An econometric analysis of energy over the next 75 years

An Econometric Analysis of Energy Next 75 Years . . BenDaniel DJ Manne

INTRODUCTION

This paper discusses preliminary results from tin econometric investigation of the mix of kc-load clec trical powel generation systems for the next 75 years.

’ Thcrc arc at Icast two reasons why WCbclievc this to bc true. First, the cxpcnditurcs arc spread over many alttxnativcs, with large sums going into highly speculative technologies like fusion. solar clcctric. and MHD. Second. ~1slower -than historic.--growth rate of electricify consumption will mc3n a proportionrrtcly slower r3tc of addition of new plants and thus rclativcly less upportunit) to embody new technology than in the past, Reprinted with permission from 113X Power Enpinccrinp Society Papers. Energy Devclopmcnt 111.

PJ.Stewart RolmdW Schhitt

technology, it is desirable to embark only on developmenls that promise a long span of applicability. It is recognized that fe$ predictions over 3 75year period are correct in detail, but we believe that with this time-horizon our view of the next SOand, cspccially. 25-year period will bc bcttcr !ilaii they would be if a “safer”. shorter period was chosc~ti. III making the forecasts presented in this paper. an attempt has been made to satisfy several critc\ria:

BENDANQEL, DAVID J. formerly with G$neral Electric, is presently Energy

Manager,

Systems

Enterprises, of

The

vania

Advanced

Area,

Exxon

Inc. He is a graduate

University and

of

holds

a

PennsylPh.D.

in

Engineering from M.1.T.

PETER ical

London ed on

nuclear a

from

He has work-

plant desiyn and

company producing controls. GE experi-

includes

velopment

is a chem-

graduate

University.

founded industrial ence

STEWART

engineering

and

new business deenergy

systems

analysis.

.qL_AN S. MANNE is Professor of 0perations -Research at Stanlforal ‘University. He is a pioneer of linear application rn the programming to oil refineries, the author of five books and over 50 technical papers, and a Fellow of Econometric Society and Lanchester Prize of Operations Fi jjearch Society.

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:, ‘8,. ‘_,-‘,_’

L .,

.:

.‘. -. ;

,.

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ROLAND W. SCHMITT is a graduate of the University of Texas and Rice Institute (PIIDphysics). He joined the General Electric Company as a Research Associate and has since held a variety of management positions. He is presently Research and Development Manager, Energy Science and Engineering.

198

internal self-consistency. i.e., that conclusions derivable from our line of argument should rlOt contradict oilc another. iI’Orepot-t on ;I 03ntinuing study). th~sc Crit&;f hrlvc t1ut hccn cotllplc~tcly tnct. For ~!XaJllldC.OIlC of OLIN first pro.jcctiotis yiClclecI an utir~afisticaliy higIl lcvcl ot’ atinud cod production by the year 2050. To corrazt this. an upper bound has been imposed on co;11 production without. 3s yc t. havi tig estal~lislta.1 ;I price sct~cdulc for c‘c~althat wot_tld 1~ ititcrtially consistat with this bound and aIs with the lower lcvcl 01’ total cticrgy consumption implid by higlicr energy prices. However, ;III cxaminrition 01‘ tlic tiiargiltal pria of coal implied by our prcscnt Ibrmulatioti lcads otic’ to believe that Ihc t-csultrs displaqd in this paj)t’r art’ close to those of’ at1 ititcrndiy xelf-cotisistctit model. The criteria arc’ L’ssetifiillly ;I statcnncnt ot’ policy t’or the conduct of this study. 13ccau~ thcsc arc’ So few un;Ltiibigtous guides to tlic t‘ir?itrc. it is iniportant to cstablisli such LLpolicy. It s)t~oulcl incrcasc file probability of being right. Ncverthclcss, thcrct are inevitably a few irreducible rtssumptions bchitd any f’orccast which may be crucial in finally detcrmining whether it turns out to be right or wrong. At least two of these should be mentioned. First, a 1 aIl0wance has not been tnade for :I dramatic sc:ientific breakthrough of importance comparable .

icaily

Competition Between Electric and Nonelectric Energy

I

1

I

Fuel Availability and Cost

FIGURE

I

Competition Between Energy and Other Uses of income I

I

l-l

1

POWER GENEMR~TION

-

L

I

t

-‘--‘---

Overall plan for determination

1.

generation

mix.

