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How Foundations Came to Be Author(s): Paul A. Samuelson Source: Journal of Economic Literature, Vol. 36, No. 3 (Sep., 1998), pp. 1375-1386 Published by: American Economic Association Stable URL: http://www.jstor.org/stable/2564803 Accessed: 23-07-2017 08:24 UTC

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This content downloaded from 193.54.110.56 on Sun, 23 Jul 2017 08:24:16 UTC All use subject to http://about.jstor.org/terms Journal of Economic Literature Vol. XXXVI (September 1998), pp. 1375-1386

How Foundations Came To Be

PAUL A. SAMUELSON'

1. Introduction duller academic scholars have above- average I.Q.'s. IF THERE ARE PEOPLE born under a By accident, the public schools I at- lucky star, there must be books that tended-in Gary, Indiana and Chi- are lucky too. Foundations of Economic cago-were unusually good ones that Analysis (Samuelson 1947) was one such. turned out many future scholars and Unlike a biological embryo, this work scientists. By chance of geography, I had no definite moment of conception. went to the University of at a Gradually, over the period 1936 to 1941, young age, and under its experimental it got itself evolved. As I was mastering New Hutchins Plan I got a deep and the existent corpus of economic theory, I wide undergraduate education. By recognized that a limited number of chance, my freshman courses included qualitative truths obtained, along with a economics under Aaron Director greater number of indefinite relation- (1901-), who was later to be founder of ships. Puzzled to understand this, I ran- the Second Chicago School of Milton sacked the mathematical libraries of Chi- Friedman, and Gary cago and Harvard to explain to myself Becker. In that academic year of 1931- what made the difference. Reading 32, although I didn't know it at the widely, I was a child of my time, but it time, Chicago was the leading world was the internal logic of the economic center for neoclassical economnics: next puzzles that guided Foundations' growth. in the hierarchy would probably have When you read biographies and come the School of Economics, obituaries of scholars, they fall into a Cambridge University, and Columbia few familiar patterns. The most inter- University. Harvard, then as now, was esting-like Albert Einstein's or Knut the greatest university in the world; but Wicksell's-are cases of early adversity with the 1929 death of Allyn Young and and then final irresistible triumphs. My the aging of Frank Taussig, its theory autobiography is of the duller kind. I was then in a lean period. began as a precocious infant, with un- The stars at Chicago's First School in usually early conscious memories. Par- economics were , Jacob ents and two brothers were congenially Viner, , and supportive. Though it was fashionable Henry Simons. As an undergraduate I to hate school, I loved it. Early bloom- came to know them all well. A legend ers develop ridiculous heights of self- grew about an unself-conscious teen- confidence, not realizing that even the ager who used to correct the omnis- 1 Massachusetts Institute of Technology. cient on the topography of 1375

This content downloaded from 193.54.110.56 on Sun, 23 Jul 2017 08:24:16 UTC All use subject to http://about.jstor.org/terms 1376 Journal of Economic Literature, Vol. XXXVI (September 1998) his graduate seminar blackboard dia- 1964) was at Harvard. Wilson was the grams. great Willard Gibbs's last (and, essen- Given my way, I would have stayed at tially, only) protege at Yale. He was a Chicago forever. Why leave Nirvana? mathematician, a mathematical physi- However, by chance, that happened to cist, a mathematical , a be the year when the Social Science Re- mathematical , a polymath search Council began an educational ex- who had done first-class work in many periment: they would scour America for fields of the natural and social sciences. the eight best economics undergradu- I was perhaps his only disciple: in 1935- ates and generously underwrite their 36, , Sidney Alexander, several years of graduate study. (Later I , and I were the only learned from the late - students in his Fetter the younger-that he had been seminar. (Our ages were 21, 19, 52, and the examiner who discovered me: suc- 20.) Aside from the fact that E.B. knew cess, President Kennedy observed, has a everything and everybody, his great vir- thousand fathers; failure is an orphan.) tue was his contempt for social scien- There was just one catch to the awards: tists who aped the more exact sciences you could not stay where you had in a parrot-like way. He detested done your undergraduate study. So pseudo-learning and debunked many a my choice reduced effectively to Co- pretentious theory (such as the Pearl- lumbia or Harvard. My Chicago men- Verhulst infatuation with the logistic tors recommended the Columbia of curve in demography). I was vaccinated Wesley Mitchell, early to understand that economics and and . Never one to fol- physics could share the same formal low slavishly the advice of mentors, I mathematical theorems (Euler's theo- opted for Harvard. (Joseph Schumpeter rem on homogeneous functions, Weier- and were not my mag- strass's theorems on constrained max- nets: at Chicago Schumpeter was known ima, Jacobi determinant identities as the eccentric who believed the rate underlying LeChatelier reactions, etc.), of would be zero in the station- while still not resting on the same em- ary state. Edward H. Chamberlin of pirical foundations and certainties. monopolistic fame, by my Publications flowed merrily from my miscalculation, attracted me to Har- pen. It was my good luck to be ap- vard; but more important was my naive pointed as the first proper economist to notion that Cambridge, Massachusetts Harvard's prestigious Society of Fel- would be a peaceful green village where lows-24 youthful princes in all fields, book learning could explode.) free to work on whatever they liked, but As mentioned, again by good chance, forbidden for three years to work to- Harvard economics was just then awak- ward any degree or Ph.D. dissertation. ening from a fallow period of sleepi- For me, those 1937-40 years were veri- ness. New European blood-Schumpe- table heaven, and had I been offered ter, Leontief, -plus the Faustian bargain of staying a Junior soon-to-come , the Fellow forever, I would have joyfully "American Keynes," was beginning to embraced it. make Harvard the mecca for advanced This explains how citations of my economic research. Perhaps most rele- journal articles had won me in my early vant of all for the genesis of Founda- twenties an international reputation as a tions, (1879- comer. Their topics were diverse: capi-

