OF THE INSTITUTE MASSACHUSETTS OF TECHNOLOGY ^ mf: T-<:-!pfmmmm':£:. \ Research Program on the Management of Science and Technology THE TECHNOLOGICAL PROGRESS FUNCTIONr A NEW TECHNIQUE FOR FORECASTINGAlan R. Fusfeld ' #438-70 January 1970 MASSACHUSETTS INSTITUTE OF TECHNOLOGY 50 MEMORIAL DRIVE CAMBRIDGE, MASSACHUSETTS 02139 U{^v:i0-^^ Research Program on the Management of Science and Technology THE TECfiNOLOGlCAL PROGRESS FUNCTION? A NEW TECHNIQUE FOR FORECASTING* Alan R. Fusfeld January 1970 " #438-70 -=Based on a paper read at the annual meeting of TIMS in Atlanta, October 3, 1969. This paper is being published in Technological Forec asting Volume 1, Issue 3, Winter 1970. , The author is a special student at MIT's Sloan School of Management, E52-530, 50 Memorial Drive. Cambridge, Mass. 02139, while on leave of absence from his senior year at The Johns Hopkins University, Baltimore, Maryland. /rv I ,-1 r • yjf- ^^^^ or. ICTO 76 t. THE TECHNOLOGICAL PROGRESS FUNCTION: A NEW TECHNIQUE FOR FORECASTING 1. BASIC ASSUMPTIONS : The core of technological trend forecasting has most often been based upon against time. a plot of a technical parameter This study concerns the implications for forecasting, when these technical parameters are plotted against cumulative production. For the examples covered in this study, the relationships between technical characteristics and cumulative pro- duction all have the mathematical form: (1) Ti = a(i)^ where and value of parameter at the i^h unit, Tj^ = i = cumulative production, a,b = constants. This dependence of a technical value upon production is defined here as the technological progress function . This paper relates the development of that function, the implications of the math- 4. ematical form just mentioned for trend forecasting, and information compiled from variety of case studies.* a It is of interest to note that the form of the technological progress function is similar to that of the common industrial "learning curve", as well as the learning curves of psychologists, The industrial "learning curve" relates cost to production (1, 2, 3) . Yi - where Yid)"^ unit y- = cost of the i i - cumulative production y-^ b = cost of 1 constant = st (2) unit . and the psychological learning curve relates the efficiency of performing a task to the number of repetitions Ejj where = k(N) b E„ = efficiency of performing N N (4, 5, 6, 7) (3) th task = cumulative task number k,b = constants * Studies completed included: civil aircraft-speed automobiles- horsepower military aircraft- speed electric lamps- lumens turbojet engines- specific weight computer programs- figure turbojet engines- specific fuel consumption of merit hovercraft- figure of merit 5. They are similar to the technological progress function, T^ = a(i) , because all three show the measure of some characteristic, for which improvement is desired, as an exponential function of the cumulative number of repetitions or production. The environment in which technology develops is clearly of additional interest and appears to affect the rate of learning through discrete changes in the learning constant, b. It must be specified here, that environment refers to the external economic factors which surround the production process. An example of this effect was the change in the government investment and market potential relating to the which automotive industry in the late twenties (8, multiplied the rate of progress, b, by factor of 6.2. a 9) , 2. INTRODUCTION AND BACKGROUND INFORMATION : The development of the technological progress function, T^, from characteristic of technological improvement, evolved a consideration of: (1) problems and background factors inherent in industrial progress relationships, (2) indications from psychology that general phenomena of "learning" were present, and 2.1 (3) difficulties in existing techniques of forecasting. PROGRESS FUNCTIONS Briefly, : industrial progress relationships are functions, such as production costs/unit, maintenance costs/unit, and manufacturing costs/unit, which can be written as of costs associated with unit number one, number, and a learning constant. functions because efficiency. a a function the cumulative unit They are termed progress reduction in costs indicates a gain in These functions, as previously mentioned, have been found to have the precise form yi - (1, 10, 2, a(i)-b 11): (1) When plotted on log-log paper, this gives a straight line, whose slope, -b, is the rate of progress, that is, the rate at which efficiency is improving. It should be