In 1990, U.S. economists Harry Markowitz, William F. Sharpe, and Merton H. Miller shared the Nobel Prize “for their pioneering work in the theory of financial economics.” Their contributions, in fact, were what started financial economics as a separate field of study. In the early 1950s Markowitz developed portfolio theory, which looks at how investment returns can be optimized. Economists had long understood the common sense of diversifying a portfolio; the expression “don’t put all your eggs in one basket” is certainly not new. But Markowitz showed how to measure the risk of various securities and how to combine them in a portfolio to get the maximum return for a given risk. Say, for example, shares in Exxon and in General Motors have a high risk and a high return, but one share tends to go up when the other falls. This could happen because when OPEC raises the price of oil (and therefore of gasoline), the prices of oil producers’ shares rise and the prices of auto producers’ shares fall. Then a portfolio that includes both Exxon and GM shares could earn a high return and have a lower risk than either share alone. Portfolio managers now routinely use techniques that are based on Markowitz’s original insight. Markowitz earned his Ph.D. at the University of Chicago. He has taught at Baruch College of the City University of New York since 1982. Selected Works   1952. “Portfolio Selection.” Journal of Finance 7, no. 1: 77–91. 1959. Portfolio Selection: Efficient Diversification of Investments. Reprint. Hoboken, N.J.: Wiley, 1970.   (0 COMMENTS)

In 2000, Daniel McFadden shared the Nobel Prize in economics with James Heckman. McFadden received the prize for “his development of theory and methods for analyzing discrete choice.” The award was given for very technical work that would be hard to explain to the layman, but it has been important for economists who want to study many important issues when the choices involve discrete rather than continuous choices. Before McFadden’s work, empirical economists who studied various issues tended to assume that the variables they were studying were continuous. This works well when one studies, say, the demand for sugar, because people buy various amounts of sugar along a continuum. But what if one is studying the demand for refrigerators? Because most people have only one refrigerator, the choice of a refrigerator is a discrete choice. Or what if one is studying people’s choice of travel modes for getting to work? Most people do not take the subway one day, a bus the next, and a car the day after that; most use one of those modes almost all the time. Economists needed a way to do empirical work on such discrete choices, but the tools to do so were missing. That is where McFadden came in. In 1965, one of his graduate students at Berkeley was analyzing thesis data on the California state highway department’s choices on where to put freeways and asked for his help. Freeway placement is an example of a discrete, rather than a continuous, choice. McFadden started to solve the problem but did not finish until 1968 (the paper was published in 1976), well after her thesis was done. In solving it, he created a technical method for dealing econometrically with discrete choices generally. McFadden tested his model with data on people’s transportation choices before the Bay Area Rapid Transit (BART) system was built in the San Francisco Bay Area. While the official forecast was 15 percent, McFadden used his model to predict that only 6.3 percent of Bay Area travelers would use BART. The actual number turned out to be 6.2 percent. McFadden has also used his own methods to analyze investments in telephone service and housing for seniors. Selected Works   1974. “The Measurement of Urban Travel Demand.” Journal of Public Economics 3: 303–328. 1976. “The Revealed Preferences of a Government Bureaucracy: Empirical Evidence.” Bell Journal of Economics and Management Science 7: 55–72. 1978 (with Kenneth Train). “The Goods/Leisure Tradeoff and Disaggregate Work Trip Mode Choice Models.” Transportation Research 12: 349–353. 1986. “The Choice Theory Approach to Market Research.” Marketing Science 5: 275–297. 1987 (with Kenneth Train and Moshe Ben-Akiva). “The Demand for Local Telephone Service: A Fully Discrete Model of Residential Calling Patterns and Service Choices.” RAND Journal of Economics 18: 109–123. 1994. “Contingent Valuation and Social Choice.” American Journal of Agricultural Economics 74: 689–708.   (0 COMMENTS)