MODEL

FORMULATION

allcl

Milllnc

allows

[

I

Technological Development

-

of base-load power

The f’orn~~tl~tirm ~lseci in this model. to

iti

whicfl is tluc 11 . jinks electric and ttoticfcctric c’ttcrg). t‘or price-ittciitccd cotiscrvlttioti and fat

arc usc’d. WC obtain from the condition

Cquilibrium consistent a,; +

$

=

QNF

(\‘I.. , aN I< =

nl.; .

gN !I

=

for economic

with Eq. ( 1):

(2)

+ flNE,

of changL! of allnllr~l rlites and nonclcctric conelectric sumption, respectively.

NONELECTRIC ENERGY

annual rates of change of cltxtric :i11d nonelcc t ric prices. rcspectivcly (constant dollars).

I

I

I

1960

“‘OYEAR

1940

I 1970

Growth rate of nonelectric energy. Data taken from U.S. Department of Commerce, Statistical Abstract of the United States, and U.S. Federal Power Commission, FIGURE 4.

Figurc*s 2, 3. 4. and Table 1 illustrate tive

claf3

[ Z 1.

rqmscnta-

Fuel Consumption of Electric Power Plants. TABLE 1 Nonelectric Energy Price Growth Per Year (1950

to 1970)

Industry Cwl Oil Gas Transyort~tinn Gasoline Domestic Coal Oil Gas

Looking

at these

data,

we find, in real dollars

We ObSWVt2 that: ( 1) the growth of electricity Data from Edison). .consumption 1lrlS I>Wll significantly grcatcr tllLll1 FIGURE 2. Growth rate of electricity. consumption, (2) this relatively rapid Electric Institute, Historic Studies of the Electric Utility i nonelectricity Industry. growth was accompanied by r~ul price dccrcases of electricity during the 40-year growth period to 1970, and (3) the past data are essentially in accord with Eq. (2). This insight may bc important because separate studies undertaken by Iho Gcncral Electric Company and others (“The Energy Conkcrsion Alternatives Studies (ECAS j” sponsored by NASA and EPRI) did not find any type of iidvanccd coal-fired system that would permit the production of sig~z~~i’ca~~tly chcapcr electricity in ._i_L_L~.._.__i..-. advances in efficicncics i__71, the future 131 . Projected . combined with price rises in fuel and materials and increased construction costs appear able, at FIGURE 3. Experience curve for electricity in the United States. Curve corresponds to a 3.3% average yearly decline best, to keep electricity prices constant in real dollrrrs in real dollars for the price of electricity (1970 dollars). in the foreseeable future. As a result, Eq. ( 1) will Data taken from Edison Electric Institute, Historic Studies predict future growth rates slower than historic of the Electric Utility Industry. rates for electricity consumption. IC

200

INPUTS For our projections. the candidates for bulk power generation have been divided into conventional. evolutionary. and spcculativc catcgorics. This classification is also applied to non&xtric cncrgy . Table 3 lists the candidates used thus far in the study and the pertinent data for the systems and for the energy resources cmploy~d in the cconomic ancllysis [ 41 , For the sjxxula t ive energy technologitls, the cost paranicters ust’d have been estinx~ted quite optimistically in line with ERDA targets. These are illustrated for solar th*rmal, sohr photovoltaic, and oct’ttn thermal graclbznt systems (Figure 5 j. Fuel availability and the rate of tecllnology dc3s constrainL:i in tiic vclopmc nt are introduced maximization program. Fuel availability may bc: expressed 3s an amount ot‘ niatcriaI 3vaiht4c withiii a number of price brackets, and the runs nlacic to date include data of this naturi‘ for uranium, derived from ERDA cstirnates as shown in Table 3. For coal, most runs to date have included a constraint upon the maximum rate at which the coal mining industry could 1~ expanded (up to 50 X 10’ 5 Btu’s per year by tllc year 2000 and up to 100 X 10’ ’ Btu’s per year by the year 2050). In runs made to date, coal prices have been held COW stant at 9 1 per million Btu’s, although price increases arc plirnned for subst’quent runs. The constraints on technology development art‘ csprescd in terms of a date of introduction for tech new teclinology, plus ;I mrlxiniuni rate of ci~ployni~nt thereafter. For some new technologies, such as tidal power, the total possi/dc~contribution 10 energy