noted here that, as previously mentioned, the technological progress function has the same form and expression, the difference being a positive rather than a negative slope. Various studies of industrial progress functions have shown that there are a number of causes or factors which are common to most of the different types (1, 2, 11, 12, 13). The more direct factors are: 1. engineering or desing improvements; 2. servicing technician progress; 3. job familiarization by workmen; 4. job familiarization by shop personnel and engineering liason; and 5. development of a more efficient parts upply system; 6. development of a more efficient method of manufacture. The innate factors are: 1. the inherent susceptibility of an operation to improve- ment and 2. ; the degree to which this can be exploited. These functions can be called "micro-economic progress functions" and (MEPF) because: 1. they are similar in mathematical form, 2. each relates to decisions of the "firm". However, their applicability to development decisions is not 8. as simple as it would seem initially since the functions contain two areas of problems. Both areas are relevant to the subject of the technological progress function be- cause the first helped to prompt its development and the second helps to explain its behavior. The first area involves certain MEPF characteristics which present problems of decision that have been unsolvable because of their link with technological innovation. The problems begin when one attempts to determine the component costs of the first unit of production and finds that one must arbitrarily set a limit upon the background development A mechanism by which background and development expenses. costs would be linked to all of the generations of a product might help to alleviate this difficulty of first unit costs; of course, this would first require a model for technological change. Further and more fundamental complications become apparent when the development of new generations of equipment is considered, as opposed to the difficulties of measuring cost for any one generation. Technical changes and design modifica- tions are part of the inherent forces that cause the MEPF to behave as it does, but there are no provisions for setting a limit on these changes; the engineering change procedure of firms being arbitrary in nature. That is to say that, after a certain number of modifications in production procedure or design, the product in reality will be a "new" product and will be so labeled by sales and management. This is often the case with developments resulting from both conscious and unconscious defensive research, which is designed to improve a product's competibility The locating of an "old-new" product line or determining where a major change begins are questions posed by users of the MEPF and seem to beg a progress function which cuts The technological pro- across individual generation lines. gress function is such a relationship and contains the same factors of engineering learning and motivation of the MEPF, which not only cause problems in its use but also provide a major stimulus for technological advancement. The other problem area relates to deviations from normal (line a-rity on log-log paper) MEPF behavior. of these differences are important, The explanations since they help to clarify the effects of external factors of the environment on tech- nological progress. Some of these deviations are due to changes in the psychological motivation of the personnel involved, as would be the case where a product line is sud- denly scheduled for discontinuance or where the success of new development is announced to the employees (1, 2, 14). a 10, others would be due to changes in design or the introduction of new people to the job. Finally, if the product or system is being constructed on parallel assembly lines the addition or subtraction of new lines, perhaps or shifts, with changes in demand, will cause anomalies in the MEPF (14). All of these deviations cause a change in the slope of the progress function. Thus, it is implied that changes in the rate of progress (i.e., the slope of the progress function) are not random but are a function of critical parameters forming part of the external environ- ment. 2.2 PSYCHOLOGY : In addition to the information supplied by analysis of progress functions, further insight has been gained from psychological learning theory. Since there is considerable dispute over exact definitions of what learning is or is not, let me point out that, here, psychological learning refers to perceptible gains in performing given tasks. These tasks in academic studies have ranged from solving puzzles and going through mazes to simple studies of response time for given stimuli. It has been noted in a variety of projects concerning both animals and people, that the efficiency of performing a 11. given tasks increases with the cumulative number of repetitions (4, 7, 5, 14, It should also be pointed out 16). 