This content downloaded from 193.54.110.56 on Sun, 23 Jul 2017 08:24:16 UTC All use subject to http://about.jstor.org/terms Samuelson: How Foundations Came to Be 1377 tal theory, lifecycle , the- A learned treatise, like a poem, ory, international , Keynesian mul- stands on its own bottom or text. Ad tiplier-accelerator dynamics, revealed horninem gabble about its author is at , and much else. Miracu- best secondary. The times were ripe for lously, it dawned on me that there was Foundations. Nature abhors a vacuum, some unity of method and logic under- and Foundations helped fill the vac- lying much of these researches as well uum. I have written elsewhere about as much of current and historical eco- how much there was back in the 1930s nomnic theory. waiting to be discovered, and aching to In mid-1940 my Society of Fellows be codified. I was like a fisher for trout prohibition against writing a Ph.D. dis- in a virginal Canadian brook. You had sertation expired. Harvard's original Se- only to cast your line and the fish nior Fellows-President A. Lawrence jumped to meet your hook. Lowell, Alfred North Whitehead, John Let me give a few examples. Jacob Livingston Lowes, and Lawrence J. Viner (1931) made a famous error, Henderson-had launched the Society when his draftsman Y.K. Wong refused as a vendetta to reform the mediocre to draw a family of descending U- American Ph.D. system. My colleagues shaped cost curves with a lower en- as Junior Fellows-Willard van Quine, velope that went through their bot- the mathematical logician; George Birk- toms. Viner was ever after sensitive, but hoff, the founder of lattice theory he conceded his error. That same Viner ; Harry Levin, the youthful (1929), in a discussion of his hero doyen of comparative literature-each , had discovered that deigned not to become Doctors of Phi- the domestic ratio of cloth to losophy. Their Harvard careers never wheat, Pc/Pw, was as much equal to suffered from this. My Protestant wife, their respective ( in Marion Crawford, and I decided to fol- Land)c/(Marginal Cost in Land)w as it low the prudent course of taking a was to (Marginal Cost in Labor)c/(Mar- Ph.D. degree. Lucky that we did, or ginal Cost in Labor)w. Viner sensed perhaps Foundations might have been that this in the deepest sense invali- pushed off my agenda by the outflow of dated the hoary Labor Theory of , new publishable ideas. a truth not understood by David Ri- From mid-1940 to January 1941, I cardo, , or George Stigler. composed and rearranged at fever pace; But Viner never connected this insight some got dictated to Marion, all got with what I waggishly called in Founda- typed in first draft by her even though tions the Wong-Viner Envelope Theo- she was a graduate-school economist in rem. Actually, that theorem is a kaleido- her own right. Although I have always scope which yields multiple insights: insisted that Foundations was formu- the direction of change of a maximum lated on Harvard grounds, before de- system when an external parameter gets gree time I was an assistant professor at perturbed; the LeChatelier theorem on MIT. With or without a Ph.D., I was constrained variables; the duality prop- not to get an early tenure offer from erty that makes Lagrange-multipliers Harvard and, without malice, I revealed measure optimizing (and mar- a preference for MIT. To everyone's ginal costs or ). surprise, including my own, that turned In postwar years I used to receive let- out to be the happiest decision of my ters from all over the world reporting life. groups of students who met in teams to

