PAGENO="0001" 94th Congress } j~p~ CO~ITTEE PRINT THE FAST BREEDER REACTOR DECISION: AN ANALYSIS OF LIMITS AND THE LIMITS OF ANALYSIS A STUDY PREPARED FOR THE USE OF THE JOINT ECONOMIC COMMITTEE CONGRESS OF THE UNITED STATES I_i t~ ? ~ ~_/_~ APRIL 19, 1976 Printed for the use of the Joint Economic Committee U.S. GOVERNMENT PRINTING OFFICE 67-369 WASHINGTON : 1976 For sale by the Superintendent of Documents, U.S. Government PrInting Office Washington, D.C. 20402 - Price 50 cents c, `~There is a minimum charge of ~I.00 for each mail order f~f_ ~ ~ VI ~` t PAGENO="0002" JOINT ECONOMIC COMMITTEE SENATE JOhN SPARKMAN, Alabama WILLIAM PROXMIRE, Wisconsin ABRAHAM RIBICOFF, Connecticut LLOYD M. BENTSEN, JR., Texas EDWARD M. KENNEDY, Massachusetts JACOB K. JAVITS, New York CHARLES H. PERCY, Illinois ROBERT TAFT, JR., Ohio PAUL I. FANNIN, Arizona HOUSE OF REPRESENTATIVES HENRY S. RETJSS, Wisconsin WILLIAM S. MOO RHEAD, Pennsylvania LEE H. HAMILTON, Indiana GILLIS W. LONG, Louisiana OTIS G. PIKE, New York CLARENCE J. BROWN, Ohio GARRY BROWN, Michigan MARGARET M. HECKLER, Massachusetts JOHN H. ROUSSELOT, California JOHN R~ STARK, Executive Director SENIOR STAFF EcoNOMIsTS JERRY I. JASINOWSRI LOUGIILIN F. MCHUGH WILLIA3IA. Cox JOHN H. KARLIK COURTENAY M. SLATKR RICHARD F. KAUFMAN, General Counsel ECONOMISTS WILLIAM H. BUECHNER ROBERT D. HAMRIN RALPH L. SCULOSSTEIN SARAH JACKSON GEORGE H. TYLER MINORITY CHARLES H. BRADFORD (Senior Economist) LUCY A. FALCONE L. DOUGLAS LEE LARRY YTJSPEH (Created pursuant to sec. 5(a) of Public Law 304, 79th Cong.) HUBERT H. HUMPHREY, Minnesota, Chairman RICHARD BOLLING, Missouri, Vice Chairman M. CATHERINE MiLLER (Economist) GEORGE D; KRUMBHAAR, Jr. (Counsel) (Ii) PAGENO="0003" LETTERS OF TRANSMITTAL APRIL 16, 1976. To the Members of the Joint Economic Committee: Transmitted herewith for the use of the Members of the Joint Economic Committee and other Members of Congress is a study en- titled "The Fast Breeder Reactor Decision: An Analysis of Limits and the Limits of Analysis," prepared for the Joint Economic Com- mittee. The study evaluates the major cost-benefit analyses, which review the benefits of developing and introducing commercially the Liquid Metal Fast Breeder Reactor. HuBERT H. HimIPHBEY, Chairman, Joint Economic Committee. APRIL 15, 1976. Hon. HtrBERP H. H1mIPHREY, Chairman, Joint Economic Committee, U.S. Congress, Washington, D.C. DEAR MR. CHAIRMAN: Ti~ansm~tted herewith is a study entitled "The Fast Breeder Reactor Decision: An Analysis of Limits and the Limits of Analysis," prepared by Mark Sharefkin of Resources for the Future, Inc., for the use of the Joint Economic Committee. This study provides a timely analysis of this nation's largest energy research and development project. Mr. Sharefkin examines the basic premises underlying the major cost-benefit analyses of the Fast Breeder Reactor. The paper raises questions about the cost-benefit analyses' assumptions concerning elec- tricity demand, uranium supply, nuclear reactor capital cost differen- tials, and discount rates. It also suggests specific ways that conven- tional cost-benefit analysis fails to shed light on the crucial breeder timing issue. The views e~xpressed in this study, of course, are those of its author and not necessarily those of the committee, any of its individual members, or the Joint Economic Committee staff. William Cox and Larry Yuspeh of the Joint Economic Committee staff managed and edited this study. JOHN R. STARK, Ea~ecutive Director, Joint Economic Committee. (III) PAGENO="0004" PAGENO="0005" CONTENTS Page Letters of transmittal - iii Point-by-point summary vii THE FAST BREEDER REACTOR DECISION: AN ANAL- YSIS OF LIMITS AND THE LIMITS OF ANALYSIS Introduction 1 Cost-benefit analysis of resource limits under uncertainty 1 Uncertainty, heroic assumptions and analysis 2 The limits of analysis 2 Uncertainty: Sources and implications 4 The uranium resource base 4 Future electricty demand 8 The LWR-LMFBR capital cost differential 11 Cost-benefit analysis of the LMFBR program 15 Limits of cost-benefit analysis 15 The major LMFBR studies 15 The range and interpretation of net benefit estimates 19 The discount rate and the range of net benefit estimates 22 Toward a broader perspective on the LMFBR decision 22 The LMFBR timing issue 23 Conclusion: The purposes and limits of analysis 28 The range of alternatives 28 The limits of analysis 29 Appendix 30 (V) PAGENO="0006" PAGENO="0007" POINT-BY-POINT SUMMARY 1. All of the major cost-benefit studies of the liquid metal fast breeder reactor (LMFBR) are incomplete, because they ignore the possibility that substantial costs in the form of long-lived radioactive wastes and their consequences will be transferred to future genera- tions. The nuclear waste question pushes cost-benefit analysis beyond its capacity. A new analytical method may be required. 2. It may be very misleading to jump to conclusions of impending uranium shortages on the basis that uranium's reserve-production ratio is declining. In 1938, oil's reserve-production ratio was about 12. It would have been a serious error, however, to argue that the United States would run out of oil in 12 years unless something drastic~ was done. Although oil production has increased at 7.5 percent per year, oil's 1974 reserve-production ratio was 18. To argue similarly about uranium in 1976 probably is just as wrong. 3. Major increases in uranium reserve estimates over the past. few years emphasize the uncertainties surrounding this resource base. 4. Because uranium reserves are expensive to prove and because uranium inventories are expensive to obtain and hold, proven reserves and inventories will tend to be low relative to other materials. 5. Uranium reserves also are low, because, until recently, uranium prices were declining. Incentives for exploration and development, therefore, have been weak. 6. The uranium resource analyses exclude consideration of major determinants of future uranium resources. They are structured in such a way as to impart a pessimistic bias to uranium supply projections. 7. Projected growth rates of electricity demand are a key to~ the decision on when to proceed with the breeder program. It appears that electricity growth rates beyond 1980 may be closer to 2 percent per year thnn to the historical growth rate of 7 percent. With ~t 2 percent growth rate, electricity consumption will be only 3.3 trillion kilowatt- hours in the year 2000, compared to projections of as high as 6.1 tril- lion in the major breeder cost-benefit studies. Thus the breeder could be delayed. 8. The major reason for slower projected power demand growth in the future is that the era of declining electricity prices seems to be over. The reasons for the end of declining electricity prices include (1) the end of scale economies for power generation, (2) the intensity of environmental, concern and the internalization of some of the external costs of power production, and (3) the recent rapid increases in fossil fuel costs and in the capital costs of light-water reactor plants. 9. The capital cost differential between light-water and breeder reactors is a key to the breeder decision. Everyone agrees that the breeder's capital cost will be much higher than that of light-water reactors, but no one is sure how much higher it will be. If the differen- tial is greater than $125 per kilowatt, the LMFBR's electricity will cost more than light-water reactor electricity. (VII) PAGENO="0008" VIII 10. Many analyses assume that LMFBR capital costs will decline with experience (i.e., "learning"). There is not much reason to believe there will be any decline, however. Light-water reactor construction on the contrary has experienced persistently increasing cost and has not displayed a learning-curve pattern. There is not much reason to believe that the breeder will fare better in this regard. 11. Most economists agree that intertemporal efficiency comparisons require the discounting of future costs and benefits, but they do not agree On what the particular value of the discount rate, should be. Because.the study by Stauffer et al. uses a discount rate for the breed- er's benefits substantially less than the 10-percent rate used in the other studies, it finds that the benefits of breeder development are quite high. 12. A problem with all of the breeder cost-benefit studies except that by Manne involves their specification of the future alternatives. The Manne study reviews two scenarios of the future-one with a certain date for breeder commercialization and one with various possible com- mercialization dates with. probabilities attached. The other studies analyze Only one future that assumes certain breeder commercializa- tion as of a certain date. If breeder commercialization has benefits, all of the studies that analyze one future `with certain breeder commer- cialization' will find that the earliest breeder commercialization date will. yield. the greatest benefits. Because of this characteristic,' these studies shed no light on the crucial issue of the' timing of the breeder's development. 13. If cost-benefit analysis is to be applied effectively to the breeder development decision, alternative' program timing strategies must be analyzed. Indeed, it can be argued that an assessment of such broadly defined alternative program strategies is the most important role for cost-benefit analysis to serve. ` ` ` ` PAGENO="0009" THE FAST BREEDER REACTOR DECISION: AN ANALYSIS OF LIMITS AND THE LIMITS OF ANALYSIS' By Mark Sharefkin2 INTRODUCTION The liquid metal fast breeder reactor (LMFBR) program has been the centerpiece of our long-term energy supply strategy for more than a decade. During that period the widening and deepening Qf. infor- mation on this technology has prompted changes in LMFBR program focus, strategy, and organization, but the underlying rationale for the program has nOt changed. Program advocates have argued that with- out the breeder, uranium scarcity will drive the real costs of producing electricity higher over the next half century. They argue that with the breeder, we can significantly expand the effective uranium resource base and thus postpone for several centuries uranium-related, electricity cost increases. COST-BENEFIT ANALYSIS or RESOURCE LmnTs UNDER UNCERTAINTY The main vehicle for formalizing and quantifying this argument has been cost-benefit analysis. The cost-benefit analyst identifies the uncertailities affecting evaluation of the LMFBR program and then specifies a consistent framework for LMFBR program evaluation. Given any set of assumptions about those uncertain elements, a. cost- benefit analysis gives a dollar figure-the discounted present value of the net benefits to the Nation from successful development of a com- mercial LMFBR. The methodology of cost-benefit analysis grew up in the evaluation of ~overnrnent watei resource pro]ects Critics argue that, even in water project evaluation, itis as much a framework for political compromise as an objective analytical method,3 but it seems clear cost-benef~t meth- ods have at least allowed spectacularly inefficient projects to. heiden- tified and, on occasion, blocked. Are the extensions of cost-benefit analysis required for the analysis of the LMFBR program appropriate and convincing; and are the analyses themselves likely to be as persuasive? A balanced answer to the first of these questions requires a hard look at the way in which LMFBR cost-benefit analyses model uncertainty. For, unlike the water resource: problems where the technologies-of dams and of hydro- electric generation-have been either stable or changing fairly pre- 1 \Iv RFF colleagues 3'oy Dunkeilev and Clifford Russell generously read and improved a draft of this paper; I lay claim to whatever faults remain. 