15, that none of the studies differentiate between the fre- quency of the repetitions as long as the frequency was within The studies found that, the maximum retention interval. Ejj where Such a efficiency in performing the N^^ task, Ejj = N - the cumulative task number, K, a = and (2) = K(N)^ constants. relation was particularly apparent in with children by Melcher by Bush and Hosteller (4) (7) . a 1934 study and in a 1955 study with dogs A similar but different relation- ship regarding repetitious activity can be derived from work presented by Frank Logan in his book. Incentive (16). noticed of his subjects, that they, "...behave in such Logan a way as to maximize reward while at the same time minimizing effort." Such behavior is not only identical with the aims of man's economic endeavors, but is also progress a . a causal factor of technological Since the progress functions discussed previously show similar dependency on repetition of tasks, it would appear that the same type of learning discussed above is involved. 2. 3 FORECASTING : The third area that has contributed to the present develop- ment of the technological progress function is technological 12, forecasting. as Delphi, The primary methods already available, trend extrapolation, such trend correlation, and growth analogy, do not allow for the easy or precise handling of environmental factors incentive to find a (17), This provided further progress function that would be a6 petent as other techniques under constant forces and yet allow for environmental change. com- 13. 3. TECHNIQUES USED IN ANALYSIS; The work involved in investigating logical progress function lines of reasoning. note and defining the techno- was completed through two separate Both paths were developed while taking of: (1) an observation, through analysis of the the independent MEPF, that variable should be the cumulative production number; (2) an implication in learning theory that the form of the function should be similar to that of the MEPF and the general structure characteristic of improvement functions; and (3) a need of forecasting techniques for a term through which environmental change could be introduced. The paths chosen for development are common endeavors. They were those to most of theoretical derivation scientific from known relationships and empirical model building from real world data. 14. The theoretical side bases itself on the eauivalence, for at least certain areas, of the rate of patent output with technological /growth or prc^-ress. Through relationships derived or shown by Schmookler (l8) and Villers (19), the rate of patent output was related to investment and expected profit functions. Prom this point, substitutions were made from investment/profit functions, denoting technical advance. The result was a rela.tionship that equated the level of technological improvement to a constant multiplied by an increasing Quantity dependent function raised to a positive exponent , i.e., T. where T. = the level of = K( f(i) )^ technology at the (3) i th unit of production, f(i) « a function which varies with the number, i, and K,c = constants. production 15. Although it seemed to substantiate earlier hypotheses, it could only be taken as a further indication that this might be the correct approach, since it was not precise enough in nature to stand by itself. The results of the theoretical derivation cleared away doubts from the proposed directions of the empirical phase of the study. At this stage, it was clear that the work should attempt to correlate technological improvement with the cumulative quantity of production. In addition, thoughts of incorporating the results with other progress functions motivated the gathering of data designed for more extensive correlations. Real data were then sought to provide information on technical parameters, production, and costs with background infor- mation to be provided where possible. One could then observe the behavior of technological parameters with respect to pro- duction under the sets of conditions forming the background environment. However, before describing the case studies and conclusions some of the difficulties involved in this work should be pointed out. The most difficult problem was that of obtaining accurate data, particularly with regard to cost information. This was 16. solved by combining data from several sources and v/here possible having the material validated by someone fa .iliar with the field. Other nroblems arose concerning the choice of technical parameters. In this care decisions were made from background information and observation of changes in the parameter with resoect to cost changes. 