This content downloaded from 193.54.110.56 on Sun, 23 Jul 2017 08:24:16 UTC All use subject to http://about.jstor.org/terms 1378 Journal of Economic Literature, Vol. XXXVI (September 1998) puzzle out the contents of Foundations. demand for their brainchild. I was no Memorable is the London-Cambridge exception. But I never dreamed of the cell that included Jan de Van Graaff, repeated printings that were to come, Harry Johnson, Will Baumol, and Frank the paperback editions, or the many Hahn: soldiers of destiny on their way translations into foreign languages. I to destiny. decided not to revise the text, instead Even the book's mistakes generated a merely correcting any errors brought to . When I was apprised of a dou- my attention. (They were relatively few ble error of sign in a LeChatelier-Ja- and trivial: reversed algebraic signs; an cobi determinant, I would write back: occasional treacherous double limit. "Congratulations! You are the seven- However, early in 1997, one new one teenth non-Japanese to notice this." got reported to me: it was an inexplica- The book won Harvard's David A. ble error alleging that when one of Wells Prize in 1941 for best publishable many independent utilities involved a thesis. Because an earlier winner had permnissible rising , then pocketed the but never revised that good could have negative income his manuscript, I was required to sub- . The gentle Leontief would mit my revised draft. Alas, World War have horsewhipped me in my first Har- II came to U.S. shores via Pearl Harbor. vard year for so crude a slip!) Nights and Sundays, while working on When Foundations was 35 years old, radar and mathematical fire control at I finally agreed to an enlarged edition. the Radiation Laboratory, I toiled over Rather than tamper with the original revisions and expansions. By 1944 I text, I added a second part that almost handed in the finished draft. Harvard's doubled the book's length. I wrote com- long-time economics department chair- pactly to cover three decades of explod- man was no admirer of me; long before, ing new results. It was good stuff. A he had counseled me against working in good deal of it was deeper than much of economic theory before I had reached the original. But the result was dramatic (his) ripe old age of 50+. Once a month confirmation of my suspicion that Foun- I checked that the manuscript still gath- dations' success came from its being the ered dust in the anteroom of Economics needed exposition for its time. The new headquarters. That was an unintentional stone caused no great ripples in the boon to me: a wartime publication pond of modern . would have been an anticlimax before By 1983 we were all, so to speak, any climax. mathematical ; and several Less lucky was the department chair- hundred specialized books were avail- man's decision to have a first printing of able to cover each corner of up-to-date only 500 copies. I objected. We comn- economics. promised on 750 copies. But he had the This is as it should be. Soft and hard last word. His orders were to destroy all sciences are cumulative disciplines. We that beautiful mathematical type after each bring our contributions of "value the first run. When the first printing added" to the pot of progress. In Max sold out immediately, all subsequent Planck's much-quoted words: Science printings had to be done by photo off- progresses funeral by funeral. Inside to- set. This turned out to be just as well morrow's physics treatise will be the for a busy author who had no relish for lasting truths of Isaac Newton and also proofreading complicated mathematics. of the professor who works down the Young authors expect a respectable hall from you. Something of the same

This content downloaded from 193.54.110.56 on Sun, 23 Jul 2017 08:24:16 UTC All use subject to http://about.jstor.org/terms Samuelson: How Foundations Camne to Be 1379 goes for economics, where often the Solow, . . .; the list is endless. As I dance must proceed Two Steps Forward later wrote: "Yes, Harvard made us. But and One Step Back. it is we who made Harvard." The Cam- Some fool (it was Henry Ford) said bridge, Massachusetts which had begun History is bunk. Actually, good history as Keynes-hostile ended up as the cho- does debunk, by means of detailed re- sen place to spend your postwar sab- porting, the mystiques of scientific bi- batical year. It came to supplant Oslo ography. "The lone genius toiling in a and Rotterdam, the London School of garret, and producing the Mona Lisa," Economics and Cambridge, . that kind of gush. What was the back- Had I remained on the Chicago Mid- ground knowledge that led to Founda- way, I might well have missed out on tions? John Livingston Lowes, in his the three revolutions that remade main- classic The Road to Xanadu, perused stream economics: the Keynesian Revo- the books Samuel Taylor Coleridge was lution, the Imperfect-Competition known to have read. The library with- Revolution, and the Mathematical-Eco- drawal records at Chicago's Harper Li- nomics Revolution. Instead I had a brary and Harvard's Widener and Baker front-row seat. In races, once you get a libraries would be an unreliable source lead you have only to run as fast as the for my 1932-41 readings. I lived and rest to stay up front. (In my own sober breathed economics much of those self-audit, my 500-odd collected scien- days' 24 hours. What this autodidact tific papers outweigh for me all text- learned (belatedly) came from auditing book bestsellers or columns math lectures and reading while stand- or governmental testimonies.) ing up deep in the stacks of Widener Library. Edward Gibbon had the seat of an historian; I had the feet of a zealot. 2. The Story By the time I came to Harvard, In 1938 I had proposed a novel para- though I was still too young to vote, I digm of "revealed preference." For the had taken more varied courses in eco- 2-good case this could provide a com- nomics than my fellow students would plete description of all the observable attend in all their graduate study: labor (and testable, and refutable) empirical economics, (both (price, quantity) data of a coherent de- European and American), public fi- mand system. As an example, it could nance, money and banking (there was prove, for as many as n-I out of n , no macro then), business cycles, statis- there could be negative income elasticity tics, everything but agricultural eco- at any specified income and prices; and nomics. Fellow students-our true that an own price elasticity, (A log qil teachers-included, at Chicago, George A log pi) ,Pj, could be Giffen positive for Stigler, Albert Hart, Allen Wallis, Mil- any such "inferior" good and only for such. ton Friedman, Jacob Mosak; at Harvard Abram Bergson, , Robert Also, necessarily aqilapi < qi(aqJalI) 0 for Triffin, Wolfgang Stolper, Richard Mus- all goods. It could also deduce cogently grave, Sidney Alexander, Joe Bain, Alice that qj demands remain invariant when Bourneuf, , John Lintner, all prices double (or halve) at the same Robert Bishop, Paul and Alan Sweezy, time that nominal expendable income Richard Goodwin, , doubles (or halves). These stated results , Evsey Domnar, Walter and are essentially the only and the exhaus- William Salant, Emile Despres, Robert tive empirical content of received prefer-