production is also constrained. The constraints on timing and rate of introduc‘tion of the brC4cr reactor usc~i in the model arc‘ iliustratk!cf in kSigilrc 0: similar data for t.hc vrrrious spCCulativc ojItiotl\ ib tiisj)laycd in Figure 7. To dak. 0th. potential Constraitit~ WC-~ ;I\ those of th cnvironm0lt. niatcrials availabilit). transportati:on. construction. or other clCniL*nts of the inli’rastructur~ -have not , lwti introdu4xxl exogL!tloml!y’; rather it has been assiimcd the>, arc reflcctcd ial the costs. ThcsC and other ;qlc‘ct\ ot’ j>olicy or rstratcgy could. it’ 0nC u-ibliL4. by* intruduccd in to tll~ motf~l.

._~ .-_____ -.-__.---__ -.----me-

~.

-__.._

I i I

i CAPITAL COST

i

$/KW

1975

2000

FIGURE

photovoltaic

:oo

costs for

and ocean thermal

Data are bar:zd on an ERDA

“During the period 2000to 2020,there is a

YEAR

E!;timated capital

5.

I

utility

*

2025

;olar

therma?,

energy conversion

solar

systems.

study soon tG be published.

YAX!YUY FER:!kTAGt iji him 8AjI LOP3 iENERATIYC CAFAClTr PEIW’TEC F?Ii LYF~R .r, f3YPL?A!:3NS

I

Yb

possibility that a ‘crunch’ will occur in U.S. energy availability ”

FlGURE

6.

Estimated

timing

for

introduction

iof LMFBR.

201

l

TABLE 2 Candidatesfor Bulk Power Generation Annual Capital cc.:t

(1975 $/kW)

Marginal cost

(1975 $/MMBtuI

funning melding

Maximum

cost fuel

(1975 $/kW-Year)

Initial

availability

Substitution

time

o/o

of total power

possible

.._ _. -__..~-..__ _._-_. ____-_I__

IO0 N.A.

_.

N.A.

s0.f

I 00

Limit of resources _--.

IOU s IO’” 3.5 h ItIt8

Ijtu/yrX Btu’

qt.)&!

IO0 x IO”

lStu/yrK

351:

100 x 10”

l$tu/yrR

2 5.5’

IJnlirniteil

..

3.5

?SF 3tJ

x

II)‘M

100 Y 10”

IHII

IHu/yrR

I? x IO’ r IHu/yr~

Runs n~adc on the model rcportcd hcrc hm.~ cmploycd a growth rate of the GNP of 3.W; ~L’I’yca~ in this cmtury, gradually shifting to 2.S’,? per year in the nest century. As shown in the rlpp~~nctis. the growth r3tc of the GNP is the kcty csogcmu~ variable ill 111~’ projections obtainat from this model. The values used in the results reported here arc. perhaps. at the high end of current long-km spccul~tions on growth rates, cspxially if zero-growth projections arc given equal credibilityl. I-Iowevcr, historically, the growth of the GNP per mmbcr of the work force has been in the range of 1.95% per year and work force growth has been 1.46% per year, giving an overall 3.41% per yea;* growth irl the GNP for the 40 yars previous to 1969 [ 5 1. (‘In the period 1940-1970, the GNP actLl;lii), gcw at a rate of 4.3% per year. 161 ) In t’uturc applicatiop of tlic niodel. wc will include ;IltmWtt czxs with sol’ncwhat slower GNP growth rates. including a irro-population growth scenario, bawd on the Census Bureau’s Series X population projections [ 71 . The ratio of the econometric constants 11,/h2 has been kept at 0.5, consistent with historic data in Eq. (o) of the Appendix. Runs have lxxn unclcrtakcn using three values of the energy price elasticity (/q + h:, .--1) + of --0.1, -0.25 rliid. --0.4. siticc from historic data this parmcter could be mywhcrc within 1his range. Chic type of assimption is inherent in the iinur progranmiing m~~thod employed. Specific ciectric gencrlttioti systems arc introduocd whenever they are calculated to produce the lowest cost of tlimtricity discounted ovcl the entire life of the plant, assurnec! to be 30 years. This implies that the planning of additions to generation is undertaken with complete foreknowledge of operating costs over 30 years. Since this is not achievable in practice. actual Edditions to capacity will probably bc more conserv;itive and less inclined toward adoption of speculative systcrns than the model wordd indicate. TABLE 3 Cumulatiw! Amounts of Uranium Available vs Price Assumed in Study Tons