4. F.IJSENTATION OF DATA; The empirical studies discussed here verified both the preliminary hyootheses and the theoretical derivation and were based upon ana.lyses of data regarding the aircraft industry, the electric lamp industry, and computer pror^rammmin" 4.1 AIRCRAFT DATA . : The data from the aircraft industry concerned turbo-jet engine development over a period of nearly twenty years and was synthesized from two Air Force Institute masters theses (20,21), sup'oorting information supplied by the Pratt & Whitnoy Division of United Aircraft (22), and Aviation I'acts and Figures 1958 (23). From these sources, production cost/ unit, production by year, ciAmulative production, and trie tech- nological parameters were observed. The results have shown, in Figure 1, that technological progress, as represented by s-ecific weignt ( dry engine weiglit/ Figure TURBO-JET ENGINE CHARACTERISTICS o f OO o OT O CM ci CM CM oj o o o o o <j- • i 1— r-~ .-I c-J • • • • in <0 00 Q in o o o o I r—l E^ 1-) I m CO CO U-t [-< t^ y-i C7> H H ^ [M - <J- 09 4J to CO •r-1 3 o <u Xs. o •H IH •f-i l-l u (U a. CO •r-l —o _ c; cr> 1 17. pounds of thrust) and specific fuel consumption (pounds of fuel/hr ./pound of thrust) is log- linear to a logarithmic quantity axis, where quantity indicates the cumulative pro- duction of engines within the turbo-jet family. It also appears that an arithmetic time axis may be used in place of a logarithmic quantity axis on many occasions for the same accuracy, whenever production undergoes constant percentage increases with respect to time*, 4.2 ELECTRIC LAMP DATA ; The Electric lamp industry data was obtained by combing information from James Bright ment , (24) Industry , ' and Arthur A. Bright (25) book Automation and Manage - s ' s book. The Electric Lamp for 60 watt lamps. These sources enabled the study to be concerned with technological progress as re- presented by the output of the lamp in lumens, production by year, and cumulative production. The many development changes made it unnecessary to examine each individual generation of lamp. The results confirm the existence of a technological progress function behaving in accordance with the generalized MEPF principles. * Figure 2, where this is illustrated, actually The bracketed points at the end of the "specific weight" curve were obtained from current advertising information of Pratt & Whitney presented in Aviation Week during March, 1969. pif^ure 2 ELECTRIC LMP LUMEN OUTPUT O O o o U5 d o •r-l •r-l H o 01 U •r-l C P D o > kJ •H o ta r-l 3 o O o o w (0 6 k4 18. indicates the existence of two rates of progress. One ex- tends from 1912 until 1920 and the second from 1920 until 1940. This would imply that the external environment affecting the lamp industry underwent a production which had been increasing at shift. a Since the steady 9.39% per year throughout the first period concurrently suddenly shifted downward to a rate of 2.74% growth at the same transition point (Figure 3), it may be concluded that one or more changes in the environment increased the value of the exponent "b" in the technological progress equation, while at the same time decreasing the rate of growth of production. fUe It IS interesting to note comparison between the progress function for lamps as shown in Figure forecasting method shown in Figure 4. a 2 with the more usual This data substantiates possible claim that forecasting results with an arithmetic time axis are as good as they have been because of the substi- tution effect. That is, an arithmetic time axis may be sub- stituted for a logarithmic quantity axis, when production quantities increase in reasonably constant percentages with time, 4.3 as in Figure 3. COMPUTER PROGRAMMING DA TA: An additional example has been drawn from a specific experience in programming. Data for this example was made pi^re ELECTRIC LAMP PRODUCTION VS 3 TllIB O n C^ H O CO > O M H O Q O in CM :=> Pi 1^ o as T H —TT— I \ 1 Figure ELECTRIC LA]\1P LUMEN OUTPUT TREND FORECASTING