  Karl Marx was communism’s most zealous intellectual advocate. His comprehensive writings on the subject laid the foundation for later political leaders, notably V. I. Lenin and Mao Tse-tung, to impose communism on more than twenty countries. Marx was born in Trier, Prussia (now Germany), in 1818. He studied philosophy at universities in Bonn and Berlin, earning his doctorate in Jena at the age of twenty-three. His early radicalism, first as a member of the Young Hegelians, then as editor of a newspaper suppressed for its derisive social and political content, preempted any career aspirations in academia and forced him to flee to Paris in 1843. It was then that Marx cemented his lifelong friendship with Friedrich Engels. In 1849 Marx moved to London, where he continued to study and write, drawing heavily on works by David Ricardo and Adam Smith. Marx died in London in 1883 in somewhat impoverished surroundings. Most of his adult life, he relied on Engels for financial support. At the request of the Communist League, Marx and Engels coauthored their most famous work, “The Communist Manifesto,” published in 1848. A call to arms for the proletariat—“Workers of the world, unite!”—the manifesto set down the principles on which communism was to evolve. Marx held that history was a series of class struggles between owners of capital (capitalists) and workers (the proletariat). As wealth became more concentrated in the hands of a few capitalists, he thought, the ranks of an increasingly dissatisfied proletariat would swell, leading to bloody revolution and eventually a classless society. It has become fashionable to think that Karl Marx was not mainly an economist but instead integrated various disciplines—economics, sociology, political science, history, and so on—into his philosophy. But Mark Blaug, a noted historian of economic thought, points out that Marx wrote “no more than a dozen pages on the concept of social class, the theory of the state, and the materialist conception of history” while he wrote “literally 10,000 pages on economics pure and simple.”1 According to Marx, capitalism contained the seeds of its own destruction. Communism was the inevitable end to the process of evolution begun with feudalism and passing through capitalism and socialism. Marx wrote extensively about the economic causes of this process in Capital. Volume one was published in 1867 and the later two volumes, heavily edited by Engels, were published posthumously in 1885 and 1894. The labor theory of value, decreasing rates of profit, and increasing concentration of wealth are key components of Marx’s economic thought. His comprehensive treatment of capitalism stands in stark contrast, however, to his treatment of socialism and communism, which Marx handled only superficially. He declined to speculate on how those two economic systems would operate. About the Author Janet Beales Kaidantzis was assistant editor of The Fortune Encyclopedia of Economics. Selected Works   1848. “Manifesto of the Communist Party.” Reprinted in Marx: The Revolutions of 1848. Harmondsworth: Penguin Books, 1973. 1858. Contribution to the Critique of Political Economy. Reprint. London: Lawrence and Wishart, 1970. 1865. “Wages, Price and Profits.” Reprinted in Marx-Engels Selected Works. Vol. 2. Moscow: Progress Publishers, 1969. 1867. Capital: A Critique of Political Economy. Edited by Friedrich Engels and reprinted in 1906, Chicago: Charles H. Kerr. Reprinted in 1976, New York: Penguin Books. Available online (Charles Kerr, ed.): Vol. I: http://www.econlib.org/library/YPDBooks/Marx/mrxCpA.html, Vol. II: http://www.econlib.org/library/YPDBooks/Marx/mrxCpB.html, Vol. III: http://www.econlib.org/library/YPDBooks/Marx/mrxCpC.html   Footnotes 1. Mark Blaug, Great Economists before Keynes (Highlander, N.J.: Humanities Press International, 1986), p. 156.   (0 COMMENTS)

  In 2000, James Heckman, along with daniel mcfadden, received the Nobel Prize in economics. Heckman won the prize for “his development of theory and methods for analyzing selective samples,” highly technical work that it is difficult to explain to the layman. Nevertheless, the work rewarded by the Nobel committee has been valuable for economists’ studies of many issues that laymen do care about. The main technical problem on which Heckman has spent much of his professional life involves self-selection. An economist who wants to know, for example, how male workers will respond to a higher wage rate can take microdata on wages and hours worked and find a relationship. This approach has a problem that economists have long recognized: some men will not work at all and, therefore, will not be in the data set. And, presumably, these men who do not work will be disproportionately from the group that, had they worked, would have earned low wages. They have “self-selected” out