____._

._-.___

(MM) _..,____.-_-2.5 3.5 4.5

Price per pound

($1 -.---- ________ _..._------_$

30 40 75

5.5 6.5 7.5

1II0 I 25

a.5 00

IS0

140 I 60

._,-- _.--.~

-..-

*t

:

.-----r-._

t ‘

~____--~.~

_.__

-

._

’

100:

202s

2000

!9.5

YEAFi

FIGURE

capacity

7.

Maximum

permitted

2025

2000 YEAR

percentage of new base-load generating

sin our computations

tive alternatives.

RESULTS Energy CoLwjmption

for various specula-

&sticity over the range of ‘- .O. 1 to -0.4 upon thCsc growth rates is mj>arently not large, as illustrtitcd by the range of results iii Figure 8.

FIGURE 8. Consumption of electric, nonelectric, and total energy (including all uses of coal). Range bars indicate results for energy price elasticities of -0.1 (top), -0.25 (middle), and -0.4 (bottom). Consumption pattern shown illustrates relative inelastic behavior in the short term and relative elastic behavior in the long term and corresponds to results illustrated in Figures 9 and 10.

Still morC consu+ativC rtlsults would lx ohtaiiiccl it‘ 3 t’urthcr clCcrease in growt Ii of tilt\ GNP (down f-J-Olll 2.5%.) were assumed for the next century. The causes for further showdown would bc the cornbincd cffccts of slow pojmlation growth, reduction of the availrtbtc work force. and z1 slower growth of the GNP per work form ratio [ 5 1. Base-load Power Getieration Mix

lower bound dccrcascs to zero over a 40-year period, rcfJcctil]g tl~c pcrsistcilcc of current t~llyillg ~XKJ~iCCS. [f’ this constraint were not introdimd, IIC‘Wadditiom which would bc ohoscn solely 011 economic grounds. would have been cntircly LWR systems. A full LWR sccn;irio would. nioreovcr, place significant pressure on uranium rcsourct‘s atid require the earliest possible introductioll of’ the liquid metal fast brcedcr reactor (‘LMt:BR). 111this mocicl, when the price of urmiim rises above $40 per p<)uljd the LM FBR ~WOIWX woiloni icd. Introduction of the LMFBR 1~;~ ~XII s~h~cl~~l~cl for the year 2000 and its maximum rrrtc of’ introduction constrained as shown it1 Figure 6. The actual rate of introduction of the LMFBR will be significantly determined by the cost of electricity from the LWR. After the year 2000. LWR clcctricity costs will begin to rise at 3 rate dqmdcnt on the ovmll CleCtricity consutnj~tioii afitl on tilt‘ availability of urmiunl rc’sourom. At itltroduction. the inifial growth of LMFBR capacity is not constrained by the availability of plutonium. which will have been built up by previous LW R opera tions (it has bce11 assumed that reprocessing and plutoniuni fuel fabrication facilities arc avtiilable). Howcvcr. by around the year 2025. the rapid growth of LMFBR capacity will require new additions of LWR capacity for supplctncnfary plutonium production, unless a brading pin of bcttcr than 474 cm 1x2;1chicvcd. Unless a very significmt relative rise trrkcs place in the costs of power gcncration by nuclear systems, tllc period 2000 to 2025 is char;icfcrizcd in all runs n1ilcjC to date by substantid additions of nuclear capacity . C‘oal-fired plants arc’ projected to produce electricity at a higher cost in this period even with the rclativcly low constatlt coal price we have assuinat. fIowevcr, tlic early years of’ the 2 1 st CL’IIW’ will bc charactcrizcd by ;I rcl;ltivcly slow introduction of the LMFBR. If the c;Ipticity to produce COlIl iS dS0 corlstrairlcci, all cticrgy “~r~j~~clj” will WLW~ whkh will provide a11 irnjlctus for tflc introduction of’ SOlllC of’ tllc n7orc specufativc tc>cflllof&S. A run illuslr~tiiig lhis possibility is illuslr:~ted in Figure 9.