u o M o f3 o M 01 4 19. available through the help of John Cleckner, a student at The Johns Hopkins University. The example represents the rate of progress in the development of a single computer program developed solely by him under special arrangement with an area firm. A figure of merit was determined which would best represent his ow aims while developing the program. This figure of merit equals the lines of output divided by the running time. The computer pro= gram dealt with an estimation of bakery goods to be sold according to the day of the week, store, and particular item. In an analogy to the development of products, it was decided to regard the last best figure of merit (Figure 5) particular run as the figure of merit to be processed. T|iis for a may or may not be the true figure of merit for that run, but it would be an accurate representation of the figure of merit of the best program available at any given point in its total development. The results illustrate several areas of interest. The first is the applicability of the technological progress function to the area of programming. There is also the observance of different slopes corresponding to different development phases. Finally, since the work was done by one person, the analysis indicates the possible role of psychological "learning" theory in techno- logical progress. ADDITIONAL EXAMPLES: Other cases studied demonstrated similar technological Figure A COMPUTER PROGRAM DEVELOPMENT L. >. H O w > o a o ex! H o o 5 20, progress functions, that is, linearity on log-log paper when the technical progress parameter is plotted against production. Those cases not discussed here are civil aircraft- speed, military aircraft-speed, automobile -horsepower hovercraft-figure of merit, and an office machine developmentfigure of merit. One could get the impression, from the data just discussed, that the trends observed were basically limited to items of hardware, but this was not found to be the case, as evidenced by studies of the totally different area of agricultural efficiency. From information pertaining to the pounds of rice produced per acre in Japan over a period of twelve hundred years, three log linear trends were noticeable (26,27). The two major lines were a "long term" or ancient trend line and a modern trend line of much steeper slope. By calculating backwards, it was found that they intersected at a period of great external change-- the "opening of Japan". The third line was a moderate decrease in slope, which prevailed during the period of World War II. 21, THE TECHNOLOGICAL PROGRESS FUNCTION : if we assume that Initial studies are correct Thus, , technological progress functions exist and are of the same general nature as other micro-economic progress functions It is then further implied, denoted by a . that technological progress, as positively increasing function is logarithmically linear with respect to a logarithmic quantity axis under con- stant external forces. Over periods of time during which external forces vary, the slope of the line, that is, the rate of progress, may undergo discrete shifts. Such a function is denoted as, T. = 1 where and a(i)^, (4) T^ = the value of the technological parameter, i = the cumulative production number, a = a constant associated with unit number one, b = the rate of progress, a variable, of the external environment. which is a function 22 5.1 MATHEMATICS : A brief glance at the mathematics shows that where b is a constant: log = b log (Tj_) (i) + log and regarding the differential of dT-L (5) (5) b di = T^ Equation (a) i (6) (6) indicates that, b, being constant, the percent- age change in a technical parameter is a linear function of the percentage change in cumulative production. it should be noted that: In addition, if i log and = (constant) = Kt + log (i) = di Kdt e (7) , (constant) (8) (9) . i Equation a (9) represents a percentage change in production as linear function of time, that is, what has been referred to as a "substitution effect". Where = di Kdt, i d T^ = bKdt, which is the traditional trend forecasting relationship 5.2 RATE OF PROGRESS (10) (28) ; From analysis of background information involved in the work discussed above and current studies, the rate of pro- grass, b, has been designated as a function of: L/ the effective sii:e of the technical labor force; o(, an intelligence factor-average educational level; n, a , pre-learning factor-average experience level; I, the level of investraent; I, the rate of change of the level of investment; d, a r.