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ence-maximization formulations. As I added to the Weak Axiom so that (pj,qj) have reported, my revealed-preference observable-data tests could be strength- innovation came from a marriage be- ened to their maximal extent? Young tween Haberler-Konus number Hendrik Houthakker (1950), on his own theory and Gibbs finite-difference for- in Holland, later supplied the needed mulations of classical phenomenological Strong Axiom. Already in 1938, before I of the 1870s. could know of Houthakker, I had con- My approach looked backward in jectured that it might be enough to summarizing "economically" (in the specify that "no chain of weak-axiom Mach-Vienna Circle sense) the "mean- rulings can ever lead to a contradiction ingful" (testable and, in principle, refut- like (A weak-revealed better than B, B able) core of constrained-budget de- weak-revealed better than C, . . ., Y mand theory. It could do so without revealed better than Z-but Z weak-re- mention of "mind" or "brain" or "intro- vealed better than A!)." I propounded spection." It had no explicit need for a this conjecture to two of the best young utility metric by which beans could be mathematicians anywhere: Stan Ulam judged to yield twice the utils of peas; and Lynn Loomis, Harvard Junior Fel- or for statements like "My love for lows of my time. (Ulam later invented Mary exceeds that for Jane in exactly for Teller the American hydrogen bomb the degree that my love for Jane ex- at Los Alamos; Loomis, knowing noth- ceeds that for Fifi." In non-stochastic ing of , after hearing John conditions, I cared not whether the ob- von Neumann issue a challenge for an served demander was risk-neutral or algebraic, non-topological proof of his risk-averting or risk-relishing. (1928) two-person, zero-sum game My good day's work was well re- theorem, went home and found the warded. My Master, Professor Schum- needed proof that night.) But, as I have peter, oh-ed and ah-ed. But in Founda- discovered in life, the great pure tions I chose to downplay this para- mathematicians I have known, except digm. One reason was substantive. For for John Nash, sensibly resist concen- more than two goods, n > 3, my so- trating on puzzles arising from esoteric called Weak Axiom was recognized to fields like economics. At the time Foun- be necessary but not to be alone suffi- dations went to press, the revealed cient to deduce transitivity of prefer- preference paradigm still lacked com- ences. It could not rule out "Jones pletion. chooses (3 rye, 2 corn, 2 peas) over (2 The second reason I soft-pedaled rye, 2 corn, 3 peas) and chooses (2 rye, claims for it went deeper and remained 2 corn, 3 peas) over (2 rye, 3 corn, 2 after Houthakker's tour de force. The peas); but also (!) chooses (2 rye, 3 Samuelson-Houthakker paradigm, cx, corn, 2 peas) over the initial (3 rye, 2 properly exposited, became equal in corn, 2 peas)!" For n > 2 goods, always empirical meaning to the indifference satisfying the Weak Axiom as applied field approach of Pareto-Allen-Hicks- pair by pair could, in the most general Hotelling, P; and equal to the ordinal- case, decidely tolerate a transitivity utility formulation of contradiction-if not after three com- (1915) or (1931), y; and parisons then after 3,333 comparisons. equal to a (1959) lat- (This could not occur if Jones really did tice-theory partial ordering, 6. When adhere to a transitive partial preference members of a class are equal, each is ordering.) What was needed to be first among equals. Also, each is last