2 Research associate, Resources for the Future, Inc. The views expressed here are those of the author. and do not necessarily reflect the views of the trustees or staff of 11FF. 2 See 3. Ferejohn, "The Half Empty Pork Barrel" (Palo Alto: Stanford University Press, 1975). (1) 67-369-76-----2 PAGENO="0010" 2 dictably, nuclear technology in generaa, and LMFBR technology in particular is extremely dynamic. And a careful answer to the second of these questions requires a close look at the correspondence between the issues that are resolvable by cost-benefit analysis and the issues central to the nuclear controversy. UNCERTAINTY, hERoIC Ass~MPTIoxs AND ANALYSIS What are the uncertain elements which must be accommodated in an analysis of the LMFBR program? `Since the prospect of future uranium price increases is basic to the argument, we must make explicit assumptions about the extent of the uranium resource base and the way in which that resource base will `change over time as uranium price.s change. Since the rate of depletion of the uranimn resource base depends upon the behavior over time of the demand for electricity from which the demand for uranium is derived, we must also have explicit assumptions about the behavior of electricity demand over time. Since the computation of a time stream of LMFBR program net benefits requires that we know how electricity i.s being generated over that time period, we must effectively forecast techno- logical `change in electric power generation over it. In sum, the list of required assumptions is long and heroic. Given any such set of assumptions, we can compute a corresponding net benefit figure; `and given any set of subjective probabilities of L*MFBR commercialization dates. etc., we can compute an expected net benefit figure; `but this is not the only wa. and perhaps not the most informa- tive way, of looking at the LMFBR problem as a decision problem under uncertainty. Because of the very long time period involved, the absolute net benefit fi~i~res are so sensitive to the chosen value of the social discount rate that an all-or-nothing LMFBR program decision based upon a net benefit estimate seems almost reckless. But there is another way to use cost-benefit analysis in guiding LMFBR decisions. Instead of casting the LMFBR problem a's one of "to have or not to have an LMFBR," net benefit estimates can be used to evaluate alternative LMFBR development strat.egie~s, with the overall sociaJ evaluation of the program left to other, `broader devices, including legislative decision. We believe that the `character of the uncertainties listed above-nnd discussed below in the section, "TJncei- tainty: `Source and Imphica.tions"-suggests such an approach. Fur- ther, posing the LMFBR ciuestion this way brings to the fore the issue of the timing of LMFBR commercialization. TIlE LIMITS OF ANALYSIS LMFBR program analyses have been built upon the analysis of uranium resource limits. Cost-benefit analysis has its limits `as well. These are limits on the kinds of questions it can answer `and the kinds of questions it' must neglect and leave to other decision mechanisms and procedures. First among these is the question of the distribution of costs and benefits. In principle the distribution of costs and benefits, both interpersonally and intertemporally, can be computed, but good cost-benefit analysis makes no pretense to competence in choosing among alternative distributions of costs and benefits. PAGENO="0011" 3 Among the most serious problems of nuclear power is the possibility that substantial costs, in the form of long-lived radioactive wastes, wil be transferred inequitably and incompensably onto future generations. None of the major LMFBR program studies examined below, in the section entitled "Cost Benefit Analysis of the LMFBIR Program," attempts to quantify these `costs. I-lad they been quantified, many people still would balk at discounting them back to present values. The procedure seems unfair, and that impression can be given a rigorous formulation. Though we will not explore the question, the point is clear: "We have reached the limits of `analysis, or at least of this kind of analysis, `and a different sort of analysis is required for thinking `about these problems. This second level of analysis is explored in a concluding section, "The Limits of Analysis." Short of analysis at this second level, we believe that LMFBR program analyses' are likely to remain unpersuasive. PAGENO="0012" * UNCERTAINTY: SOURCES AND IMPLICATIONS We have identified the sources of uncertainty in the economic analy- sis of any technology, such as the LMFBR, intended as an offset to cost increases for exhaustible resources. But identifying uncertainties is only a first step toward properly accommodating them in an eco- nomic analysis, for there are various kinds of uncertainty requiring distinct modeling approaches. Our purpose here is a clear understand- ing of the character of the major uncertainties in LMFBR program analysis, so that later we can see how well these distinctions are cap- tured in the LMFBR program studies and how sensitive the conclu- *sions of the studies may be to the choice of modeling approach. TilE UIIANm3I R.ESoDI~CE BASE The fact of resource exhaustibility seems self-evident. Since the earth is finite, resources such as uranium and coal are obviously finite. It is tempting and customary to identify that unknown, ultimately finite stock of resources using the many presently available measures of the size of exhaustible resources, but this temptation should be resisted. Proven reserves-particularly of minerals like uranium which are ex- pensive to prove~are those amounts that enterprises have found it profitable and prudent to "prove," and are more analogous to a firm's inventory of some raw material input than to the finite stock of non- renewable supplies which textbook economics forces shipwrecked sail- ors to allocate over time. Because inventories are costly to obtain and hold, no firm will hold an unlimited inventory of any input. The amount actually held will be determined by balancing off the benefits, such as assurance of supply and continuity of the production process; and the balancing of costs, such as the interest or carrying charges on the investment represented by the inventory and the costs of storage of that inventory. Similarly, no firm will hold infinite reserves of the exhaustible resource input. Reserves that are actually proven through exploration and to some extent developed to the point of relatively ready access will be determined by their value to the industry in re- duced uncertainty and supply continuity, weighed against the costs of exploration and development required to prove reserves. Thus it may be seriously misleading to jump from declines in the reserve-production ratio to conclusions about impending shortage. The notion that the resource may "run out" in a number of years approxi- mately equal to the reserve-production ratio is almost certainly mis- leading. In 1938, the reserve-production ratio for oil was roughly 12. In 1974, though production increased at roughly 7.5 percent per annum in the interim, that ratio had increased to roughly 118. One would have been entirely mistaken to conclude, in 1938, that the world would he out of oil in 12 years unless "something were done." One would he equally mistaken `to argue similarly at any other time.. In general, where a resource is expensive to locate and develop, as in the case of (4) PAGENO="0013" 5 oil, we expect the optimal reserves held by the industry to be lower than in the case of an industry, such as coal, whose `reserves are rela- tively inexpensive to locate and develop. Turning to the case of uranium, it is vital to note the newness of uranium as an economic resource and the dominant position of the Government on the demand side of the market for most of that short history. Relative to the enormous sums expended in the, search for exhaustible resources, such as oil, which `have been of major impor- tance in the' domestic economy for over 50 years, uranium exploration and development is in its infancy. The present 18-month-old program to obtain a more definitive assessment of our uranium reserves, the Preliminary National Uranium Resource Evaluation Program (PNTJRE), is budgeted for millions of dollars over its 5-year life. The way in which reserve estimates have shifted in the recent past and the dramatic way in which they have shifted in the first 18 months of the PNURE program' are indicators of the uncertainties surrounding the assessment of `this resource base. Table `1' below appears in the AEC's "Proposed Final Environ- mental Statement for the LMFBR Program" 1 (hereafter this docu- ment is referred to as AEC (1974)) and represents the AEC's best estimates. as of January 1974, though they are based upon earlier data ~nd analyses. Table 2 below appears in ERDA's `first published docu- ment, "RepOrt of `the Liquid Metal Fast Breeder Reactor Program Review Group," 2 and represents best estimates as of September 1974. Obviousl~ti~b1e `9 is more extensively differentiated and more informa- tive than table 1, but the two are essentially comparable. Above we have spoken of reserves as `an inventory, but the analogy with an inventory of goods on the shelf is overly simplistic and inade- quate for real reserve classification. Since exhaustible resource reserves are costly to "prove.," i.e., to establish with reasonable certainty, mining firms generally will hold a "portfolio" of reserves proven in varying degrees of certainty. In recognition of this important distinction, AEC data differentiates ~ "reserves" (referred to as "identified" in table 2) from "potential reserves." Reserves include only uranium in known deposits, for which the quantity, grade and physical character- istics have been established with reasonable certainty by detailed sam- pling, and which these tests indicate can be recovered at costs less than or equal to an assumed price level. T'he AEC "reserve" figure is there- fore what elsewhere is called a proven reserve figure. The AEC reserve estimates in .this category are relatively uncontroversial, and one writer on uranium resource problems suggests that the AEC reserve category be understood as "reasonably assured resources." ~ Note that the reserve estimates of tables 1 and 2 are identical. Cumulative reserves below $30 per short ton "forward costs" are, in both cases, 700,000 short tons.5 1U.S. Atomic Energy Commission, "Proposed Final Environmental Statement, Liquid Metal Fast Breeder Reactor Program," wASH-1535, December 1974. 