\aturation na, the anticipated raue of change of raarket derriand-slope factor-durability of item-corripatability; of sales curve; and c, tha corrjTiunica'cion or diffusion rate. Currently, work is being done to define the exact nature of the function just described within the inherent constraints that b is greater than, or equal to, that if L,c^, 6, 6. SUMMARY I, 7ero and never infinity and or m go to ^ero, then b also goes to ?ero : This study has been concerned with the technological pro- gress function. The study proposes that the technological pro- gress function may be based on the cumulative production unit number on a logarithmic scale, as opposed to the arithmetic time series base used for most forecasts. In this form, the techno—- logical progress function allows for environmental changes to act upon the rate of progress in a precise manner, that is, dis- crete changes in the slope of the function. be noted, However, it should that no less care must be taken when employing this 24, technique in addition to or instead of existing methods, particularly with regard to physical constraints imposed upon the system. 7. FUTURE WORK - The technological progress function is a tool to be used with other techniques by the foresighted corporate and military development planner, who can no longer overlook the effect of technological change upon his proposals for future development. Although, it is doubtful that a true "Newton's Law" for pre- dicting technological advancement will ever be made, it is believed that the development of the technological progress function is a step towards more effective predictive methods. Considerable work remains to be done in exploring the nature and anomalies of the technological progress function itself. There is, of course, the need for a precise definition of the rate of progress function. In addition, there are avenues of research concerning macro-economic implications and ways in which the function might be of maximum value to technologically oriented firms. 25. REFERENCES (1) H. Asher, Cost-Quantity Relationships in the Airframe Industry (2) . Project Rand-291, July, 1956. W, B. Hirschmann, "Profit Prom the Learning Curve", Harvard Business Review (3) J. L. , Jan-Feb, 1964. Kottler, "The Learning Curve- A Case History In Its Application", The Journal of Industrial Engineers , AIIE, July-Aug, 1964. (4) R. R. Bush, F. Llosteller, Stochastic Models of Learning , John V/iley and Sons, Inc., New York, 1955. (5) J. Deese, Psychology of Learning , McGraw-Hill, New York, New York, 1967. (6) C. I. Hovland, I. L. Javis, H. H. Kelley, Communication and Persuasion , Yale University Press, New Haven, Conn., 1953. (7) H. T. Melcher, Children's Motor Learning Vision , Vv'ith and V/ithout The Johns Hopkins University Ph.D. Dissertations, 1934, p. 333. (8) W. Owen, Automotive Transportation , The Brookings Institutim, Washington, D.C., 1949. (9) F. Stuart, ed.. Factors Affecting Determination of Market Shares in the American Auromobile Industry University Yearbook of Business, Series New York, October, 1965. 2, , Hofstra vol. 3, 26. (10) J. Abramowitz, G. A. Shattuck, Jr., "The Learning Curve", G. IBM Report No. 31.101, 1966. (11) J. Kneip, "The Maintenance Progress Function", The G. Journal of Industrial Engineers (12) R. A. Conway, A. Schultz, , AIIE, Nov-Dec, 1965. "The Manufacturing Progress Function", The Journal of Industrial Engineers (13) M. , AIIE, Jan-5'eb, 1959* Salveson, "Long Range Planning in Technical Industries", E. The Journal of Industrial Engineers , AIIE, Sept-Oct, 1959. (14) J. H. Russell, "Predicting Progress Function Deviations", IBM Teclinical Report TR 22.446, August 28, 1967. (15) C. L. Hull, C. I. Hovland, R.T. Ross, M. Hall, D. T. Perkir^ B. Fitch, F. ing (16) F. A. , Mathematico-Deductive Theory of Rote Learn- Yale University Press, New Haven, Conn., 1940. Logan, Incentive , Yale University Press, New Haven, Conn., I960. (17) M. J. Cetron, "Forecasting Technology", Science and Technology Sept, 1967. (18) J. Schmookler, Invention and Economic Growth , Harvard University Press, Cambridge, Mass., 1966. (19) R. Villers, Research and Development; Planning and Control , Rautenstrauch and Villers, New York, New York, 1964. (20) R. E. Burckhardt, Major USAF, ''Cost Estimating Relationships for Turbo-jet Engines", masters thesis, GSM/SM/65-3, December, IS 65. , 27. (21) R. P. Gould, Major USAP, "Turbo-jet Engine Procurement Cost Estimating Relationships" , masters thesis, GSM/SM/65-10, August, IS 65. letter to author, November (2?) N. Turkowitz, (23) Aviation Facts and Figures- 19^8 > 5, 1968. American Aviation Publicatit-n 1958. (24) J. R. Bright, Automation and Management , Harvard University, Boston, Mass., 1958. (25) A. Bright, The Electric Lamp Industry , McGraw-Hill, Nev/ York, 1949. (26) H. Kahn, A. J. Wiener, The Year 2000 , The MacMillan Co., New York, 1967. (27) W. W. Lockwood, The Economic Development of Japan , Princeton University Press, Princeton, New Jersey, 1954. (28) R. C. Lenz, Jr., "Technological Forecasting, Air Force Systems Command, Wright Patterson Air Force Base, Ohio, AD 408 085, ASD*TDR^62-414, June, 1962. 