A11 runs undcrtakcrl to date inclicatc that. for the rtmaind~r of this century, the key ddifions ttr hsc-load power gc~i~ration [nix a-t’ c’od-fird steam system md the light-water ructor (LWR) sys1cms. With flit’ costs that wt‘ have cstitnafc’d, LN’R clcctricity is 20 to 307; chcapcr over 3 SOyear discounted lif‘c cycle and would be the f~ivorcd Nonelectric Fuel Mix clioicc. Nevertheless, the nc’w capacity additions A total of 3.5 X IO’” Utu in domestic and inlhave IXCII constrained to bc at least 50:s fossil fuel j>orfCd oil and gas available has been assumed. With for the r:~fmind~r of the century; thcrcxftcr the this gcncroils assuinpfi::)n, the nonclcctric cnt~gy 204

REOUIREMENTS FOR TRANSPORTABLE

Energy Prices

160-

HYDROGEN OR ELECTRIC CAR)

140-

60-

tb~RO

AND

/

YEAR

FIGURE 9.

Electric

energy

consumption

and power genera-

tion mix.

sector

rctnaills

dcpcmicnt

on tticse rcsourccs into century. with significant

the early part of the 2 I st reductions thcroaftor. Figure 10 illustrates the noneicctric Fuji mix that corresponds to the electric generation mix of’ Figure 9. Like Figure 10. it ~110~~s i1 period of cncrgy “~runcii“ within the first tlircbe &!C’rrdes of the 2 I st century. Trmsportation fiicis t’rorn oil and gas will be dcciiIiing tiicri and the most acccp ta bit and ~cononiicl-liiy viabit riiternativc will be coal-based synthetic fi~eis. The timing of their irltroduction is dcpendcnt to ;1 large Cxtt!nt FIGURE 10. upon govcrnmcnt policies. However. the optimum rate of introduction is very rapid ?inci may 1X c‘onstrained hy capit;ii or, as in the run illiistratd in TABLE 4 Figures 9 and 10. by coal availability. ‘Tilt2 result Approximate is that a f’uei “~rurich” dcvciops with rising pica. oil from shale is introduced as rapidly’ 3s possibic. and solar hclrting and cooling is 3iso introduCc’d to free up oil for transportation. This “crunch” wo~ticl tiot occur if ~o:iI produdion wcrc um:onstrriind and runs in which no such constraints were irltrodud showed co;~i-h;~s~d synthctk 1’ut_!is btlmnling 01‘ ovt‘rriding inlportancC by the year 3025. and coal produCtion rising to 3s much as 36 tinitls tllc prcsUl1 icvel by the year 2030. At thcsc production ICVC~S.

Nonelectric

Marginal

energy

Prices for Energy

consumption

(1970

to 20301

and fuel mix.

conclusion appears to be only weakly dependellt upon the exact value of energy elasticity with the which have been assumed costs and constraints here. If these prices are roughly represented by exponCntials, then t’.q. (2) can be expressed for this 7S-yi2ar pcrioc.13s:

iinported, is less than tk 3.5 X 1O*8 Btll assllllld in the results reported here then (1) the energy

will occur correspondingly earlier, (2) “crunch” greater pressure on synthetic fuels and other higher cost alternatives willresult earlier. and (3) the shift to electrificlation will increase.