of the workforce. So the economist’s estimates on the effect of wages on hours worked will be biased. How is the economist to deal with this fact if he wants to generalize from his sample to the male population in general? Enter Heckman. Heckman came up with a clever econometric approach to figuring out how to correct for this self-selection problem. In fact, empirical economists now know his correction as the “Heckman correction” or the “Heckit method.” In 1985, using his own method to study the connection between work and wages noted above, Heckman found a bigger elasticity of labor supply among American men than had previously been thought to exist. That was because a given increase in wages did not just cause an increase in hours among those already working, but also caused relatively low-wage workers to reenter the labor market and get jobs. In his Nobel lecture, Heckman laid out some important implications of self-selection for U.S. and European labor markets. One is that the vaunted diminution of the gap between black men’s and white men’s wages in the United States between 1940 and 1980 was due almost entirely to low-wage black men dropping out of the labor force. Another implication concerns the much-higher equality of wages in Europe compared with the United States that many economists and others have noted. Heckman pointed out that much of this difference is due to the fact that many low-skilled potential workers in Europe are not working. This is presumably because of high minimum wages, strong labor unions, and laws that make it hard for employers to lay people off (and therefore make the employers hesitant to hire). The Nobel Web site refers to Heckman as “the world’s foremost researcher on econometric policy evaluation.” In 1999, Heckman and coauthors Robert LaLonde and Jeffrey Smith found that government programs to train workers are generally ineffective at increasing those workers’ wages and long-term employment prospects. The reason they appear effective is that the average wage gain of people in these programs is high. But Heckman and his coauthors showed that this occurs because the trainees typically have lost or quit their jobs prior to entering the training program and that training is a form (albeit inefficient) of job search. Much of the improvement in their posttraining fortunes would have occurred without a government program in place. This would probably come as no surprise to people who have been in such programs. In 2002, with Pedro Carneiro, Heckman also showed that lack of credit is not a major constraint on the ability of young Americans to attend college. They found that credit constraints prevent, at most, 4 percent of the U.S. population from attending. Heckman has also weighed in on the issue of racial discrimination in U.S. labor markets. In 1998 he wrote, “[M]ost of the disparity in earnings between blacks and whites in the labor markets of the 1990s is due to the differences in skills they bring to the market, and not to discrimination within the labor market.” Selected Works   1974. “Shadow Wages, Market Wages and Labor Supply.” Econometrica 42: 679–693. 1975. “The Common Structure of Statistical Models of Truncation, Sample Selection and Limited Dependent Variables and a Simple Estimator for Such Models.” Annals of Economic and Social Measurement 5: 475–492. 1976. “A Life Cycle Model of Earnings, Learning and Consumption.” Journal of Political Economy 84: S11–S44. 1979. “Sample Selection Bias as a Specification Error.” Econometrica 47: 153–161. 1981 (with Thomas MaCurdy). “New Methods for Estimating Labor Supply Functions.” In Ronald Ehrenberg, ed., Research in Labor Economics. Vol. 4. Greenwich, Conn.: JAI Press. 1998. “Detecting Discrimination.” Journal of Economic Perspectives 12, no. 2: 101–116. 1999 (with Robert LaLonde and Jeffrey Smith). “The Economics and Econometrics of Active Labor Market Programs.” In Orley Ashenfelter and David Card, eds., Handbook of Labor Economics. Amsterdam: North-Holland. Chap. 31. 2002 (with Pedro Carneiro). “The Evidence on Credit Constraints in Post-secondary Schooling.” Economic Journal 112: 705–734.   (0 COMMENTS)

