or transortation rocess attached to the link. The equilibrium rices and quantities are those for which all aggregate suly/demand curve airs are simultaneously balanced at all material nodes; or equivalently for which all suly/demand curve airs are balanced on all the links of the network. The oeration of the model The SRI model is best described in terms of the algorithm used to solve for equilibrium, and in terms of the relationshi of the algorithm to the satial network and its comonents. Therefore, in this section we shall describe the algorithm in considerable detail. When we say that this algorithm "solves" the satial network we simly mean that it determines the set of equilibrium rices and quantities which obtain at each oint (link and node) in the network. The algorithm consists of four essential stes which are reeated at each iteration. The rocedure is illustrated at a fairly abstract level in Figure 7. Beginning with an initial "guess" at the equilibrium quantity qk-l, the four stes of the algorithm are: SUPPL Y FUNCTION f2\ TRANSFORMATION I...:J 1 I I~_---JI.:+, P k ql:-1~" o INVERSE SUPPLY FUNCTION -1 S (qk) Figure 7-SRI model algorithm,demand I f4\ FUNCTION 'V TRANSFDRMATIDr~ We will now discuss each of these four stes in some detail, and in a less abstract manner. 1. Inverse Suly Function: In the first ste of the algorithm, the inverse suly function describing each of the rimary resources at the bottom of the network in Figure 6 is alied. The algorithm begins with a "guess" at the ro- 1. To aly (inverse) resource suly function* Pk= S-l[qk_l] 2. To roliferate rices u the network (suly function transformation) Pk+t = 1's [Pk] 3. To aly usable energy demand function qk+t = D[Pk+t ] 4. To roliferate quantities down the network (demand function transformation) qk+2 = TD[qk+t] * An inverse suly function exresses rice as a function of quantity. \ Figure 8-Illustrative gas network SYNTHETIC "AS

11 General Equilibrium Models for Policy Analysis 21 duction level over time for each of the rimary resources (denoted qk-i (t) as in Figure 7, where the t denotes a vector over time). Using the guess qk-i (t), the inverse suly function is alied to give Pk(t), the rice of the corresonding rimary resource. Schematically, Ste 1 is given by Pk(t)=S-I[qk_I (t)] The inverse suly functions are given exogenously, one for each rimary resource. The first ste of the algorithm is to guess initial quantities qa 0, qb 0 of natural gas and synthetic gas resectively and, using the natural gas and synthetic gas suly curves, to calculate the corresonding rices PA 1 and PB 1 for natural and synthetic gas. These rices aly at the rocess boxes A and B in Figure Suly Function Transformation: In the second ste of the algorithm, the intermediate technology submodels are used to comute roduct rices given inut fuel rices. The technology models begin by assuming that the measure of rofitability to a firm which builds a unit of caacity at time t is given by the net resent value of the cash flow generated by that unit of caacity: where t+l (T)-c/>(T) NPV(t)=-c(t)+ ~t (1 +ry-t c(t)=caital cost of the new unit of caacity built at time t; (T)=roduct rice at time T; c/>(t)=oerating cost (including fuel cost) at time T; r=discount rate (cost of caital) L=life of technology. In order to simlify our discussion, we will assume that technologies have a useful life of three years (L =3) and that we wish to consider the interrelationshi of rices over a three-year time horizon. It is known from elementary economic theory that at equilibrium, rofit maximizing firms earn zero rofit. Exressed in terms of net resent value, the zero rofit assumtion is equivalent to: NPV(t) =0 t=i,2,... where we have assumed that the cost of debt and equity caital are included in the discount rate r. Assuming NPV(t) =0 for new lants built in Years 1, 2, and3, we can write: c(i)= (1)-"'(1)+ (2)-c/>(2) + (3)-c/>(3) P 0/ l+r (l+r)2 c(2)= (2)-"'(2)+ (3)-c/>(3) + (4)-c/>(4) P 0/ l+r (l+r)2 c(3)= (3)-"'(3)+ (4)-c/>(4) + (5)-c/>(5) Po/I + r (1- r)2, which interrelates the equilibrium rices (and, of course, the caital and oerating costs and the discount rate). If the firm which is trying to decide whether to add new caacity at time t=3 knew with certainty what future rices [(4) and (5)] and future oerating costs [c/>(4) and c/>(5)] would be, it could, by rearranging the third equation above, calculate the minimum rice in Year 3, (3), below which it would not add caacity and above which it would add more caacity. * (3)=,/..(3)+c(3)- (4)-c/>(4) _ (5)-c/>(5) P 0/ 1 + r (1 + r )2 = c(3) + caital charge Knowing (3), c(3), (4), and c/>(4), the second equation of the above three can be used to solve for (2). A similar calculation gives (1). To summarize, for each technology, given the fuel rices (contained in c(t», given assumtions about rices and oerating costs ast the end of the model horizon, and given rocess economic data (c(t) and c(t», roduct rices are calculated recursively backward in time (3), (2), (l) as indicated above. When we arrive at the to of the network, we will have calculated the rices Pk+1 (t) in Figure 7. We have denoted this uward roliferation of rices by using the notation Pk+1 (t) = Ts [Pk (t)]. Returning to Figure 8, Ste 2 of the algorithm involves taking the rices PA 0, PB 0 (and the quantities qa 0, qb 0) and determining the corresonding rices PI 0, P2 0 at the to of the network. The first ste is to comute the average rice of gas entering the ieline at a in Figure 8 as follows: _ PA qa o+pboqb O P= qao+qbo The rice of gas delivered to the two end users (i.e., to f3 in the figure) and would simly be 3. Demand Function: The third ste in the algorithm is to aly the direct demand function at the to of the network using the rices Pk+1 (t) comuted on the way u in Ste 2. That is, an estimate of demand is obtained by alying the demand function qk+1 (t)=d[pk+1 (t)]. Returning to Figure 8, this ste of the algorithm involves taking the rice Ploof residential gas determined by Ste 2 and finding the residential demand qi O at that rice using the residential demand curve. A similar rocedure yields the industrial demand q2 0 corresonding to the industrial gas rice P2 0 determined in Ste Demand Function Transformation: In the fourth ste of the algorithm, the technology submodels are used to comute fuel requirements given roduct demands, and market share submodels are used to divide demand among comet- * Equilibrium would obtain at the rice (3) itself because the firm would just be indifferent between adding and not adding caacity.