2Energy Research and Development Administration, "Report of the Liquid Metal Fast Breeder Reactor Program Review Group," January 1975. For definitions of the AEC categories see AEC, "Statistical Data of the Uranium Mining Industry" (Grand Junction, Cob.: Grant Junction Office), June 12, 1974, p. 13. `Electric Power Research Institute, "Uranium Resources To Meet Long Term Uranium Requirements" (Palo Alto; Calif.: Electric Power Research Institute, November 1974), p. 44. See p. 7 for discussion of the concept of "forward cost" PAGENO="0014" 6 `The AEC's potential reserve (or potential resource) category includes by definition only "conventional" uranium deposits ami uranium surmised to occur in (1) unexplored extensions of known deposits, (2) postulated deposits within known uranium areas, or (3) postulated deposits in other `areas known to be geologically favorable for uranium. In sum, these potential reserves (see tables I and 2) are resources whose existence is inferred from existing information and experience, but not yet confirmed by direct sampling. The significant comparison between tables I and 2 is between the sum of reserves plus potential reserves at $30 per poimd forward cost in table 1-2,400,000 short tons of 1J308-and the corresponding total of 3,450,000 short tons in table 2. As the footnote on the new total indi- cates, the increase of 1,150,000 short tons is entirely due to the results of the first 18 months work of the PNTJRE program. TABLE 1.-AEC ESTIMATES OF U.S. URAN1UM RESOURCES Cumulative thous ands of short tons of U303 Reserves Potential Total UsOg cost up to (per pound): $8 $10 $15 $30 280 340 520 700 450 700 1000 1,700 730 1,040 1,520 2,400 Source: U.S. AEC, proposed final environmental statement, liquid metal fast breeder program (December 1974), p. 11.2-67. PAGENO="0015" 7 $3 03-10 $10-.', 015-3 $30 0100 $1OO~ $l5O~' ISDICATID PIWOAILE POSSIBLE 501COnArIvE ENOWN 5501UCCO'JZ 10E1J 53B$C53 DISr&tCtS PaaVLNCIS * PI300CTIVE PR000CIIVO 10118 FORS4AT!033 D3R1ATSONS 0087'.AT10NS SE 010010 cost, IDESTIFIED 5 I 3 213 300 211 30 ~ 53 130 3 190 83 - R~sc~t~b1y 2 iso 233 ` 100 C I 183 280 710 ` 210 620 ~ 490 7~0 0380 TOTSLS 700 970 433 (5) DZCIL'SINC 010001 OF A300535C0 -0 101St T0I5'A0102S, 0T510 THAN SANDSTONE (011 TABLE 4), 100.500 pp~ 0303 7~ ,. IoxrtA10000A SHALES, 6080 0753 U~0~ Appraz. j 5000 ~ CHAITH10000L SHALE. 25-60 0253 07308 Approz. J 8oo~j (1) 1.3 Short Tons UoOs=1.1S Metric Tonnes UoOg=1000 kilograms uranium. (2) Ores to grades down to approximately 0.12% USO8: approximately 95% from sandstone host rocks. (3) Ores to grades down to approximately 0.10% UsOs, primarily from sandstone host, but including small contributions from other host formations such as veins, conglomerates and tuffaceous material at grades down to approximately 0.025% tT3O8, where there are sufficient data to judge the possible quantity of uranium. (4) The index cost is not the average cost of production. And more importantly, it is not the prfce at which uranium will be sold. See text for a discussion of index costs, projected actual costs and prices. (5) This is a new total, approximately 1,200,000 short tons U30s higher than 1-1-74 estimates, a result of the Preliminary National Uranium Resource Evaluation Program (PN U RE), started approximately 18 mos. ago. (6) There are other small domestic sources of uranium: 200,000 metric tonnes of depleted uranium tails, available to stock LMFB Es (sufficient for at least 2000-1000 Mwe LMFB Rs). 20,000 short tons of U3O8 recoverable from copper ore leach solutions between now and year 2000. 70,000 short tons of UaOs recoverable from phosphoric acid made from Florida phosphate rock between now and year 2000. 2,000-3,000 short tons U~Oi per year by year 2000 from lignite gasification assuming 75% recovery of U308 and 20% of natural gas demand supplied from lignite. (No production now planned.) Source: ERDA, Report of the Liquid Metal Fast Breeder Reactor Group (January 1975), p. 16. There are other circumstances which reinforce what seem to be the optimistic implications of this recent substantial upward revision of potential uranium reserve estimates. `The behavior over `time of `uran- ium reserves, production and prices seems, in a very rough way, to be similar to the pattern typical of other mineral resources, with similar implications about fears of exhaustion and of impending rapid price increases.6 The definition of potential reserves is itself fairly conserva- tive, with estimates of higher cost reserves and potential reserves not encompassing all such resources but only those in presently known producing areas and in areas geologically similar to presently known The AEC source cited in footnote 2 above has time series on reserves, production, and prices. TABLE 2.-ERDA estimates of TJ.& uranium resources [Thousands of Shoot Tons U3O~(1) as of September 1974] po-rnrrnx (L'sOOSCoVIoto) (~) PAGENO="0016" 8 producing areas.7 Until very recently, uranium markets have been soft, with declining prices, so that incentives for exploration and development have been weak. Finally, the uranium resource data base, excellent when compared to what faces the analyst of other mineral resources, is structured and reported in. a way that may impart a pessimistic bias to the uranium resource picture. Thus the AEC's tabulation of reserves and of poten- tial reserves by cost levels indicates the amounts of each of these cate- gories presumed to be available at less than certain levels of so-called "forward cost," -which is the cost of future extraction. This extraction cost concept, which excludes past or "sunk" cost, is the economically relevant cost concept. But since maximum1 forward cost figures are used to demarcate the reserve tabulation, the actual cost of extraction for much of the reserve under each cost ceiling is well below the max- immn forward cost figure. And since the forward cost intervals are stated in current dollars, inflation erodes the better grade resources in the lower cost intervals in such a way Ihat changes over time in the resource distribution among cost intervals are not good indicators of changes in the. physical resource stock. Thus there are several ways in which the uranium reserve estimates may be biased downward. Moreover, the analyses that have been done do not get full mileage out of the present data base. They are struc- tured in a way which may impart a further pessimistic bias to uranium supply projection and which certainly excludes consideration of major determiliants of future uranium resources. There are ways to bring some of the economic incentives that bear on resource exploration and discovery into an economic model for forecasting future reserves, but I am not aware of any published modeling effort of this kind for the American uranium resource base. Such modeling is a difficult task. Poor models can and have produced silly results. But present reason- ing frori "models" which in effect neglect the economic determinants of the extractive resource base is almost certainly worse. Thus, an OECD model of the uranium resource exploration and development process ~ reportedly projects uranium resources larger by a factor of 15 than present estimates. The OEOD results suggest that partial models of the future uranium . resource base may understate that base by a very large amount. Moreover those partial models allow only the crudest explo- ration of the sensitivity of LMFBR cost-benefit results to resource base assmñptions. Below we will comment on the sensitivity problem, and in our overview of LMFBR cost-benefit analyses we will set out some criteria for the modeling of the uranium resource sector in anal- yses.of the LMFBR program. FUTURE ELECTRICITY DEMAND The demand for uranium and plutonium for fueling light water reactors (L\VB's) and LMFBR's alike is of course derived from the The traditional ARC "potential" resources category is restricted to "conventional" uranium deposits-deposits in sandstone or veins, much like present reserve-category deposits. See the discussion in Electric Power Research Institute, op. cit., pp. 4G-47. Here I am reporting the very brief description of results obtained with this model given In I. C. Bupp and J. Derian. "The Breeder Reactor in the U.S.: A New Economic Analysis," Technology Review (~u1y-August, 1974). Reporting the results of a model of this kind at second hand is always tricky. Time did not permit me to obtain a first-hand description of this modeL PAGENO="0017" 9 demand for electricity produced by those reactors, and any projection of uranium "requirements" depends upon an electricity demand forecast. Demand forecasting builds upon economic models and economic data and is relatively free of the serious uncertainties about the nat- ural world that plague resource reserve estimates. But demand fore- casts have their own particular uncertainties and instabilities, and these can be as serious for LMFBR program analysis as the uncertain- ties in uranium resource estimates. Although there is a range of demand forecasting methods, that range is illuminated by contrasting two approaches. The first amounts to simple extrapolation of past consumption trends; we will call the second econometric demand analysis. Though different in concept, they can give similar results if `pasl trends in economic growth and elec- tricity rates `are expected to continue. In other cases the results of the two kinds of `analyses can be wildly divergent. Econometric demand analysis yields forecasts based on `the separate influences of various determinants of demand and therefore is more useful in a period dur- ing which those determinants are changing at rates markedly different from the past. The method of extrapolating past growth means just that. Trends in electricity consumption over some past period are summarized in a single number-a growth rate; then ignorance of future conditions is recognized by adopting a span of growth rates around this historical average. Because the growth rate of electricity demand over the 25 postwar years, 1945-70, was exceptionally high-roughly 7 percent in the 1960's and much higher than that of the economy as a whole- the band of growth rates of electricity consumption frequently used for projections covers a range around 5 percent or 6 percent. There are numerous vari'ations on this method. In one, the growth of GNP is forecast, and the ratio of electricity consumption to GNP is assumed constant, thereby providing a forecast of the growth rate of electricity demand. The kinds of electricity consumption estimates produced by this extrapolation method are illustrated by table 3, taken from a uranium resource study which extrapolates electricity con- sumption based upon "an excellent correlation between real gross national product and total electricity generation." For comparison with the results of forecasts based on econometric demand analysis, the reader should focus on the column headed "Reference based upon GNP," in particular the forecasts of 2.9 trillion kWh consumption in 1980 and 6.1 trillion kWh consumption in 2000. TABLE 3.