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.among equals. Why debate the different elasticity, it can never display a positive merits of essential equals? Since the 6 [Giffen] own-price elasticity-even if version is the most "intuitive" one, be indifference contours cease to be con- satisfied when you demonstrate that cx vex and demand functions are neither does exhaust all the valid empirical con- single-valued nor uniquely invertible.)2 tent of (ci, P, y, 6). Professor E. Roy Weintraub (1983) 3. Admired Influences has astutely recognized that Samuel- Who were the major writers influenc- son's (1938) Weak Axiom was already in ing Foundations? They were many and Abraham Wald's (1934-35) second pa- various. E. Roy Weintraub (1989, 1991) per on determinateness of Walras- suggests that there is some mystery Cassel-Schlesinger general equilibrium. here, even maybe some cover up. Inter- But I did not in 1938 "refine" that: as ested readers will want to compare the often mentioned, my approach arose following paragraphs with his account from considering Haberlerian restric- and with earlier memoirs by me. tions that apply to Laspeyres and First, my heroes in economics were Paasche quantity index numbers for a scholars such as Leon Walras, Antoine "rational consumer." Wald's arose from Augustin Cournot, Francis Edgeworth, a search for a set of sufficient condi- , , and tions to guarantee uniqueness of equi- . (This was after my infan- librium; if I had known Wald's paper tile infatuation with Frank Knight sim- and had had the wit to see in it the mered down to measured respect for a Weak Axiom, I would certainly have in- brilliant but erratic economist and theo- voked the prestige of Wald's name to logian.) Among working economists help sell the Weak Axiom to readers. during the 1930s, John Hicks and Rag- It has been said that no good deed nar Frisch (two very different egoists) goes unpunished. As a result of my (un- characteristic) modesty in playing down 2 Prior to Houthakker, for n > 2, I tended to revealed preference in Foundations, side with Roy G.D. Allen rather than with Hicks's some writers have suspected some fail- insistence upon integrability. Why not be general ure in the paradigm. On reflection, and be happy to posit non-integrability and global non-transitivity? In those cases, only the Weak Ax- thanks to Houthakker, all I hoped for iom could be validly posited as a constraint on em- (or could rationally have hoped for) was prical demand observations. My reading of Grif- attained by it. fith Evans (1930), Allen (1932), and Nicholas Georgescu-Roegen (1936) softened me up for Revealed preference, aside from such a half-way house compromise. But, Freud- looking backward to consolidate and ianly, that was perhaps making a virtue of neces- elucidate received doctrines, inadver- sity. Once Houtlhakker delivered me from such ne- cessity, in a 1950 exchange with I tently looked ahead into the finite- lost my tolerance for global intransitivity, which mathematics of inequality-duality rela- came to smack of uninteresting formalism for its tionships that formed the modern Age own sake. See Stanley Wong (1978) for related discussions. A reader of Philip Mirowski (1989) of Debreu in economics. Gibbs led me may find some difficulty in reconciling remarks to the promised land before there was a there and remarks here. Remark: The deep points promised land. Indeed, among my alter- raised by Dr. Wong can, I believe, be argued out in the 2-good case without prejudice to their native 1938 formulations (with respect evaluations. Presence or lack of presence of to ">" or "2"), can be found valid rela- Giovanni Antonelli's (1886) observable integrabil- tions applicable to admissible specifica- ity conditions introduce interesting technical points but Wong's preoccupations wi [remain to tions of non-convex sets. (Example: If a be addressed even when integrability is assured good never displays negative income (as in the 2-good case).

This content downloaded from 193.54.110.56 on Sun, 23 Jul 2017 08:24:16 UTC All use subject to http://about.jstor.org/terms 1382 Journal of Economic Literature, Vol. XXXVI (September 1998) got the most attention from me. (In my of great originality, which built up a 1932 Chicago freshman year, my tutor readership for the problems Founda- Eugene Staley told me that John May- tions grappled with and for the explo- nard Keynes was then the world's great- sion of mathematical economics that est economist. This was after the Trea- soon came. tise on Money (1930) but before The General Theory (1936). I had no reason 4. Mysteries Deciphered to disagree. In 1936 at Harvard, Assis- tant Professor John M. Cassels told me In this English version of my pub- that John Hicks was the world's leading lished German essay (Niehans, et al., younger economist. I could believe that, 1997), I can be brief on certain queries based on the Theory of (1932) that over the years have arisen about and the Hicks-Allen (1934) collabora- Foundations. (1) Why does it seem to tion. Allen, who visited Harvard, became say nought about use of a Lyapunov a good friend, and I always thought he Function that ever decreases towards a received too little credit. zero rendezvous at the equilibrium was an admired role model, and I asymptote of a dynamic system, and approved when Frisch and Tinbergen thereby deprive itself of a classic shared the first in 1969.) method of proving damped stability of In 1935, still ruled an ? (2) Herbert Simon the roost in fame. What goes up too far (1959) and Joel Cohen (1987) have comes down too low. Like Gustav noted that was an ad- Cassel's, his textbook filled a real need; mirer of Alfred Lotka, the mathematical but, like Isaac Newton, he had an inhib- biologist; but did he covertly owe more iting influence on two generations of to Lotka than is explicitly acknowledged followers. Marshall never lived up to his in footnotes and bibliographic refer- potential, for reasons of health and tem- ences? (3) How important an influence perament. Before 1890 he knew the de- on Samuelson was the Gibbsian bio- fects in his own constructs (consumers chemist L.J. Henderson at the Society surplus, , . . .) but of Fellows and in connection with his never did he follow up with the needed Pareto cell at Harvard? E. Roy Wein- improvements. As Whitehead said to traub (1989, 1991) has nominated ques- me, "Marshall was more Popish than tions like these and assayed in a lengthy saintly. We liked Mary Paley Marshall article on Foundations' dynamics to better." provide them with critical answers. In- When I came to know John and Ur- terested readers may be referred to my sula Hicks well, I said to him: "I have German text's detailed attempts to pro- the best of both worlds. I know your vide dialogue on these topics. work and know my own, too." In this 1. I did not use the name "Lyapunov relative neglect of other scholars Hicks Function" in stability analysis for a sim- was even-handed. For him the sun rose ple reason: not until World War II did I when he opened his eyes. He wrote well know that name for this 1892-and-ear- and lectured badly. In Britain, Hicks's lier technique. But repeatedly Founda- originality and breadth never received tions did use such Lyapunov Functions, its full due, perhaps in part for reasons roses by whatever name. Thus, from of personality and of "political incor- J.W.S. Rayleigh's monumental Theory rectness.': Hicks's Value and of Sound (1870), I had early learned to (1939) was an expository tour de force prove stability in the following fashion:

This content downloaded from 193.54.110.56 on Sun, 23 Jul 2017 08:24:16 UTC All use subject to http://about.jstor.org/terms Samuelson: How Foundations Came to Be 1383 x + ax + x = 0 - 1xx + -a2 + =X in connection- 0 with dynamnics (as for example his autonomous one-sex < (d/dt)[x2 + x2] = - x2 < 0 populationfora > 0.growth (1) model, and his The above bracketed expression is a Lotka-Volterra predator-prey model). Lyapunov Function that ever declines to- My three Lotka references came appro- ward zero, thereby entailing [(x(t) xs(t)] - priately late in the book because dy- [0 0] as t -o. namics came late. See the German text Similarly, Foundations repeatedly for more detail on my admiration for studied gradient motions: Lotka. Here I need only stress that it was his physical-reductionist biology Xi = aJF(xli.. ..x)/ axi that interested me, and this is far re- i=1,2,...,n;a>0. (2) moved from Marshall's palaver about a For F a strictly concave function with biological paradigm in economics. A a maximum at (xj) = (0), century on, it is Darwin-Lotka-Fisher- Haldane-Wright-Hamilton mechanisms lim[xl(t) ... X?l(t)] = [0 ... 0] that have made some progress in eco- t-x (3) nomics. by virtue of strict concavity's entailing 3. My relation to the Pareto-Hender- the following Lyapunov Function rela- son-Homans-Curtis coterie at the Soci- tions: ety of Fellows can be simply put. These turned out to be purely social. I went F(xi. ) . . F(x,...,) = EXj6F/6xj < 0. but once to the famous Henderson soci- 1 (4) ology seminar. That was either once too many or many too few. When I would Again, Foundations innovated the want to talk about Gibbs to Henderson, then-new concept of quasi-definiteness he would prefer to enumerate the short- for an n2 matrix [aiy], and demonstrated comings of Franklin Delano Roosevelt. by Lyapunov Function reasoning that In 1937 it was a case of Henderson's 71 being too old or Samuelson's being too Xj = -E, aijxj, [aij + aji = as,pos.d ef young, or both. My guarded admiration 1 (5) for Pareto has been is locally and globally stable. My German great; but during the vogue for his soci- text gives page references that dispel ology, I stayed out to lunch. mystery about a failure in Foundations to employ the rudimentary Lyapunov tech- 5. Th-e Road Not Taken nique. My actual 1947 explicit references to Alexander Lyapunov, Emnile Picard, Foundations, for the most part, had a and Birkhoff had mostly to do with the unifying theme: how and why one could more delicate cases of borderline stabil- predict with qualitative certainty the di- ity related to measure-preserving conser- rection of change for an optimizing vative Hamiltonian and more general mnaximnal variable when its exogenous systems; prior to the 1960s break- price in the bilinear product . . throughs in chaos theory, I in the late pjqj . . . is perturbed upward. 1930s was too unsophisticated to grapple Chapter 3 outlined the general de- with Henri Poincare, George Birkhoff, ductive logic; Chapter 4 applied it to Edward Lorenz, and sub- cost minimization and supply response; tleties. Chapters 5-7 handled the implica- 2. My major benefit from Lotka came tions for constrained-budget demand