12 22 National Comuter Conference, 1978 ing technologies based on the rice comuted for those technologies in Ste 3. We will discuss both calculations briefly. First, each technology is characterized by a thermal efficiency e(t) for new units built at time t and thus by an average efficiency e(t) for all lants in lace at time t. Hence, the fuel required is given by qk+2(t)=qk+1 (t)!e(t). Second, if the quantity qk+2(t) is to be slit among a number of cometing suliers, a "market share" model is alied to the quantity qk+l (t) to slit it among cometing suly technologies based on the rices comuted for those technologies in Ste 2. We do not have sace enough to discuss this market slit model here. This ste of the algorithm is better exlained in terms of the network in Figure 8. Referring to that figure, the fourth ste of the algorithm actually consists of two oerations. First, the residential and industrial quantities ql and q2 resectively determined in Ste 3 are added to give the total demand for gas q=ql 0+q2 at {3 in the figure. In order for the ieline to deliver q units of gas at {3, it must take in qfe units of gas at a, where e is the thermal efficiency of the ieline, including transortation losses. Given the demand qfe of gas at a, we then aly the market share model to comute how much of that gas would be synthetic and how much would be natural at the rices PAo, PBo determined in Ste 2. That is, we would comute QA 1 =MSA(PAO, PBO)xq/e qb 1 = MSB (PAO, PBO)xq/e where MSA (PA 0, PB 0) is the fraction of the demand that would be satisfied by Process A (natural gas) if the rices of natural and synthetic gas were PA and PB resectively, and similarly for Process B. Characterization of equilibrium in the network If qa L=qA and qb 1 =qb equilibrium has been achieved (recall that qa and qb were our initial guesses in Ste 1). If not, we return to Ste 1 with the new guesses qa 1 and qb 1, and reeat the four stes, as many times as necessary to achieve equilibrium. THE ROLE OF ECONOMIC MODELS IN NORMATIVE POLICY ANALYSIS We shall conclude the resent essay by issuing some recautionary remarks about the role of economic models in normative ublic olicy analyses. The interested reader will find an elaboration of these remarks in Chater I of Brock and Nesbitt. 3 It must be areciated that the models discussed in this reort are economic in nature. That is, their aim is to roject rices and quantities of energy (and, sometimes, non-energy) commodities. Yet normative olicy analysis is interested not only in the economic dimension of alternative olicies, but also in the olitical and the ethical dimensions. For examle, a olicy maker might well wish to have at least robabilistic information about the likely rice/quantity imacts of ursuing alternative strategies. For an examle of this, see the comanion aer resented by Dr. Steven N. Tani. Tani oints out how rice quantity data generated by an energy model can be used to make economic welfare judgments about alternative olicies by means of the criterion of "net social surlus." This is imortant-indeed, it is far the most imortant role of strictly economic models in normative olicy analyses. But the same olicy maker might also wish to know the olitical imlications of ursuing alternative strategies. For examle, a olicy which looks good on economic grounds may for various reasons be "olitically unaccetable." Game theoretic models can in rincile be used to determine which olicies are olitically accetable in a balance-ofower sense. But economic equilibrium models are not game theoretic models, and should not be confused as such. Finally, there are the distributional concerns which are central to normative ethics. Economic lanning models in and of themselves cannot furnish us with the answer as to which olicy is most "fair." President Carter has reeatedly emhasized his concern with equity. But in this matter we have a roblem for ethics-not for rice/quantity models. While these oints may seem too obvious to need exlicit statement there is often confusion about the roer role of economic data in normative olicy analysis. For this reason, we felt it worthwhile to close with a reminder. There is one other imortant limitation to economic models of the kind reviewed above. This concerns the use of an "equilibrium" methodology in the context of regulated commodities such as natural gas. Many roblems of interretation arise here; but they are outside the scoe of the resent aer. REFERENCES 1. Hudson, Edward and Dale W. Jorgenson, "U.S. Policy and Economic Growth, ," Bell Journal of Economics and Management Science, 1974, Volume 5 No Hnyilicza, Esteban, "An Aggregate Model of and Economic Growth," M.I.T. Laboratory Working Paer MIT-EL-75-01OWP, Brock, Horace W. and Dale Nesbitt, "Large-Scale Planning Models: A Methodological Analysis," Reort reared for the Office of Policy Research and Analysis of the National Science Foundation, May 1977.