-ELECTRICITY CONSUMPTION FORECASTS BASED UPON EXTRAPOLATIONS OF HISTORICAL CONSUMPTION Total (tril lion kilowatt hours) Reference Assumed based on Assumed Year low' GNP high' 1980 2.9 2.9 2.9 2000 4.5 6.1 9.2 2020 6. 7 10. 6 18. 9 2040 10. 0 15. 9 38. 8 1 These figures lie far outside 3 standard deviations from the reference case. Source: Electric Power Research Institute, "Uranium Resources To Meet Long Term Uranium Requirements" (November 1974) p. 12. O7-369-7O----3 PAGENO="0018" 10 In econometric demand and supply analysis, there is an effort to identify the causal factors involved in shifts over time in the demand for electricity and in shifts over time of the costs of supplying elec- tricity. On the demand side, electricity prices and the incomes of consumers are typically important variables, and, on the supply side, technological change and changes in environmental standards and the costs associated with those standards are likely to be significant. In a recent report prepared for the Federal Power Commission,9 such an analysis gives an estimate of 2.2 trillion kWh for 1980 elec- tricity generation, to be compared with the estimate shown in table 3 of 2.9 trillion kWh for 1980, based on a GNP-related extrapolation. Utility industry estimates of 1980 generation have been as high as 3.2 trillion kWh. The FPC study makes no estimates beyond 1980, but the growth rates implicit in its estimates for 1980-closer to 2 percent per annum than to the historical 7-percent rate-will obviously give consumption figures for the years 1980-2000 much lower than estimates based on extrapolation of history, such as those of table 3, since small changes in compound growth rates result in successively larger divergences in the estimate over time. With a 2-percent annual growth in electricity consumption, for example, a 1980 consumption estimate of 2.2 trillion kWh grows to roughly 3.3 trillion kWh by the year 2000. To gage the difference between the results of this method and those of historical extrapolation, compare the "reference" forecast in table 3 of 6.1 tril- lion kWh for the year 2000 and the "low" estimate of 4.5 trillion kWh for that year with this 3.3 trillion kWh figure. None of this should be surprising to anyone familiar with the mechanics of compound growth. The vast range of demand forecasts which reasonable demand estimation methods can give is clear. The problem for an assessment of the LMFBR is to choose between the assumptions which underlie the extrapolation and the demand analysis methods and to judge which more appropriately describes the eco- nomic environment for the future. The two forecasting methods need not give dissimilar results. When relative production costs and prices are changing as in the past, and when the economy is expanding more or less proportionately across sectors, the two methods should give results in close agreement. That they do not concur implies that some of these conditions do not hold `and is indicative of the superiority, for present purposes, of econometric demand analysis. The 1960's pattern of rapid expansion in electricity consumption- expansion at rates higher than the real growth of GNP-follows a pattern observed in several other industries during that period, such as data processing, long-distance communications and commercial air transportation.1° All of these industries grew much more rapidly than the rest of the economy in the 1960's, and all were the locus of rapid technological change during that decade-change which significantly lowered the costs of producing and delivering existing services and which introduced a wide range of substantially new services. With the apparent exhaustion of that burst of technological change, the related declines in cost and the supernormal industry growth rates also slowed. Duane Chapman et al, "Power Generation: Conservation, Health, and Fuel Supply," draft report to the Task Force on Conservation and Fuel Supply, Technical Advisory Com- mittee on Conservation of Energy, 1973, National Power Survey, U.S. Federal Power Commission. 10 I am indebted to Lawrence Moss for this analogy. PAGENO="0019" 11 Similarly, electric power costs and prices declined both relatively and absolutely during the 1960's, as successively larger generating units exploited the substantial economies of scale then remaining in genera- tion. For a variety of reasons the era of declining electricity prices seems to be over. These include (1) the apparent end of scale economies of generation, (2) the period of intense environmental concern and the internationalization of some of the external costs of power produc- tion, `and (3) the recent rapid increases in `fossil fuel costs and in the capital costs of thermal and nuclear LWR plants. Extrapolation fore- casts of power consumption which abstract from these recent changes in the price trends are incomplete `and subject to the same kinds of errors as the extrapolation forecasts of commercial aid travel with which the airlines planned their way into the 1970's, only to be left with substantial excess capacity. In sum, the extrapolation of past electricity demand growth at a fixed growth rate is an inferior method of projecting future electricity consumption. It probably leads to an upward bias in future consump- tion estimates for the next quarter century, and in the estimates of net benefits from the LMFBIR program. Electricity demand projec~ tions rooted in a more complete demand analysis not only tend to yield scenarios with lower consumption growth rates but, if properly struc- tured, also allow additional flexibility and realism in LMFBR cost- benefit analyses.' We return to these problems in our survey of the existing LMFBR studies, and there we will draw some guidelines for an adequate projection of electricity demand. THE LWR-LMFBR CAPITAL COST Drn~sm~wm&L The rational for the LMFBR program, as noted above, rests on the exhaustibility of uranium and other fossil fuels and upon the rising market prices that uranium depletion will impose over time. Presumably the utilities will begin buying LMFBR's when their elec- tricity is economically competitive with LW1R electricity, i.e., when uranium prices have risen enough to offset the expected higher capital costs of the LMFBR. Cost analysts are in general agreement that LMFBR installations will be more costly than LWIR's. For any time path of future nuclear fuel prices there is obviously some LMFBR capital cost disadvantage at which cost-minimizing utilities will balk at purchasing LMFBR's. And the commercial future of the LMFBR therefore rides on the size that LMFBR-LWB capital cost differential. Hence, the capital cost differential assumption is a key determinant~ of the results obtained by any LMFBR program cost-benefit analysis. Unfortunately there is no consensus about the probable size of that differential. And the uncertainties surrounding this number are, harder to strip away than the uncertarnties surrounding many other economic variables, largely because a major source of uncertainty about nuclear capital costs is the lack of consensus on the social acceptability of nuclear power of any kind, and the reflection of that lack of consensus in the regulations on the expansion of nuclear power. Our experience with LWIR capital cost forecasting is directly rele- vant and instructive here. The rapid and unanticipated increases in the capital costs of LWR plants over the past decade are familiar to all energy analysts. While in 1965 estimates of $130 per kW were typical PAGENO="0020" 12 for large LWR's, capital costs for the 1,000 MWE plants now on order and expected to be on line in the early 1980's are being estimated at $700 per kW. Some plants scheduled to be on line in the mid and later 1980's are already being estimated at $900 per kW. The reasons for these cost increases are not at all clear, and there is substantial dis- agreement implicit in the explanations offered by the principal con- cerned parties. Some contributing factors are not in dispute. The kind of LWR built has cha.nged over time in step with technological improvements and with changes in licensing and other procedural requirements, so that later and earlier installations are of different kinds, and their capital costs not directly comparable. But most other elements of the LWR capital cost picture are shrouded in controversy. A recent analysis of LWR cost trends 11 has skillfully summarized the depth and breadth of that controversy by highlighting the extent to which the AEC and the utilities have developed distinctive and opposing views of the capital cost problem. The utility view emphasizes changes which have been imposed upon the industry principally in response to environmental and safety concerns-the burden of prepar- ing environmental impact statements and answering AEC information requests, the provision of additional radiation shielding to meet "as low as practicable" radiation release standards, and of safety equip- ment required by the AEC's upward revision of safety standards. The AEC's view has, on the other hand, emphasized production-related difficulties-declining construction labor productivity, late delivery of major equipment, and legal challenges to plant siting and to regulatory practice, the latter often requiring changes in regulatory procedure. The authors of this analysis, basing their conclusions on an unpub- lished analysis of LWB cost data, offer their own interpretation of LWR cost increases. First, the source of the problem can be somewhat more precisely located. The constant-dollar costs of the nuclear steam supply system itself-the "heart" of a nuclear power plant, built by one of the major reactor vendors-have not been increasing; they have, if anything, been decreasing. The component of the nuclear power plant cost under the control of the architect engineer, who oversees the design and construction of power plants built around the vendor- supplied nuclear steam system, is almost entirely responsible for the bi~ LWR capital cost increases. Those cost increases are, in turn, at- tributable primarily to plant changes and delays arising from the licensing procedure. But it is crucial to recognize that the common interpretation of those delays as either the unfortunate result of willful obstructionism or the fortunate result of dragon-slaying are misdirected. What really matters is that we have no broad consensus on the social costs and benefits of nuclear power. Nor have we any decisive consensus on the procedures appropriate to establishing those social costs and benefits: For weighting claims of distributional burdens imposed upon some by nuclear power, for arriving at some overall policy on fission