Li/)litCc/ Crrallilrrll A wilahility ad Price Rises. 111 the cvctlt that available uranium resources prove to be less than the EDRA cstimatcs used in these runs, t.he LWR electricity costs will retlect uranium earlier. This will put which again confirms the rule-of-thumb provided price rises correspondingly greater pressure on the introduclion of the LMFBR. by this quation. ’ whose introduction would then definitely be limited by the rate of technical development. Once available, Effects of Other Variables the LMFBR contribution to the power generation Cod fricvs: A major assurnntion of the projcctioiis mix would need to grow rapidly, in this case accomreported here is that tile price of coal will remain panied by further symbiotic growth of other nuclear *in the neighborhood of Y$ I .OO/MMBtu (in 1975 systems as required for supplementary plutonium dollars.) for the forcsecjblo future. This assumption production or ;I greater breeding gain than the 4’::. may not be valid, espec:ially should demand outrun assumed here. supply at any fime or high grade reserves hxomc depleted by massive coal use. A moderate rise ir; the LMHIR Capital Cost Rises: The $8OO/kW capital price of coal will leave the electric power generation cost of the LMFBR used to date is an estimate mix largely unchanged 1 fhough it will accelerate taken from the mainstream of present predictions the penetration of nui,hzar systems. On the other [ 81 . In the event that technical factors cause significant cost escalation. the breeder may not be costhtlnd, ;i large rise in the price of coal will significantly lower nonelectric energy consumption and could effective. Then (1) the LWR will become a much ca~lst’ still further electrification. more important factor in the power gt!Jlcra~iOJl mix for ti longer period, depending upon electricity WC are presently studying separately the question of coti1 availability. possible range of prices as a consumption, uranium availability. and price; (2) function of cumu1ati\,e consumption timid forescc- the resultant rise in the price of electricity will able environmental liqiitations on coal use for em- reduce electricity consumption and the progress of ployincnt in future runs of this model. Our early clcctricity substitution will slow: and (3) 0~1~’ Or Jnore reskllts have convinced us of the great dependence Of the speculative alternatives may enter the power of our present projections on coal futures. generation mix in a major way in the 2000-2050 time period. However, hard data on the eventual CoStS Of speculative alternatives is nonexistent at this 0 4:;;. per year growth plus l/2% per year price rise of electricity: 0 l-l /2% per year growth plus 3T.G per year price rise of non&xtric energy;

“If the breeder can be introduced at costs which now seem reasonable, it will dominate the U.S. energy picture by 2030.”

“In the future,’ Pnk’ticul atrcl /~~~Ili~or~rltc~lrt~rl Liirritirtiot~.~~ oil Lb /do!‘tricJ/lt oj’ Vuric.,us A lter*rlatiI1cs: A similar san;rrio

costs of all forms of energy will rke in real terms.”

to tticb above results if brcccler introduction is impcdcd or abort4 by political or citvironriiclital frlctor,i. It’ the wflole nuclerlr industry is thus restricted. massive coal use could resuit. with cc.)ncomitant higher cxi! prices, higher elcc:ric;ity costs. and lower encrsy consumption. Furthci~;?l~~rC. if cod USC is udditionally restricted by environmental CONCLUSIONS Icgisla’tion. then a shift to the spcculativc alternatives of tllc llcxt higher cost will result. In ttliit cxic. clectrie energy consumption would fall significaitly below the levels presented in this report, reflecting the cost rise, and nonelectric energy consumption would bc somewhat greater, rctlecting the effect of competition. Tw/~~ukui ’ ‘Break tlrro Irglrs” iu Oil0 or ~lloi’c 0J’ tlw Spiwh fiw Aitmuztiws: The economic effect ot tech t1b:al cannot bc estimated. “brrakthrou~hs” Howe\lcr, our cost projections for the speculative dterna fives arc’ alrcdy optimistic and envision rapid technical progress, made possible by continuctl massivl: subsidization of research and dcveloptnent by ERDA. The most sensitive candidate for a r;lclical ttxllllir.Yll “hrc~iktfiro~~gl~” is solar photovolt~ic. In this ,case. however, lowering of the effective cost of the system below $lOOO/kW for bulk power generation would require a wholly new concept. and the ultimate limitation would still be costs of’ energy storage and conversion equipment and ot lad

.,

Altcwruti~xv:

Thus far. this study has not included still more speculative altcrnatives, such as thcrmonuclcar fusion or thcrinochemical hydrogen production; there exists no present credible basis for estimation of costs of such alternatives. In addition, the study ciot2i not yet include the hiph-tcrnpcraturc gas reactor (HI‘GR) or the CANDU reactor systems. which appear to be minor factors in the domestic power gencrrrtion mix unless LMFBR development is significantly delZlyed. EII~C~~O~IW of