28. BIBLIOGRAPHY BOOKS Almon, C. Jr., The American Economy to 1973 > Harper and Row, New York, 1966. Automation and Technological Change , The American Assembly at Columbia University, Prentice-Hall, Enrlewood Cliffs, New Jersey, 1962. Ayres, K., Technological Forecasting and Long Range Planninf- , McGraw-Hill, New York, 1969. Bright, J. R., Research, Development and Technological Innovation , Richard D. Irwin, Homewood, 111., 1964. Bright, J. R., (ed.) Technological Forecasting for Industry and Government Prentice-Hall Inc., Englewood Cliffs, New , Jersey, 1968, Brown, M. On the Theory and Measurement of Technological Change , Cambridge University Press, Cambridge, England, 1966. Cetron, W. J., Technological Forecasting - A Practical Approach , Gordon and Breach, New York, 1969. Hitch, C. J., Roland N. Mokean, The Economics of Defense in the Nuclear Age , Harvard University Press, Cambrid;':e, Mass., 1967 Human Relations in Industrial Research Management, (ed) .^obert Teviot Livingston, Stanley H. Milberg, Columbia University Press, New York, 1957. 29. Ma.nsfield, E., The Economics of Technological Change , W. W. I Norton and Co., New York, 1968. Mansfield, E., Industrial Research and Technological Innovation W. Quinn, J. B. W. , Norton and Co., New York, 1568. Yardsticks for Industrial Research , The Ronald Presc Co., New York, 1959. Schon, D. A., Technology and Change Delacorte Press, New York, , 1967. Servan-Schreiber, J. -J., The American Challenge , Athenum, New York, 1968. Technological Innovation and Society , ed. Dean Morse, Aaron Warner, Columbia University Press, New York, 1966. \V. , 30. ARTICLES Bright, J. R., "Can We Forecast Technology?", Industrial Research Cetron, M. J. , March 5, 1968. ,R.J. Happel, W.C. Hodgson, W.A. McKenney, T.I. Monahan, "A Proposal for a Navy Technological Forecast", Naval Material Command, Washington, D.C. Part I- Summary Report AD 65919 9 Part II- Back Up .{eport Cetron, M. J., A. L. V/eiser, AD 659 200 May 1, 1966. "Technological Change, Technological Forecasting, and Planning R&D, R&D A View Prom the Manager's Desk", The George Washington University Law Review , Vol. 36, No. 5, July, 1968. Darracott, H.T., M.J. Cetron et al, "Report on Technological Forecasting", Joint Army Material Comrn and/Naval Material Command/ Air Force Systems Command, Washington, D.C, AD 664 165, June 30, 1967. Duranton, R. A., "Quelques Remaroues Sur Les Courbes D Accoutumance" ' Internal IBM Report, May 13, 1965. Mahanti, B., "Progress Report/Manufacturing Progress Function Report", Internal IBM paper (German Office), April "The Growth Force That Can't Be Cverlooked", Business Week McGraw-Hill, New York, August 6, I960. , 9, 1964. 31^ "The Dynamics of Automobile Demand", General Motors Corp., New York, 1939. Technology and World Trade Pub. 284, (symposium — , US Department of Commerce, NBS Misc. 11/16, 17/66) ACKNOWLEDGEMENTS The author offers special thanks to John Cleckner, Class of 1970, The Johns Hopkins University, for his suggestions and help in preparing the data on computer programming. The author is also indebted to Lisa Geiser, Class of 1972, Goucher College and Nancy Smith, Class of 1972, Goucher College for their help in developing additional data. In addition, Norman Turkowitz of Pratt and Whitney must be noted for supplying the supporting information for the aircraft engine study, for which the author is also very grateful. .!!JL a .r^ VN ^» tt1A ^ ft5 ai-T* ui<^' I mm BASfj^ Date Due 5 '7^ DEC OCT 1 2 198!^ FEB 23 78] SEP 24 7, 1^ P^ .* AUG 2 "* \ -irt L)b-26-67 MIT LlBHAHltS nil III II mil ill ill nil DD3 TOb ^DflD 3 bfil MIT LIBRAfilfS HD28 D03 TDb 7DS TDflD 3 it MIT LlBRAHir^ ^3^ '(,f DOB TQb 751 TDflD 3 MIT LIBRARIES 4-;'5-M DD3 TQb 73^ TDflD 3 MIT LIBRARIES '^^'^^^'^ III 111 III II TDfiD D D3 fi75 "^bT MIT LIBRARIES 43?--'''? 3 Toao D 03 675 Tia MIT LIBRARIES mh-70 TOfiO 003 fi7S 7' M%-7(? TOfiO 003 fi75 657 ^3f' 70 T060 03 675 635 MIT LIBRARIES Lft^o- T060 003 TOb 7b5 70