power, or, for that matter, on the many smaller decisions which have arisen and will arise along the way. `~ I. C. Bnpp and J. Derian, "The Economics of Nuclear Power," Technology Review (February 1975). PAGENO="0021" 13 In this no-consensus situation the evaluation of the social costs and benefits of nuclear power is being carried out, de facto, in a variety *of forums-regulatory, judicial, and administrative-and under a variety of arrangements not always suitable for this purpose. But these are the only forums and arrangements we have. If one believes that it is improbable that a clearer and more definitive consensus on fission power will emerge, then there is little reason to believe that LWR costs are about to fall, and much reason to fear that present LWR cost trends may persist. It is against this background that projections of capital costs differ- entials between LWR's and LMFBR's should be interpreted. The LMFBR's economic competitiveness with the LWR is based upon its lower fuel costs, and those fuel costs must be sufficiently `lower to off- set what almost all analysts believe will be the higher capital cost of LMFBR's. It is estimated that, if the LMFBR-LWR capital cost dif- ferential is more than $125 per kW, LMFBR electricity will be more expensive than LWR power over the entire "reasonable" range of fu- ture nuclear fuel prices. It follows that if the uncertainties in the esti- mates of the LMFBR-LWIR capital cost differential are larger than $125 per kW, the future competitiveness of the LMFBR is uncertain, and so are both the magnitude and the sign of the benefit-cost differ- ence imputed to the LMFBR. Our experience with commercial LWR's is still very narrow and we are still unsure of their ultimate capital costs. But it can easily be ap- preciated that the situation is far worse for the LMFBR's, where we have no commercial experience to draw upon. The Clinch River Breed- er Reactor, the first in a proposed series of demonstration plants in- tended to bring the LMFBR to full commercial status, now bears a capital cost estimate of $3,000 per kW. Clinch River is a one of a kind plant and emphatically not a commercial design, so this figure must be somewhat discounted, but it is not reassuring. So much for the magnitude, character, and importance of the uncer- tainties surrounding the LMFBR-LWR capital cost differential. How well or badly are these uncertainties mirrored in analyses of the LMFBR program? Cost-benefit analyses typically assume that a high initial LMFBR-LWR capital cost differential is gradually reduced by learning: That is, that experience with the technology lowers its costs so that ultimate LMFBR-LWR capital cost differential falls into a range-usually $100 per kW or less-in which the LMFBR is eco- nomically competitive with the LWR. There is no question that some- thing like this does happen in some industries and for some production processes. In a classic example, the cost of assembling a standardized airframe was found to decrease with the number of airframes pro- duced, the explanation presumably being the accumulation of exper- ience by the assembly crews. Unfortunately, the history of LWR costs raises serious doubts about the relevance of this kind of learning effect to the LMFBR problem. Ten years after completion of the first non- turnkey reactors, we have not yet gotten this technology on a classical learning curve. The LWR case, in fact, has been a social learning process. Over time we have tried to evaluate the social costs and bene- fits of the most important new technology of the postwar period. I find little reason to believe that the way for the LMFBR has been cleared PAGENO="0022" 14 by this experience, and much reason to believe that this newer kind of learning effect, not the "airframe effect," will dominate the LMFBIR commercialization process. I do not believe that present LMFBIR pro- gram analyses capture this feature of the problem; below I argue that a program analysis can be structured to reflect some of these crucial difficulties. PAGENO="0023" COST-BENEFIT ANALYSIS OF THE LMFBR PROGRAM Our purpose in this section is an overview and assessment of the major cost-benefit analyses of the LMFBR program and, in particu- lar, an understanding of how well or poorly they come to terms with the problem of uncertainty. Beginning with a few comments on the general problems of cost-benefit analysis, we then turn to a detailed comparative evaluation of the major program studies, and finally to ways in which the program analyses can be broadened and improved. LIMITS OF COST-BENEFIT ANALYSIS The principle underlying cost-benefit analysis is simple and unex- ceptional. One should not undertake a project unless the aggregate benefits flowing from the project can be expected to exceed project costs. Where the budget of the decisionmaker is constrained, so that not all beneficial projects can be undertaken, the bundle of projects yielding the highest aggregate net benefit within the budget constraint should be chosen. This principle is relatively easy to apply when the set of alterna- tives open is small and relatively well defined, where there is little ambiguity and uncertainty on the demand side, and where technology is relatively stable. And the cost-benefit analyst's decision rule- proceed with the project if aggregate net benefits are positive-is likely to be `acceptable when the distribution of benefits and costs is relatively equitable. How many of these preconditions for the accuracy and acceptability of cost-benefit analysis are present in the LMFBR case? We shall argue below that the answer is almost none. The range of energy policy alternatives faced by the Government is very broad, and arbitrary constraints of the range of alternatives considered can bias the con- clusions ofa cost-benefit analysis. "Cost" cannot `be correctly measured without reference to the corre'ct range of alternatives. Nuclear power technology is still developing rapidly and, as we have `argued above, the cost of that technology is still very much the subject of regulatory determination. Central to the arguments against fission power of any kind is the fear of an inequitable and noncompensable transfer of costs onto future generations. Still, as we shall see `below, most of the major LM'FBR cost-benefit studies are quite conventionally conceived. THE MAJOR LMFBR STEImES Cost-benefit analysis of the LMFBR program has become a smali industry in the past few years, but many of the published analyses are upd'ates or revisions, so that it is sufficient to consider five major recent analyses. Only the latest of the three AEC analyses published during the 5-year period, 1969-74, need be considered here, since the (15) PAGENO="0024" 16 three differ mainly through updating to incorporate revised and im- proved information on costs and technology `and in efforts to be responsive to critics of the earlier versions,1 but not in method or policy conclusions. Prominent among the critics of the AEC analysis has been Thomas Cochran of the Natural Resources Defense `Council, whose book on the LMFBR program 2 is a lengthy critique of the AEC's `1972 update of the 1970 cost-benefit `analysis. Professor Alan Manne, now at Harvard University, has published several cost-benefit analyses of the LMFBR, some of them in collaboration with other authors.3 And Professor Thomas Stauffer of Harvard, H. `L. Wycoff of Commonwealth Edison Co., and R. S. Palmer of the General Elec- tric Co. have published still another.4 All of these studies are cast within the usual `cost-benefit framework. Nevertheless they generate widely divergent "base case" net benefit figures for the LMFBR. In gaging the relevance of these conclusions for policy, it is important to understand the sources of this divergence. First, all of the studies acknowledge the existence of uncertainties in uranium availability, electricity demand growth and future LMFBR- LWR capital cost differentials, but they differ on the likely range of these uncertainties, and on the likelihood of the individual values within each range. Each calculation puts forward a "base case"-or most probable case-for these uncertain conditions, and the `different studies put forward different "base cases." But even if the `authors of all of these studies were in agreement on a sing~1e base case, their net benefit results would differ for several rea- sons. First, in order to compute a net benefit figure for the LMFBR program, each study constructs a model of the electric utility industry, tracing the expansion of generating cap'acity to meet base case elec- tricity demand over some planning horizon. (Only one of the studies, Manne (1973), considers scenarios in which demand is price depend- ent; in all the others, the effects of price changes on consumption are subsumed into the growth rate of consumption chosen. Though there are difficulties of interpretation involved in direct comparisons of the Manne (1973) study with the others, the `study results are sufficiently important in their implications, for overall energy policy and for the interpretation of the other studies, to warrant inclusion here.) There is no unique way to model utility behavior, and in choosing `among alternative models there is a tradeoff between fidelity to detail and simplicity affording a clearer understanding of the workings of the model. The divergence between net benefit results arising from dif-, 1 These successive AEC studies are as follows: AEC "Liquid Metal Fast Breeder Reactor Program Plan" vols. 1-10, WASH 1101-1110 (1968) AEC, updated (1970) "Cost-Benefit Analysis of the US. Breeder Reactor Program," WASH 1184 (January 1972) ; and "AEC, Proposed Final Environmental Statement, Liquid Metal Fast Breeder Reactor Program," WASH 1535 (December 1974). 2 Thomas B. Cochran, "The Liquid Metal Fast Breeder Reactor: A'n Environmental and Economic Critique" (Baltimore: The Johns Hopkins University Press for Resources for the Future, Inc., 1974). 2 A. Manne a'nd 0. Yu, "Breeder Benefits and Uranium Ore Availability," preliminary draft (Oct. 1, 1974) and A. Manne, "Waiting for the Breeder," in M. Macrakis (Cd.) Energy (Cambridge. Mass.: MIT Press, 1973). ~ The results of this study are summarized in T. Stauffer, H. L. Wycoff, and R. S. Palmer, "The Liquid Metal Fast Breeder Reactor: Assessment of Economic Incentives," preliminary (1975). The model of the electric utility sector employed in calculating these results is described In general terms in this reference. but a detailed description of this model Is not yet available, and time did not permit me to discuss details of the model with the authors. The theoretical justification for the relatively low-base-case discount rate employed In this paper. 