  William Jevons was one of three men to simultaneously advance the so-called marginal revolution. Working in complete independence of one another—Jevons in Manchester, England; leon walras in Lausanne, Switzerland; and carl menger in Vienna—each scholar developed the theory of marginal utility to understand and explain consumer behavior. The theory held that the utility (value) of each additional unit of a commodity—the marginal utility—is less and less to the consumer. When you are thirsty, for example, you get great utility from a glass of water. Once your thirst is quenched, the second and third glasses are less and less appealing. Feeling waterlogged, you will eventually refuse water altogether. “Value,” said Jevons, “depends entirely upon utility.” This statement marked a significant departure from the classical theory of value, which stated that value derived from the labor used to produce a product or from the cost of production more generally. Thus began the neoclassical school, which is still the dominant one in economics today. Jevons went on to define the “equation of exchange,” which shows that for a consumer to be maximizing his or her utility, the ratio of the marginal utility of each item consumed to its price must be equal. If it is not, then he or she can, with a given income, reallocate consumption and get more utility. Take, for example, a consumer whose marginal utility from oranges is 10 “utils,” and from cookies 4 utils, when oranges and cookies are both priced at $.50 each. The consumer’s ratio of marginal utility to price for oranges is 10/$.50, or 20, and for cookies is 4/$.50, or 8. Jevons would have said (and modern economists would agree) that this does not satisfy the equation of exchange, and therefore the consumer will change purchases. Specifically, the consumer could increase utility by spending $.50 less on cookies and using the money to buy oranges. He would lose 4 utils on the cookies, but gain 10 on the oranges, for a net gain of 6 utils. He will have this incentive to reallocate purchases until the equation of exchange holds (i.e., until the marginal utility of oranges falls and the marginal utility of cookies rises to a point where, as a ratio to their prices, they are equal). Of course, as is true with most new developments in economic theory, one can always find earlier writers who said some of the same things. Jevons’s role in the marginal revolution is no exception. Much of what he said had been said earlier by Hermann Gossen in Germany, Jules Dupuit and Antoine Cournot in France, and Samuel Longfield in Britain. Yet historians of economic thought are sure that Jevons had never read them. Jevons put much less thought into the production side of economics. It is ironic, therefore, that he became famous in Britain for his book The Coal Question, in which he wrote that Britain’s industrial vitality depended on coal and, therefore, would decline as that resource was exhausted. As coal reserves ran out, he wrote, the price of coal would rise. This would make it feasible for producers to extract coal from poorer or deeper seams. He also argued that America would rise to become an industrial superpower. Although his forecast was right for both Britain and America, and he was right about the incentive to mine more costly seams, he was almost surely wrong that the main factor was the cost of coal. Jevons failed to appreciate the fact that as the price of an energy source rises, entrepreneurs have a strong incentive to invent, develop, and produce alternate sources. In particular, he did not anticipate oil or natural gas. Also, he did not take account of the incentive, as the price of coal rose, to use it more efficiently or to develop technology that brought down the cost of discovering and mining (see natural resources). Born in Liverpool, England, Jevons studied chemistry and botany at University College, London. Because of the bankruptcy of his father’s business in 1847, Jevons left school to take up the position of assayer at the Mint in Sydney, Australia. He remained there five years, resuming his studies at University College on his return to England. He was later appointed to the post of chair in political economy at his alma mater and retired from there in 1880. Two years later, with a number of unfinished books in process, Jevons drowned while swimming. He was forty-six. Selected Works   1863. A Serious Fall in the Value of Gold Ascertained, and Its Social Effects Set Forth. 1863. Reprinted in Jevons, Investigations in Currency and Finance. London: Macmillan, 1884. 1865. The Coal Question. 1st ed. London: Macmillan. 1866. The Coal Question. 2d ed. London: Macmillan. Available online at: http://www.econlib.org/library/YPDBooks/Jevons/jvnCQ.html. 1871. The Theory of Political Economy. Reprint. Edited by R. D. Collison Black. Harmondsworth: Penguin Books, 1970. 1875. Money and the Mechanism of Exchange. London: C. Kegan Paul. Available online at: http://www.econlib.org/library/YPDBooks/Jevons/jvnMME.html. 1875. “The Solar Period and the Price of Corn.” First published in Jevons, Investigations in Currency and Finance. London: Macmillan, 1884. Pp. 194–205. 1881. “Richard Cantillon and the Nationality of Political Economy.” First published in the Contemporary Review. Available online at: http://www.econlib.org/library/NPDBooks/Cantillon/cntNT8.html. 1888. The Theory of Political Economy. 3d ed. Available online at: http://www.econlib.org/library/YPDBooks/Jevons/jvnPE.html. 1894. Investigations in Currency and Finance. Edited and with an introduction by H. S. Foxwell. London: Macmillan. 1906. The Coal Question. 3d ed. Revised and edited by A. W. Flux. London: Macmillan.   (0 COMMENTS)