0~1~

-

“Nonelectric energy costs appearto rise significantly faster than electric energy costs, so that electricity substitution is expected to continue.’ domestic supplies and increasing competition for world supplies. A rapid rise in the price of uranium as used in light-water react, brs, caused by deplction of lower cost rCS~?UTct!S. Constraints on the. further growth of coal production, which will already have risen to 5 or 6 times present production by the first decade of the 2 1st century. If coal is requirecl to grow at a rate to offset ~:ompletely the loss of oil and gas, then upward pressure: on prices, and ultimately depletion, will result. ’ 0 An LMFBR which, while developed, will not yet be in a position to become the main workhorse of U.S. energy production. (5) The “crunch”, if it occurs. will result in the following changes: 0 ?ressurc for rapid developmtnt of, a large synthetic fuels industry,. limited by the availability and price of coal and by competition with the use of coal for the gcncration of electricity. l The introdrrction of shale dil and solar heating and cooling of buildings (although we believe that these alternatives will probably be limited by environmontaf 2nd capital constraints, rcsfiectivcly). . 0 Increasing concern about energy for transportation which, in the cast of limited coal availability, will likely translate into a major shift to electricity (either for direct use in clcctrit vehicles or for producing electrolytic hydrogen fuel). Consequently, the price 01’ nonelectric energy will rise rapidly, and consumption will decrease. ( 6 1 It’ the hxxicr can bc introduced at costs which now seem reasonable (around bgOO/kW if1 208

1975 dollars). it will dominate the U.S. energy picture by 2030 and will result in electricity prices remaining relatively low. In this event, further growth of speculative energy technologies may not oc’c’ur, although some of thetn may have been rushed into use’ in an earlier “energy crunch” period. APPENDIX .

The economic analysis is based on obtaining the equilibrium conditions which maxitnize an objective function of the form

whcrc the various terms are &fined in the text. We find a maximum at any time. I, by differentiating with respect to q, and q2 and setting the equations to 233-o: 4s

-_--

a

-I

=

a(t)

6, qll

dC

-- 4,

&

=

o

’

dS = a( 1) 62 f/f 1 y$2 -’ a: .I’-rlyz -. ----- = 0,

d(/,

C/J,-- 1) I )1 (y, ) + h,

I t1

(42 ) = I I1 $!.

0 (f?, -

1) If&)

+b,

In(q)

=

--II n(u),

1

PZ In ?;- In@). 0 2

IXt’th-cmthting the to time!, wc obtain

!

above

a1 + *I =

equations

with

rrqcct

a!y2 + 7r2 .

.

0

These Malaybe cotnbincd to giic

.jTI .

When 7r2 = 0 konstant prices). then, under the assutnpl/ion that in cquilibriutn at constant prim a constant share of GNP is rnaintaincd. WC obtain

Y

Wc have extended this analysis. optimizing 75year time periocl, by using the cxprcssioti

c)vc’r ;t

By similar derivation,

the condition y + 6, (x1 + b2@2 = oL2 t 1r2 = cq t nl , which comes from Eq (3), permits the determination of atI from historic by *

u,

=

--b&)bl

P2 (cl;Ib2

- ’

*

(7)

Pl ----

=

271’ (4;

)bI-

;.(q;)b

2

l

As described in the text, the condition (x1 + 7r1 = (x2 c 7rq appears to be reasonably in accord with historic data. The condition y + b,q t b2a2 = (x2 + 7~~ = (x1 + ?rl is difficult to determine within the accuracy of economic statistics but is also within the statistic range provided by historic data. and we have tkrcfore used Eq. (7) to determine ao.

210

REFERENCES

AND NOTES

Marine, A. S., ETA: A Model for li’nerg~) Tccknology Asscwwrr, Energy and Enviromncnt Policy Center, John Fitzgerald Kcnncdy School of Govermnent, Harvard Unkrsity, Cambridge, Mass. 2. Various references for historic data included in figure captions. * Data for Table I from International instittite for Applied Systems Analysis, Schloss Laxenburg, Austria. General Electric Company, The Energy Conwrsiun Al?cwativcs 3. Study (ECAS), sponsored by NASA and EPRI, private communication based on completion of Phase II by Corporate Rcscarch and Development, General Electric Company, Schenectady, N.Y. 4. References to Input data arc included in notes Table 2. 5. Denison. E. I:., Acctmnting ftitbvUnited States Iz’cortovric Growtlr 1929-l 969. 6. U.S. Department of Commerce, Stutistical Absfvact o_/’tlw Unitd States. 7. Vermilyca, D. A., Population Stabilization and k’ncrg_vCor~slrn~ption. General Electric Company, private communication. ** Levenson,zM., Murphy, P.M., and Zaleski, C! P. L., Relative Capital Cost 01 th LMFBR. Electric Power Research Institute, Inc. report, prcsentcd at American Power Conference, Chicago, Ill., April 20, 1976.

‘*