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optimization. Had I been a strict consti- Two on dynamics, even though much of tutionalist, I might well have stopped my focus there was on "macro- there. The result would have been a economics" (a word not yet coined by shorter 200-page book with one fully- , Peter de Wolff, or integrated theme. ). No one associates a Young men in a hurry are prone to Keynesian system with a maximizing want to tell all they know (and some- single mind or even to an as-if-pretend times we overshoot!). It seemed a pity maximizing system. Yet from considera- not to add an eighth chapter which tion of The General Theory's "stable" would explicate, a la Bergson, for the dynamics, one could predict that a rise great pioneers in "modern" welfare eco- in the propensity to invest would in- nomics-Arthur C. Pigou, Lionel Rob- crease, not lower, underemployment bins, Hotelling, Hicks, , equilibrium and GNP. Why that Pareto, Tibor Scitovsky, John Stuart might be possible needed to be re- Mill, Ian Little, , . . . searched in the late 1930s. Catastrophe (note the admixture of nineteenth cen- theory and chaos theory were not yet tury savants, 1930s pioneers, and writ- born or reborn in the math literature, ers not yet born in the antebellum but I caught a look at heuristic "corre- status quo)-their own meanings. Hav- spondences" between dampening in dy- ing, in King Alphonso's words, "been namics and qualitative direction of present at the creation," I understood (comparative-statics) equilibrium re- precisely the clarification achieved for sponses to exogenous perturbations. "If by Bergson's (1938) one's reach cannot exceed one's grasp," magisterial synthesis. Using the words what is innovating for?3 the poet Alexander Pope addressed to In retrospect, I have never regretted Newton, I later wrote, not taking the road not taken. Founda- tions came a bit too late to be responsi- Ethics and Ethics' laws lay hid in night: God said, "Let Bergson be!" And all was light. 3 In reading this essay, remarks on the surprising absence of general equilibrium Bergson's Welfare Function of Individu- as an explicit topic in Foundations. Why? I recon- struct memory of my then state of mind as follows. alistic Type made clear for Hicks and When many folks are alike with (quasi-concave, Kaldor-had they deigned to pay heed- smooth) tastes, and like initial endowments of exactly how their Mill-Pareto Optimality goods, it is easily provable that a general equilib- rium would exist and be unique. From 1879 on, calculus (in which winners can overcom- Marshall and I knew that the exchange equilib- pensate losers) fits in with exogenously rium need not be unique when tastes and/or en- prescribed interpersonal value norms. dowments differed; but I sensed topologically that at least one equilibrium existed. (Only Iater, from Responsive to Geoffrey Chaucer's "And Gerard Debreu, did I realize that "almost always" gladly teach," I composed Chapter 8's the number of possible equilibria would be finite.) exposition of Bergsonian welfare eco- From Irving Fisher (1892) and Wicksell (1893), Franz Zeuthen (1933), Hans Neisser (1932), Hein- nomics even though that strayed from rich v. Stackelberg (1933) and Hicks (1931), I un- early chapters' central theme. Ralph derstood the Schlesinger-Wald duality relation, ac- Waldo Emerson and Einstein would cording to which a good's non-negative price would be zero when its supply was redundant. And have approved: consistency can be a hob- from early Pareto I had learned that a competitive goblin, and elegance is indeed for tailors equilibrium could support any defined feasible rather than serious scholars. normative optimum a la . So with the naive optimism of youth I didn't know enough to One liberty begets another. I could miss the fixed-point theorems of Debreu-Arrow not resist the temptation to add Part (1954) and Lionel McKenzie (1959).