Frank H. Knight was one of the founders of the so-called Chicago school of economics, of which milton friedman and george stigler were the leading members from the 1950s to the 1980s. Knight made his reputation with his book Risk, Uncertainty, and Profit, which was based on his Ph.D. dissertation. In it Knight set out to explain why “perfect competition” would not necessarily eliminate profits. His explanation was “uncertainty,” which Knight distinguished from risk. According to Knight, “risk” refers to a situation in which the probability of an outcome can be determined, and therefore the outcome insured against. “Uncertainty,” by contrast, refers to an event whose probability cannot be known. Knight argued that even in long-run equilibrium, entrepreneurs would earn profits as a return for putting up with uncertainty. Knight’s distinction between risk and uncertainty is still taught in economics classes today. Knight made three other important contributions to economics. One is The Economic Organization, a set of lecture notes originally published in 1933. In it he laid out the circular flow model of the economy and emphasized that investments will be made until the returns to investments in each use are equal at the margin. These elements still survive in textbooks today. Knight’s famous article “Some Fallacies in the Interpretation of Social Cost,” in which he took on arthur pigou’s view that congestion of roads justified taxation of roads, is another of his contributions to economics. Knight showed that if roads were privately owned, road owners would set tolls that would reduce congestion. Therefore, no government intervention was required. Knight’s final contribution is his work on capital theory in the 1930s. Knight criticized eugen von böhm-bawerk’s view that capital could be measured as a period of production, and is widely thought to have won the debate over the Austrian concept of capital (see austrian school of economics). But Knight was much more than an economist. He was also a social philosopher, and most of his writings are in social philosophy rather than technical economics. A strong believer in freedom and a strong critic of social engineering, Knight worried that freedom would be undermined by increases in monopoly and income inequality. George Stigler tells of Milton Friedman challenging Knight’s view

In 2003, econometrician Clive Granger, along with econometrician Robert Engle, received the Nobel Prize in economics. Granger’s award was “for methods of analyzing economic time series with common trends (cointegration).” Trained in statistics, Granger specializes in the behavior of time-series data (i.e., data that are recorded in calendar sequence, annually or at shorter or longer intervals). Early in his career, the best-developed statistics assumed that time series were stationary—that is, that they tended to vary randomly around a common long-run mean (or average) value or around a nonrandom trend. Many economic time series, however, appear to be nonstationary—to follow processes related to the random walk. The term “random walk” is suggested by the metaphor of a drunken man stumbling in the street—just as likely to go one way as another. A time series is a random walk when the next period’s value is as likely to be higher as it is to be lower, so that the best forecast of the next period’s value is just whatever today’s value happens to be. For lack of better techniques, economists often applied statistics designed for stationary data to nonstationary data. In 1974, Granger and coauthor Paul Newbold, building on the 1920s work of the English statistician G. Udny Yule, showed that pairs of nonstationary time series could frequently display highly significant correlations when there was no causal connection between them. For example, the U.S. federal debt and the number of deaths due to AIDS between 1981 and 2000 are highly correlated but are clearly not causally connected. Such “nonsense correlations” called into question the meaningfulness of many econometric studies. Short-run changes in time series are frequently stationary, even when the time series themselves are