6 percent, is the subject of another paper, presently In circulation only In prelimi- nary draft form: T. Stauffer. "A Generalized Cost-Benefit Calculus for Selecting Alternate Energy Technologies," preliminary (Mar. 2, 1975). PAGENO="0025" 17 ferences among studies in the modeling of the electric utility sector is relatively minor, I believe, and the direction of that minor difference- the sign of the differential net benefits obtained-is predictable and consistent with the results of the different studies.5 Second, though most economists agree that intertemporal efficiency comparisons require the discounting of future costs and benefits, there is very little agreement on a particular numerical value for the discount rate. One of the studies, Stauffer et al. (1974), argues for a discount rate substantially smaller than the rates in the other studies and lower than the 0MB-recommended 6 uniform rate of discount of 10 percent. The argument for that lower rate, an argument circulated in a preliminary report by Stauffer,~ is discussed below. Third, the various studies are based upon very different assumptions about the way in which the IR. & D. costs of the LMFBR program will be incurred over time. For most of the studies, and some of the cases in all of the studies, the net benefit figure is sensitive to this assump- tion. The structure of the individual studies therefore restricts, and is intended to restrict, both the range of LMFBR program strategy options and the broader range of energy policy options which can be compared. In particular, a major LMFBR program issue, the "timing" of LMFBIR commercialization, cannot be considered at all in most of these models, and in the discussion below we will see why. Fourth, because of the way in which electricity consumption growth is specified, many of the models cannot provide a measure of the rela- tive value of supply-oriented energy programs, such as the LMFBR program, versus demand-oriented strategies, such as the peakload pricing of electricity. One of the models compared here, Manne (1973), is very different in emphasis from the others and has been included here because it can do this, or at least points the way to the compara- tive evaluation of supply-side and demand-side strategies within a consistent framework. All of the cost-benefit studies surveyed here, except for Stauffer et al. (1974), are based upon once-and-for-all optimization of electric generating capacity expansion over some time horizon extending into the next century. Since Stauffer et al. allow utilities to reformulate their plans-as they in fact can and do-during this period, it is conceivable that these additional degrees of freedom contribute to a higher net benefit estimate. But Stauffer et al. iterate until plans are always consistent with realized time paths, and therefore these degrees of freedom may not exist. It is difficult to say without detailed descriptions of the model. In any event, it seems reasonably certain that the major factor in the large net benefit figure obtained by Stauffer et al. is the low-base-case discount rate these authors argue for, and use. o Office of Management and Budget, circular No. A-94 (revised), Mar. 27, 1972, a memo- randum on "Discount rates to be used in evaluating time-distributed costs and benefits," suggests that a rate of 10 percent be used, except that, "where relevant, any other rate prescribed by or pursuant to law, Executive Order, or other relevant circulars" be employed The caveat is very likely intended in deference to legally mandated discount rates for the evaluation of water resource projects. `T. Stauffer, op. cit., in footnote 4 above. PAGENO="0026" PAGENO="0027" THE RANGE AND INTERPRETATION OF NET BENEFIT ESTIMATES Table 4 compares the five major cost-benefit analyses of the LMFBR program. Column (6) of that table shows the net benefits in the "base ease"-the case rated most probable by the authors-for four of the five studies. Those results range from a high figure of $79 billion 1974 dollars, the base-case net benefit figure computed by Stauffer et al. (1974), to a low figure of $16 billion, the base-case result obtained on a comparable basis by the most recent (1975) version of the AEC IJMFBR program analysis. The figure entered in the corresponding column for the Manne (1973) study is not strictly comparable to these figures, as noted in footnote h to the table, but is recorded there for reasons to be explained shortly. With the exception of Manne (1973), all of these studies pose the LMFBR decision problem in the same way. They identify the same Tange of alternatives, and they implicitly suggest that `choice among those alternatives be guided by aggregate net project benefits. And, further, they are similar in that the calculation of costs and benefits is based upon internal costs and benefits only. Though AEC (1974) goes to considerable length to enumerate the environmental impacts of f is- sion power with and without the LMFBR, these impacts are. never reduced to dollar terms, and they do not enter into the cost-benefit calculations. To be more precise about the similarity in specification, the cost- benefit calculations of AEC (1974), Manne and Yu (1974) and Stauf- fer et al. (1975) are a comparison of two future worlds. In the first, `the range of technologies available for generating electricity includes several present technologies but not the LMFBR; in the second, an LMFBR R. & D. program adds the LMFBR to this mix of te.chno- Thgical alternatives at some future date. Assuming that electric utilities choose new generating plants by minimizing cost, LMFBR's will be `purchased when they become commercially competitive, and the costs of generating electricity to serve any specified future. consumption pattern will be lower in every year following the commercial introduc- tion of the LMFBR than they would have been without the LMFBR. Of course each comparison of these two worlds requires a specific set of assumptions regarding the four maj or uncertainties discussed above, but the essential comparison in the three LMFBR cost-benefit analyses is between these two alternative futures. Although it is not clear that `this is done consistently in all these studies,1 it is the clear intent of all `of them. 1 For example, the AEC cost-benefit analysis appears, for the cases in which HTGR capacity is constrained, to calculate net benefits by comparing two cases. In one there is an LMFBR and the HTGR is constrained up to the year 2000, while in the other there is no LMFBR and the HTGR is constrained up to the year 2000. The correct comparison is, of course, one between two worlds differing only in that in one there is an LMFBR and in the other there is no LMFBR. This possible inconsistency was noted by EPA in their comments in the AEC Preliminary Final Environmental Statement. (19) PAGENO="0028" TABLE 4.-COMPARISON OF MAJOR-COST BENEFIT ANALYSES OF TUE LMFBR PROGRAM Base case assumptions , , * * LMFBR-LWR * Uranium resources (millions of short tons Study of U309) Electricity demand growth rate capital cost differ- ential (dollars per kWe) Discount rate (percent) LMFBR-R. & 0. program cost assumptions LMFBR program net benefits (billion 1975$) Optimum LMFBR commercialization date Modeling of electric power industry (Explicit or implicit) Criterion for decision under uncertainty (1) (2) (3) (4) (5) (6) (7) (8) (9) AEC (1974) Price Cumula- (1974$lb) tive supply 8 0 13 i 21 Z 30 3 60 4 5.2 percent a 100 when LMFBR 10 first available; decreases linearly to 0 in year 2000. * , Assumed to increase if commerciali- zation delayed; for specific pro- gram costs see table 5. 15.8 , . . 1985-Earlier LMFBR comnicr- cialization always implies higher not benefits, ~. . industry-wide linear programing model, minimizing discounted present value of cost of meeting demand; plus "introduction con- No explicit criterion; see discussion in text of this paper. ~ 60 4 * ~ straints" on Manne (1973) * 80 5 Unlimited uranium resources available at a constant cost equiv- alent mills/kWh (for LWR's) and 1 mill! KWh (for LMFBR's). 6 6 percent 1981-90; 5.3 percent, 1991-2000; 3 percent thereafter. «=50 d otherwise 10 LMFBR's not competitive.in this model. . . . ~ . No discussion of R. & D. costs. , ` 8 ~ ~ No optimum LMF/BR commercialization date in this model; competetiveness date a random variable. * . LMFBR capacity expansion. lndustrty wide se quential linear programing model, miaimiz- ing discounted present value of cost of meeting demand. * . Minimize discounted present value of expected cost of meeting demand, with expected values based upon (subjective) proba- bility estimates of year of LMFBR commercial activity. PAGENO="0029" 97 based upon assumed LWR capital costs of $385/kW and an assumed LMFBR capital cost dif- ferential of 25 percent. Imputed from the exponential curve drawn for base case electricity demand growth on p. 11.2-107 discussion, is considered below. The $4,800,000,000 figure represents cost savings from certain 1990 of AEC (1974). Though no compound orowth rate ic stated-electricity demand assumptions are given availability as opposed to uncertain availability, and is therefore not strictly comparable with the in terms of the 2020 demand of 27.~x10'2 kWh-the base case demand seems to be a compound other net benefit estimates in this column. growth curve drawn through the 1975 and 2020 demand points, fin actual calculations, Manne and Yu (1974) use step-function approximation of a quadratic ~-` This is the case on p. lV-D-1 of AEC (1974) in which the IITGR is constrained until 1998. fitted to those 2 points. "Introduction constraints" mean that the rate of change of generation mode mix is effectively g Manna and Yu (1974) actually do calculations over a range of discount rates, and do not favor any constrained, though the constraint may not be stated in terms of the rate of change variable. Both one rate as more reasonable than any other; the 10 percent case has been chosen here for com- AEC (1974) and Manne and Yu (1974) use such constraints. parability with 2 other studies that use this rate. d This is a somewhat ad hoc assumption, apparently required by the mechanics of the mode!- h Stauffor et xl. argue that a reasonable approximation to economic cost is obtained by doubling since for higher LMFBR-LWR capital cost differentials this model never "builds" any LMFBR's-and the AEC's forward cost estimates for uranium supplies. They report this doubled estimate as "eco- notindicativeofanyguessoftheauthor'sastotheprobableactualvalueofthecapitalcostdifferential nomic cost," rather than as price, presumably because user cost will push price above economic in this model "availability" and "commercial competitiveness" dates are definitionally identical; cost. the distinction between the two, which can be made operationa Ibut is not in any of the models under Maone and Yu 2 base case assump- .5 percent 50 10 do 25 in pessi- Availability and Industry-wide Minimize discounted (1974). boos: pessimistic mistic case; 2 commerciali- linear programing; present value of case (assumption 1).' in optimistic zation date discounted expected costs of Price Cumula- case. identical under present value of meeting demand (1974$ tive cost assumptions cost of meeting with expected lb) supply of this model. demand; plus values based 15 1. 