This content downloaded from 193.54.110.56 on Sun, 23 Jul 2017 08:24:16 UTC All use subject to http://about.jstor.org/terms Samuelson: How Foundations Came to Be 1385 ble for the first J.B. Clark Medal of the tions and Orderings," Economica, 73, pp. 292- 308. AEA in 1947. But it is a safe guess that Arrow, Kenneth and Gerard Debreu. 1954. "Ex- it did accelerate a 1970 Nobel Prize istence of an Equilibrium for a Competitive that came, if anything, a little too early ," Econometrica, 22, pp. 265-90. Bergson, Abram. 1938. "A Reformulation of Cer- for Platonic justice. tain Aspects of Welfare Economics," Quart. J. Econ., 52, pp. 310-34. 6. Finale Birkhoff, George D. 1927. Dynamical Systems. NY: American Mathematical Society. The above memoir was written before Cassel, Gustav. 1932. The Theory of Social Econ- omy. NY: Harcourt, Brace & Co., English trans- I could read the many kind words of lation of 1918 German version. Schefold, Niehans and von Weizsacker. Cohen, Joel E. 1987. "Lotka, Alfred James," in The As Dr. Samuel Johnson observed, those New. Palgrave Dictionary of Economics, John Eatwell, Murray Milgate, and Peter Newman, who communicate at a birthday party eds., London: Macmillan, pp. 245-47. are not strictly under oath. Nonethe- Evans, Griffith C. 1930. Mathematical Introduc- less, among the compliments were just tion to Economics. NY: McGraw-Hill. Fisher, Irving. 1961. Reprint. Mathematical Inves- qualifications: thus, Niehans and Sche- tigations in the Th-eory of Value and Prices. fold are right to hint that the heuristic New Haven: Connecticut Academy of Arts & "correspondence principle" failed to de- Sciences. Orig. NY: Augustus M. Kelley. Georgescu-Roegen, Nicholas. 1936. "The Theory velop the scope of the "maximizing of Consumers' Behavior," Quart. J. Econ., 50, principles." And von Weizsacker, him- pp. 545-93. self a deep analyst of Marxian and non- Hices, John R. 1931. "The Theory of and Profit," Economica, 11, pp. 170-89. Marxian capital theories, is all too cor- . 1932. The Theory of Wages. London: rect in the observation that my Macmillan & Co. demonstrations on the confusions and . 1939. , an Inquiry into Somne Fundamental Principles of Economic The- sterilities of the Marxian novelties- ory. Oxford: Clarendon Press. equalized rates of surplus values, the Hicks, John R., and Roy G.D. Allen. 1934. "A Re- as simply an consideration of the Theory of Value," Pt. I-II, Economica, 1, pp. 52-76; 1932, 1, pp. 196-219. initial return by Marx from his Houthakker, Henadrik. 1950. "Revealed Preference Mehrwert cul de sac back to the bour- and the Utility Function," Economica, 17, pp. geois square one-has had few converts 159-74. Keynes, John Maynard. 1930. A Treatise on on the Left. Still, like Galileo, I mutter Money. Reprinted in The Collected Writings of under my breath the symbolic, "But it , Vol. V. London: Macmil- does move." lan for Royal Econ. Society. . 1936. The General Theory of , Interest and Money. Reprinted in The Collected Worse than an ungrateful child is an Writings of John Maynard Keynes, Vol. VII. ungrateful parent. And I have many London: Macmillan for Royal Econ. Society. Lefschetz, Solomon. 1946. Differential Equations: times been a grateful parent. At its fifti- Geometric Theory, 2nd edn. NY: Interscience eth birthday, I hail Foundations of Eco- Publishers. nomic Analysis: Lorenz, Edward. 1993. The Essence of Chaos. Se- attle: U. Washington Press. Parens gratvs filio pergrato gratias Lotka, Alfred J. 1934. Elements of Physical Biol- agit. ogy. Baltimore: Williams & Wilkins Co. Also (1924) as Elements of Mathematical Biology. NY: Dover Publications. REFERENCES Lowes, John Livingston. 1927. The Road to Allen, Roy G.D. 1932. "The Foundations of a Xanadu, a Study in the Ways of the Imagina- Mathematical Theory of Exchange," Economnica, tion. Princeton: Princeton U. Press. 42, pp. 323-26. Lyapunov, Alexander. 1892. "Obshcaya Zadaca ob Antonelli, Giovanni B. 1952. Reprint. Sulla Teoria Ustoicivosti Dvizeniya," Soc. Math. Kharkov. Matematica dell'Economia Politica. Pisa. Orig. English translation 1992, The General Problem Milan: Malfasi, 1886. of the Stability of Motion. London: Taylor & Arrow, Kenneth. 1995. "Rational Choice Func- Francis.

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Marshall, Alfred. 1890, 1891, 1895, 1898, 1907, Sharpe, F.R. and Alfred J. Lotka. 1911. "A Prob- 1910, 1916, 1920, 1961. Principles of Econom- lem in Age-," Philosophical Maga- ics. London: Macmillan & Co. zine, 21, pp. 435-38. McKenzie, Lionel. 1959. "On the Existence of Simon, Herbert. 1959. "Review of Elements of General Equilibrium for a Competitive Mar- Mathematical [Physical] Biology," Econo- ket," Econometrica, 27, pp. 54-77. metrica, 27, pp. 493-95. Minorsky, Nicolai. 1947. Introduction to Non-lin- Slutsky, Eugen. 1915. "Sulla Teoria del Bilancio ear Mechanics. Ann Arbor, MI: J.W. Edwards. de Consumatore," Giornale degli Economnisti e Mirowski, Philip. 1989. More Heat Than Light. Rivista di Statistica, 51, pp. 1-26. Translated as NY: Cambridge U. Press. "On the Theory of the Budget of the Con- Neisser, Hans. 1932. "Lohnhbhe und Beschefti- sumer," in Readings in Price Theory. Kenneth gungsgrad im Marktgleichgewicht," Weltwirt- E. Boulding and George J. 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