nonstationary in the long run. So one strategy in the face of nonstationary data was to study only short-run changes. But Granger (working with Engle) realized that such a strategy threw away valuable information. Not all long-run associations between nonstationary time series are nonsense. Suppose that the randomly walking drunk has a faithful (and sober) friend who follows him down the street from a safe distance to make sure he does not injure himself. Because he is following the drunk, the friend, viewed in isolation, also appears to follow a random walk, yet his path is not aimless; it is largely predictable, conditional on knowing where the drunk is. Granger and Engle coined the term “cointegration” to describe the genuine relationship between two nonstationary time series. Time series are “cointegrated” when the difference between them is itself stationary—the friend never gets too far away from the drunk, but, on average, stays a constant distance back.1 Many economic time series are nonstationary. For example, over long periods, federal revenues and spending appear to be nonstationary, but they also appear to be cointegrated, in the sense that when they are far out of line, they tend to be drawn back into close proximity. Granger developed econometric methods for testing whether the relationships among these time series were genuine cointegrating relationships or nonsense, and for correctly estimating the genuine relationships. In addition to his work on cointegration, Granger is famous for his earlier development of the concept of Granger causality, an idea with roots in the work of the mathematician Norbert Wiener. The current value of a time series is often predictable from its own past values. For example, GDP this quarter is imperfectly predicted from information about GDP over the past few years. A second time series is said to “Granger-cause” another if its past values improve the prediction one would get just from the past values of the first time series. Granger causality is related to cointegration. Granger and Engle demonstrated that when two variables are cointegrated, then at least one of them must Granger-cause the other. The first important application of Granger-causality to economics appears in a 1972 article by Christopher Sims in which he showed that money Granger-causes nominal GNP, apparently bolstering the monetarist idea that fluctuations in money are the major cause of business cycles (see monetarism and milton friedman).2 In the debate that followed, the limits of Granger-causality were clarified: the concept concerns predictability and not control, so that a finding that money Granger-causes GNP does not imply that the Federal Reserve has an effective instrument to steer the economy. While Granger himself had referred simply to “causality,” the adjective “Granger” is now always attached to his idea to distinguish it from causality based on control.3 Granger was born in Wales. He attended the University of Nottingham, where he earned a B.A. in mathematics and economics in 1955 and a Ph.D. in statistics in 1959. He was on the faculty of the University of Nottingham until 1973, with occasional visiting positions at other universities. In 1973, he became a professor at the University of California at San Diego. He retired in 2003, just two months before winning the Nobel Prize. He was knighted in 2005. In reminiscing about his childhood, Sir Clive wrote, “A teacher told my mother that ‘I would never become successful,’ which illustrates the difficulty of long-run forecasting on inadequate data.” About the Author Kevin D. Hoover is professor in the departments of economics and philosophy at Duke University. He is past president of the History of Economics Society, past chairman of the International Network for Economic Method, and editor of the Journal of Economic Methodology. Selected Works   1969. “Investigating Causal Relations by Econometric Models and Cross-Spectral Methods.” Econometrica 37: 424–438. 1974 (with Paul Newbold). “Spurious Regressions in Econometrics.” Journal of Econometrics 2: 111–120. 1981. “Some Properties of Time Series Data and Their Use in Econometric Model Specification.” Journal of Econometrics 16: 121–130. 1987 (with Robert Engle). “Co-integration and Error-Correction: Representation, Estimation and Testing.” Econometrica 55: 251–276.   Footnotes 1. A fuller explication of the notion of cointegration is found in Kevin D. Hoover, “Nonstationary Time Series, Cointegration, and the Principle of the Common Cause,” British Journal for the Philosophy of Science 54 (December 2003): 527–551.   2. Christopher Sims, “Money, Income, and Causality,” American Economic Review 62 (September 1972): 540–552.   3. See Kevin D. Hoover, Causality in Macroeconomics (Cambridge: Cambridge University Press, 2001), esp. chap. 8.   (0 COMMENTS)