7 "introduction con- upon (subjective) 30 2.3 . straints" on rate probabilities of of change in gen- various states of eration mode mix. the world. Stauffer et al. (1975). Economic Cumula- 6 percent 6 Assumed in the 76 Earlier LMFBR intro- Sequential instan- Argues that the maxi- cost b tive 5 to 10 . . duction always taneous cost- mum loss from supply billion implies higher net minimizing ca- the LMFBR pro- $10415 0. 75 1975 dollar benefits. pacity decisions by gram (essentially $15465 2. 43 range. individual utili- the program cost) ties; iterated to . much less than assure consis- the (social) cost ency (at all of bearing the times) of capac- risk of future ity decisions aiid uranium prices, scarcity. PAGENO="0030" 22 Manne (1973) poses the question quite. differently, and provides some perspective on the definition of this LMFBR/non-LMFBR dichotomy and on cost-benefit calculations based upon this dichotomy as guides to LMFBR program policy. Below we will see that this seemingly innocent change in formulating the question leads to answers differing considerably in their policy implications from the more conventional analyses. Before turning to this broader LMFBR analysis, we con- clude our overview of the more conventional analyses by examining the major source of the discrepancies in the net benefit estimates re- ported by the three studies: The different discount rates employed. TI-TE DISCOUNT RATE AND THE RANGE OF NET BENEFIT ESTIMATES The extreme estimate is the very high base-case net benefit figure obtained by Stauffer et al. This high estimate is almost elltirely a con- sequence of the choice of a relatively low, 6-percent discount rate in this model. It can be seen from column (6) of table 4 that all the other studies choose a 10-percent discount rate and obtain net base-case. benefits of the order of $10 billion. Below we shall see that a decision to proceed with the project based on benefits of this size easily could be reversed by plausible changes in LMFBR program cost assmnptions. The argument for a 6-percent rate of discount has not been circulated in final form by Stauffer. Pending the circulation of a revision of a preliminar~~ verson of their paper judgment on these results must be suspended. TOWARD A BROADER PERSPECTIVE ON THE LMFBR DECISION Rather than comparing futures with and without the LMFBR, ~ [anne compares two kinds of futures, both with LMFBR's. In one, the date at which the LMFBR becomes available and . commercially competitive is certain and is set in 1990. (The availability and com- mercial competitiveness are identical in Ma.nnes' analysis, though they need not be in general and, as we shall see, the difference can matter.) Iii the second scenario, the introduction date for the LMFBR is un- certain, and Manne takes for illustrative purposes probabilities of 0.2, 0.4. and 0.4 for LMFBR introduction in the periods 1988-92, 1993- 97. and 1998-20O2~ respectively. I-Ic then calculates the discounted pres- ent value of meeting electricity consumption in these two futures. In the case with introduction certain in 1990, the calculation is similar to that in the three other studies, while the calculation in the uncertain case is done by finding the pattern of generating capacity expansion that minimizes the discounted present value of the expected costs of meeting consumption requirements. Naturally, it is more costly to meet demand in an uncertain future. The $4.8 billion entry for the Manne study in column (7) of table 4 is the measure of the costs this uncertainty will impose upon the economy. Put another way, accord- ing to the Manne (1973) calculation, the Nation should be willing to pay up to $4.8 billion now for certain "delivery" of the LMFBR tech- nology in 1990, given the other assumptions of the study. ~ T. Statiffer, op. cit. PAGENO="0031" 23 THE LMFBR TIMING IssuE It may be instructive to compare this $4.8 billion figure with the LMFBR program cost estimates. Tables S and 6 below, identical in format but differing in contents, are from two recent government documents. Table 5 is from AEC (1974), the Proposed Final Environ- mental Statement. and table 6 is from a recent General Accounting Office report ~ to the Congress on the LMFBR program. The two estimates of total undiscounted program costs for the period 1975-2000 differ by roughly $700 million. (By the year 2000 the LMFBR pro- gram is assumed completed with no public money going to LMFBR development.) Since table 5 is in fiscal year 1975 dollars and table 6 in fiscal year 1976 dollars. one might assume that this difference is almost entirely due to inflation, but inspection of the differences in individual entries makes it clear tha.t inflation cannot be the source of all the differences. Let us suppose, based on these studies, however, that future undis- counted program costs are roughly $8 billion. How should these pro- gram costs be deducted from the reduction in discounted costs of meeting electricity requirements to arrive at a net benefit. figure? Unfortimately the answer depends upon the time pattern in which R. & D. costs are incurred, and there is no agreement upon the time patterns of R. & P. costs likely to be associated with alternative LMFBR program stra.tegies. All of the cost-benefit analyses listed in table 4 make assumptions about the time pattern of LMFBR R. & D. expenditures which favor the LMFBR net benefit figure, and in most cases the result of the net benefit calculation is sensitive to this assumption. Column (6) of table 4 summarizes the. LMFBIR program cost assumptions, and it is important to realize that one important range of possibilities is excluded from all of them. Scanning column (6), one sees that AEC (1974) assumes that the undiscountech LMFBR program costs are as shown in table 5. These costs are t.hus discounted to 1975 at the. same rate of discount applied to LMFBR program benefits, and the difference between the two discounted figures is the net LMFBR program benefit. Possibly superior H. & ID. timing strat- egies are not considered here. implicity, the assumption is that we either incur the time pattern of program costs illustrated in table 6 or we do not get an LMFBR. General Accounting Office, "The Liquid Metal Fast Breeder Reactor Program, Past, Present anti Future" (Apr. 28, 1975). PAGENO="0032" TABLE 5.-DETAIL OF LMFBR PROGRAM COST PROJECTIONS (1975 THROUGH 2020) BASED UPON 1987 LMFBR INTRODUCTION [Millions of fiscaL year 1975 dollarsj . 1975 1976 3 mo transition 1977 * 1978 1979 Subtotal, 1975-79 Subtotal, 1980-2020 Total 1975-2020 Liquid metal fast breeder-reactor: Research and Development: R.& D. 65 46 12 46 37 37 CRBR 44 44 12 64 50 33 Support facilities 43 47 13 60 63 63 Engineering and technology: Technology 52 53 15 57 60 63 Engineering 49 53 15 69 94 123 Cooperative projects: CROR 21 73 5 155 160 140 NCBR 5 18 64 Capital equipment 19 17 5 23 24 26 Construction projects: FFTF 132 74 Plant component test facility 5 9 41 110 Rad and repair eng. facility 9 18 14 Advanced fuel laboratory 9 18 Fuels and materials exam facility 23 Hot reprocessing pilot plant 2 7 28 Miscellaneous projects 15 18 3 20 28 17 Total, LMFBR Supporting technology: Safety: Research and development Equipment Construction: Safety test facility . 3 Transient reactor safety test facility 11 Advanced fuel technology 12 15 5 18 Total, supporting technology ~. 53 62 19 . 88. Total, IMFOR and support 493 492 99 Source: U.S. AEC, proposed final environmental statement, liquid metal fast breeder program (December 1974), p. 11.2-34. 243 526 769 247 67 314 289 613 902 299 588 887 403 759 1, 162 554 200 754 87 189 276 114 201 315 206 706 165 203 368 41 5 46 27 27 23 23 37 239 276 101 91 192 440 430 80 551 618 718 2,836 3,681 6,517 37 4 40 4 12 2 46 4 52 3 58 4 245 21 646 49 891 70 9 23 7 28 27 101 . 352 . . 27 453 105 143 - 470 1155 1 625 639 723 861 - 3,306 * 4;33Q, . 8, 142 PAGENO="0033" TABLE 6-DETAIL OF LMFBR PROGRAM COST PROJECTIONS (1975 THROUGH 2020) BASED UPON 1987 LMFBR INTRODUCTION LMFBR: E1.& 0.: FFTF - 65 50 13 CRBR 42 50 13 Support facilities 43 51 14 Technology 52 56 16 Engineering 49 55 15 Cooperative projects: CRBR 14 35 20 NCDR Capital equipment 19 18 .5 Total LMFBR 430 417 Support technology (LMFBR): Safety: R. & D 36 41 11 63 69 Equipment 4 3 1 5 6 Construction; Safety research experiment facility 13 29 Sodium loop safety facility up- grade 4 Advanced fuel technology 11 13 1 20 25 Total support technology (LMFBR) 51 Total LMFBR and support technology - 481 474 114 751 312 200 36 54 50 300 40 202 [In millions of fiscal year 1976 dollarsl Fiscal year- 1976 3 me transition Fiscal year- Total 1975 1977 1978 1979 1975-79 1975-87 1987-2020 1975 2020 50 40 40 258 565 265 58 46 44 253 351 65 68 69 310 776 101 62 65 60 319 833 121 75 103 134 439 1, 170 84 169 178 177 593 838 5 20 70 95 300 25 26 28 121 291 53 Construction projects: IFTF 132 80 100 Plant component test facility 13 53 65 Ilacsation and repair enpineeringfacili y 4 11 High performance fuel laboratory 9 18 18 LMFBR fuels and materials examination facility 5 18 LMFBR fuels reprocessing hot pilot plant 9 37 Sodium pump test facility 9 18 Miscellaneous projects 15 . 23 9 19 11 19 830 351 977 959 1254 838 100 344 312 131 17 45 23 46 37 99 98 650 665 312 200 36 54 50 300 40 202 818 3,078 6,323 724 7,047 Source: U.S. GAO, "The Liquid Metal Fast Breeder Reactor Program-Past, Present and Future" (Apr. 28, 1975), 57 16 . . 101 333 177 . 535 6 25 62 18 80 61 101 230 230 3 7 7 7 30 101 378 108 486 798 995 3,613 7,773 3,065 8,873 .1,453 . 371 .1,876 PAGENO="0034" 26 Manne (1973), as we have explained above, does not compute a net benefit figure in the same sense that the other studies do but rather estimates the penalty the Nation will pay if, rather than assuring LMFBR. introduction in 1990, it allows the introduction date to remain subject to the probabilistic uncertainties he assumes for illustrative purposes. Were all observers in agreement on the probability assump- tions which give the $4.8 billion penalty figure in Manne's example, one could compare that $4.8 billion figure with the additional costs required to bring the LMFBR program to certain fruition in 1990. But without an estimate of what those added costs might be, this com- parison-the relevant comparison for comparing alternative LMFBR program strategies given a commitment to some LMFBR program- cannot be made directly. Since this is not Manne's purpose lie does not make this kind of comparison; below we shall consider what such a comparison might indicate. In Manne and Yu (1974) there is no explicit treatment of LMFBR program costs and consequently no explicit treatment of corresponding alternative LMFBR timing strategies leading to commercially coin- petitive reactors in different years at different costs. But this range of alternatives can, in principle, be compared within the framework of this model. The assumption on capital cost differentials of Manne and Yu (1974) defines the date at which the LMFBR becomes commer- cially competitive and therefore defines an optimal introduction date for any given LMFBR program cost assumption. Introduction of the breeder at any later date imposes a power cost penalty which, when -weighed against the development cost reductions associated with stretched-out LMFBR development strategies, defines an optimal or least-cost LMFBR program strategy. Finally. Stauffer e.t aL define net benefits gross of IR. & P. costs; since their result.s for net benefits thus defined are so much larger than their estimates of future LMFBR R. & P. costs-they cite $5-$1O billion in costs hut specify no time pattern-the question of LMFBR develop- ment timing cannot be raised in their framework. In sumriiary. none of the LMFBR cost-benefit studies which corn- pare a world without an LMFBR to one with an LMFBR is structured so as to answer questions about the best timing strategy an LMFBR program might pursue. Cousequently~ they give the same answer to the question of the optimal timing the LMFBR.'s commercialization: as shown in column (9) of table 4. Earlier introduction dates always give higher net benefit figures. and the optimum commercialization date is the earliest feasible date. it is relatively easy to see that this result is a consequence of the assun~tion that the time pattern of LMFBR. program costs is not a ~`decision variabie~" i.e.. that there are no alternative LMFBR program strategies with diffei~ent time patterns of B. & P. costs, or that LMFBR program costs are necessarily higher the longer the introduction is delayed. it is easy to clemoustrate that, once the distinction is drawn between "availability date" (the date at which some LMFBR tech- nology is "on the shelf") and "commercialization date," (the date at which the LMFBR generates electricity more cheaply than alternative technologies), and once there is a range of B. & P. strategies with dif- 4~eieut associated time patterns of cost, it is no longer true that an PAGENO="0035" 27 earlier LMFBR introduction date always increases net benefits. To the contrary, there will be an optimum introduction date, and what has been called an "LMFBR timing" issue arises.4 The LMFBR program as presently constituted is an enormous and complex undertaking-indeed some observers believe that it is orga- nizationally too complex to operate effectively.5 One should not under- estimate the difficulty of guiding the strategy of such an enterprise using cost-benefit criteria. But if cost-benefit calculations are to be applied to the program as a whole, then it seems reasonable to ask that some alternative program timing strategies be analyzed, and none of the major studies do this. It might even be argued that such an assessment of broadly defined alternative program strategies, rather than provision of a single number or set of numbers as an evaluation of the program, is the role for which cost-benefit analysis is best suited. ~ See appendix to this study. `See the remarks on IJMFBR program structure and program performance in General Accounting Office, op. cit. PAGENO="0036" CONCLUSION: THE PURPOSES AND LIMITS OF ANALYSIS The energy R. & D. budget is limited, and energy R. & D. programs are among our major instruments for broadening our energy supply options and thus for widening the range of futures we will have to choos~ among and live within; But framing that allocation problem in waysthat are useful as guides to energy B. & D. policy is exceptionally difficult. A correct understanding of the range of alternative futures is required, and that understanding turns on identification of variables detei~thinin~ thOse futures which are either under control or can rea- sonably be brought under control. That cho'ice of variables limits the range of strategies among which we can choose and influences ranking of those strategies. Finally, we need criteria in order to choose among alternative futures; criteria applicable when we are certain that par- ticular strategies will lead to particular futures, and criteria for pro- ceeding when uncertainty obscures the linkage between present strate~ies and alternative futures. In order to slice into this circle of circumstance and choice, it is necessary to limit the full range of possibilities to a smaller range and then to introduce simple criteria for choice among these plausible futures. All of the cost-benefit studies of the LMFBR we have sur- veyed do this, and all do it in ways that are very similar. There can be no quarrel with the necessity of this reduction. But the particular range chosen and the particular criteria chosen for the guidance of choices among those alternatives, if overly narrow and/or excluding some major alternatives, can seriously constrict our view of the op- tions open to us and of the strategies available to us for broadening those options. Ti-in RANGE OF ALTERNATIVEs Here an illustrative example may be useful in sharpening the moral of the LMFBR timing issue story. A slight change in the range of alternatives considered can lead to a significant change in program evaluation. All the major LMFBR cost-benefit analyses we have sur- veyed, except for Manne (1973), compare LMFBR and non-LMFBR futures and therefore focus entirely upon energy supply-side alterna- tives. Only Manne (1973) attempts a comparative evaluation of the payoff to one major demand-side energy measure, the peakload pricing of electricity, and the numerical results are strikingly larger than the computed payoffs to LMFBR development. Manne computes many cases, but one can be taken as illustrative. Under the assumptions summarized in table 4 the cost `savings from certain 1990 availability of the LMFBR are roughly $4.8 billion, while the generating capacity cost savings from improved pricing of peak- demand period electricity-a halfway version of peakioad pricing- are roughly S38 billion. There is some danger of misinterpretation in (28) PAGENO="0037" 29 citing these two figures for comparison but not, I think, as much dan- ger as there is in leaving out this kind of comparison. The point is that the economic benefits from removing one of the major distortions in energy pricing are significantly larger than the economic costs we may incur by delaying the introduction of the LMFBR. There is overwhelming evidence suggesting that we have, in the past, and especially in the recent past, systematically underestimated the difficulties in supply-side energy strategies, whether these be solu- tions involving previously unexploited exhaustible resources oi the intioduction of new energy technologies The e~p'tnsion of L'WR capacity has been significantly slower than was foreseen 5, 10, and 20 years ago. In the light of this history the projected LMFBR pro- gram schedule seems optimistic. There are numerous technical, dead- lines to be met, the numbei of demonstiation plants that will be re- quired before full commercialization remains uncertain, and there is little that can be said with assurance ~abou't the licensability Of the ultimate `commercial LMFBR. Given the technological and institu- tional constraints and irncertainties surrounding supply-side solutions, it seems imperative that supply-side solutions be explored and evalu- `ated in a framework allowing consistent comparison with deman&side energy strategies. . ``` . " ` THE LIMITS OF ANALYSIS Finally, many of the opponents of nuclear power-in their argu- ments against a commitment to an expansion of nuclear power, both LWB's and LMFBR's, stress the problem of intertemporal equity, especially the unresolved problems of disposing of long-lived actinide. Because plutonium `and the other actinides have half-lives ranging into the hundreds of thousands of years, the possibility of an e~iOñ~ious transfer of environmental costs onto future generations cannot be entirely ruled out short of a resolution of the waste disposal problem. In this case, the earlier generations benefiting from fission clearly cannot compensate later, unluckier generations, `and the cost-benefit criterion loses both its regorous `basis and its, aura of fairness~ This is a dilemma'that'cannot be resolved by cost-benefit analysts.'Decisions that may involve significant non'transferable gains for some ~ndmajor noncompensable losses, for others are decisions that should be made in the final analysis `by legislatures and courts, `arenas in which poten- tial'losers can get a hearing. `While the future cannot representitself, we can and `do on' occasion arrange for decision rules and prôcess~s~ that make the time perspective of the decision `either shorter ` ot' lOnger. The deftnition of `appropriate institutions and procedures for nuclear decisionmaking requires'more serious and precise thought. I do not believe that this dimension of the problem has received due consideration in our public deliberations, most of which have been concerned with particular aspects of the nuclear fuel cycle. Short of tackling these broader aspects of the problem, the stalemate over nuclear power is unlikely to be broken. *` ` PAGENO="0038" APPENDIX Here is a simple example: There are two technologies (1, 2) for meeting some constant demand over some finite time horizon T. Technology 2, the "LFMBR," is initially expensive than technology 1, the "LWR." But with learning-assumed proportional to operating time-technology 2 becomes cheaper. To "buy into" technology 2 there must be a one-time payment, P, of R. & D. funds. That payment and the switchover to technology 2 define a, the "availability" date. The commer- cialization date, C, is the date at which technology 2 expenses have been "learned down" so that technology 2 is competitive with technology 1. Summarizing and setting out the model: C1(d)=total cost of meeting demand d with technology 1 C2(d, t-a) =total cost of meeting demand d, with technology 2, at (t-a) after the availability date a T=time horizon of problem P=one-time H. & D. payment at a for "availability" of technology 2 r=soeial rate of discount Then the problem of meeting demand d at minimum present value of cost is: minaZ where (1) z=fe-r~ci(d(t) )dt+Pe_rt2+fTe_rtC2(d(t), t-a)dt The corresponding first-order condition -~=0 implies (2) T ÔC (d(t) t-r) C1(d(a))-rP-C2(d(a), 0)+e?a$ dte-rt ~2 ôa' =0 If we take a simple explicit form for the time dependence of C-one consistent with the assumption that technology 2 costs are reduced over time due to learn- ing to a level below technology 1 costs, such as (3) C2(d(t), t-a) = (C2(d(t)) (l~ge_~~(t_0))) where g>0,. h>0 are constants parameterizing the effect, then the integral in. (2) can be explicitly evaluated, and an analytical solution can be obtained for the optimum availability time a*: (4) a*=T+_~~_1n (i+ft±~~\ (CiC2rp r+h \. \gh)\ C2 From this model one can see bow changes in capital cost differentials (01-C2),. learning rate assumptions (g, h), H. & D. costs (P), and the discount rate (r) affect optimal timing. The important point for our purposes is that there is a timing issue, and that there will be one in any model that specifies the range of alternative program strategies somewhat more broadly than most of the studies~ surveyed here. (30) 0