In 1989 Norwegian economist Trygve Haavelmo was awarded the Nobel Prize “for his clarification of the probability theory foundations of econometrics and his analyses of simultaneous economic structures.” He made two main contributions in econometrics. The first is a 1943 article that shows some of the statistical implications of simultaneous equations. The second is a 1944 article that bases econometrics more firmly on probability theory. During the war years Haavelmo worked for the Norwegian government in the United States. He was a professor of economics at the University of Oslo from 1948 until his retirement in 1979. Selected Works   1943. “The Statistical Implications of a System of Simultaneous Equations.” Econometrica 11 (January): 1–12. 1944. “The Probability Approach in Econometrics.” Supplement to Econometrica 12 (July): S1–S115. 1960. A Study in the Theory of Investment. Chicago: University of Chicago Press.   (0 COMMENTS)

Roy Harrod is credited with getting twentieth-century economists thinking about economic growth. Harrod built on Keynes’s theory of income determination. The Harrod-Domar model (named for Harrod and Evsey Domar, who worked on the concept independently) is explained in Towards a Dynamic Economics, though Harrod’s first version of the idea was published in “An Essay in Dynamic Theory.” Harrod introduced the concepts of warranted growth, natural growth, and actual growth. The warranted growth rate is the growth rate at which all saving is absorbed into investment. If, for example, people save 10 percent of their income, and the economy’s ratio of capital to output is four, the economy’s warranted growth rate is 2.5 percent (ten divided by four). This is the growth rate at which the ratio of capital to output would stay constant at four. The natural growth rate is the rate required to maintain full employment. If the labor force grows at 2 percent per year, then to maintain full employment, the economy’s annual growth rate must be 2 percent (assuming no growth in productivity). Harrod’s model identified two kinds of problems that could arise with growth rates. The first was that actual growth was determined by the rate of saving and that natural growth was determined by the growth of the labor force. There was no necessary reason for actual growth to equal natural growth, and therefore the economy had no inherent tendency to reach full employment. This problem resulted from Harrod’s assumptions that the wage rate is fixed and that the economy must use labor and capital in the same proportions. But most economists now believe that wage rates can fall when the labor force increases, although they disagree about how quickly. And virtually all mainstream economists agree that the ratio of labor and capital that businesses want to use depends on wage rates and on the price of capital. Therefore, one of the main problems implied by Harrod’s model does not appear to be much of a problem after all. The second problem implied by Harrod’s model was unstable growth. If companies adjusted investment according to what they expected about future demand, and the anticipated demand was forthcoming, warranted growth would equal actual growth. But if actual demand exceeded anticipated demand, they would have underinvested and would respond by investing further. This investment, however, would itself cause growth to rise, requiring even further investment. Result: explosive growth. The same story can be told in reverse if actual demand should fall short of anticipated demand. The result then would be a deceleration of growth. This property of Harrod’s growth model became known as Harrod’s knife-edge. Here again, though, this uncomfortable conclusion was the result of two unrealistic assumptions made by Harrod: (1) companies naïvely base their investment plans only on anticipated output, and (2) investment is instantaneous. In spite of these limitations, Harrod did get economists to start thinking about the causes of growth as carefully as they had thought about other issues, and that is his greatest contribution to the field. Harrod was a close colleague of Keynes, and his official biographer. The Life of John Maynard Keynes was a second, and only slightly less theoretical, product of Harrod’s long association with Keynes. Born in Norfolk, England, Roy Harrod graduated from New College, Oxford. After spending a term at King’s College, Cambridge, where he came in contact with Keynes, Harrod returned to Oxford to administer and teach at Christ Church College until his retirement in 1967. Assar Lindbeck, the chairman of the Nobel Prize Committee, wrote that Harrod would have been awarded a Nobel Prize if he had lived longer. The backlog of other economists awarded the Nobel Prize caused Harrod to miss getting it. Selected Works   1936. The Trade Cycle: An Essay. Oxford: Oxford University Press. 1939. “An Essay in Dynamic Theory.” Economic Journal 49 (March): 14–33. 1948. Towards a Dynamic Economics: Some Recent Developments of Economic Theory and Their Application to Policy. London: Macmillan. 1951. The Life of John Maynard Keynes. London: Macmillan.   (0 COMMENTS)

John C. Harsanyi was corecipient (with John Nash and Reinhard Selten) of the 1994 Nobel Prize in economics “for their pioneering analysis of equilibria in the theory of non-cooperative games.” Harsanyi’s interest in working on game theory was triggered when he read John Nash’s contributions of the early 1950s. He took up where Nash left off. Nash had focused on games in which each player knew the other players’ preferences. Harsanyi wondered how things would change when he introduced the (often more realistic) assumption that players have incomplete information about other players. He assumed that each player is one of several “types.” Each type represents a set of possible preferences for the player and a set of subjective probabilities that that player places on the other players’ types. Each player then chooses a strategy for each of his types. Harsanyi showed that for every game with incomplete information, there is an equivalent game with complete information. The Nobel committee also noted Harsanyi’s contributions to moral philosophy. As early as 1955, Harsanyi had pioneered the “veil of ignorance” concept (though not by that name) that philosopher John Rawls made famous in his 1971 book, A Theory of Justice. Harsanyi was a strong defender of the “rule of utilitarianism,” the idea that the most ethical act is to follow the rule that will yield the most happiness. During his early years Harsanyi escaped from two of the twentieth century’s most vicious totalitarian regimes. He grew up in Hungary in the 1920s and 1930s. He had wanted to study philosophy and mathematics, but because he was of Jewish origin and saw Hitler’s steadily rising influence, he took his parents’ advice and became a pharmacy student, knowing that that would help him maintain a military deferment. In the language of game theory, he “looked forward and reasoned back.” After the German army occupied Hungary, he worked in a “labor unit”—that is, he was a slave—from May to November 1944. When the German government tried to deport him to a concentration camp in Austria, he escaped from the railway station in Budapest. Harsanyi earned his Ph.D. in philosophy at the University of Budapest in 1947 and became a junior faculty member at the University Institute of Sociology. He resigned from the institute in June 1948 because, he recalled, “the political situation no longer permitted them to employ an outspoken anti-Marxist as I had been.” The fact that his wife “was continually harassed by her Communist classmates to break up with” Harsanyi “made her realize … that Hungary was becoming a completely Stalinist country.” In April 1950, he and his wife escaped across the Hungarian border to Austria. “We were very lucky not to be stopped or shot at by the Hungarian border guards,” he wrote.1 Harsanyi moved to Australia, where he spent most of the 1950s. He earned a master’s degree in economics in 1953 and spent two years at Stanford, beginning in 1956, where he earned his Ph.D. in economics. In 1964 he became a professor at the University of California at Berkeley. Selected Works   1950. “Approaches to the Bargaining Problem Before and After the Theory of Games: A Critical Discussion of Zeuthen’s Hicks’s and Nash’s Theories.” Econometrica 24: 144–157. 1955. “Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility.” Journal of Political Economy 63: 309–321. 1967–1968. “Games with Incomplete Information Played by ‘Bayesian’ Players.” Parts I–III. Management Science 14: 159–182, 320–324, and 486–502. 1973. “Games with Randomly Distributed Payoffs: A New Rationale for Mixed Strategy Equilibrium Points.” International Journal of Game Theory 2: 235–250. 1975. “Can the Maximin Principle Serve as a Basis for Morality? A Critique of John Rawls’s Theory.” American Political Science Review 69: 594–606. 1985. “Does Reason Tell Us What Moral Code to Follow, and Indeed, to Follow Any Moral Code at All?” Ethics 96: 42–55.   Footnotes 1. See http://nobelprize.org/economics/laureates/1994/harsanyi-autobio.html.   (0 COMMENTS)