An Eponymous Dictionary of Economics
An Eponymous Dictionaryof EconomicsA Guide to Laws and Theorems Named after EconomistsEdited byJulio SeguraProfessor of Ec...
© Carlos Rodríguez Braun and Julio Segura 2004All rights reserved. No part of this publication may be reproduced, stored i...
ContentsList of contributors and their entries               xiiiPreface                                             xxvii...
vi ContentsBuchanan’s clubs theory                          34Buridan’s ass                                    35Cagan’s h...
Contents   viiEngle–Granger method                                            72Euclidean spaces                          ...
viii   ContentsHeckscher–Ohlin theorem                    109Herfindahl–Hirschman index                 111Hermann–Schmoll...
Contents    ixLagrange multiplier test                                      144Lancaster’s characteristics                ...
x   ContentsNewton–Raphson method                   185Neyman–Fisher theorem                   186Neyman–Pearson test     ...
Contents    xiSamuelson condition                                   225Sard’s theorem                                     ...
xii   ContentsVeblen effect good                                                264Verdoorn’s law                         ...
Contributors and their entriesAlbarrán, Pedro, Universidad Carlos III, Madrid, SpainPigou taxAlbert López-Ibor, Rocío, Uni...
xiv   Contributors and their entriesAyuso, Juan, Banco de España, Madrid, SpainAllais paradox; Ellsberg paradoxAznar, Anto...
Contributors and their entries   xvCallealta, Francisco J., Universidad de Alcalá de Henares, Alcalá de Henares, Madrid,Sp...
xvi   Contributors and their entriesDíaz-Emparanza, Ignacio, Instituto de Economía Aplicada, Universidad del País Vasco-EH...
Contributors and their entries   xviiFreire Rubio, Mª Teresa, Escuela Superior de Gestión Comercial y Marketing, Madrid,Sp...
xviii   Contributors and their entriesGuisán, M. Cármen, Universidad de Santiago de Compostela, Santiago de Compostela, AC...
Contributors and their entries   xixLasheras, Miguel A., Grupo CIM, Madrid, SpainBaumol’s contestable markets; Ramsey’s in...
xx Contributors and their entriesMartín-Román, Angel, Universidad de Valladolid, Segovia, SpainEdgeworth boxMartínez, Dieg...
Contributors and their entries   xxiNovales, Alfonso, Universidad Complutense, Madrid, SpainRadner’s turnpike propertyNúñe...
xxii   Contributors and their entriesPolo, Clemente, Universitat Autònoma de Barcelona, Barcelona, SpainLancaster–Lipsey’s...
Contributors and their entries   xxiiiRodríguez Braun, Carlos, Universidad Complutense, Madrid, SpainClark–Fisher hypothes...
xxiv   Contributors and their entriesSantos-Redondo, Manuel, Universidad Complutense, Madrid, SpainSchumpeterian entrepene...
Contributors and their entries   xxvUrbanos Garrido, Rosa María, Universidad Complutense, Madrid, SpainWilliams’s fair inn...
PrefaceRobert K. Merton defined eponymy as ‘the practice of affixing the name of the scientist to allor part of what he ha...
Mathematical notationA vector is usually denoted by a lower case italic letter such as x or y, and sometimes is repre-sent...
AAdam Smith problem                                work. More recent readings maintain that theIn the third quarter of the...
2   Adam Smith’s invisible handdiscussion of the origins of polytheism: ‘in              As every individual, therefore, e...
Akerlof’s ‘lemons’ 3Smith, Adam (1795), Essays on Philosophical Subjects,    2001 (jointly with A. Michael Spence and   re...
4   Allais paradoxbeen extensively applied to the study of                  dropped, your choices above (as mostmany other...
Areeda–Turner predation rule     5basis of their claim was that companies that       The adequacy of average variable cost...
6   Arrow’s impossibility theoremBibliography                                              formal framework. Consider a so...
Arrow’s impossibility theorem     7A first quick answer would be to say that the    studied and proposed different methods...
8   Arrow’s learning by doingparticular, the condition of independence of               Arrow’s learning by doingirrelevan...
Arrow–Debreu general equilibrium model         9Bibliography                                             to deliver amount...
10 Arrow–Pratt’s measure of risk aversionaggregate amount of income distributed            theory is that it constitutes a...
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Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg
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Segura j., braun c. (eds.) An eponymous Dictionary of Economics (elgar, 2004)(isbn 1843760290)(309s) gg

  1. 1. An Eponymous Dictionary of Economics
  2. 2. An Eponymous Dictionaryof EconomicsA Guide to Laws and Theorems Named after EconomistsEdited byJulio SeguraProfessor of Economic Theory, Universidad Complutense, Madrid, Spain,andCarlos Rodríguez BraunProfessor of History of Economic Thought, Universidad Complutense,Madrid, SpainEdward ElgarCheltenham, UK • Northampton, MA, USA
  3. 3. © Carlos Rodríguez Braun and Julio Segura 2004All rights reserved. No part of this publication may be reproduced, stored in a retrievalsystem or transmitted in any form or by any means, electronic, mechanical orphotocopying, recording, or otherwise without the prior permission of the publisher.Published byEdward Elgar Publishing LimitedGlensanda HouseMontpellier ParadeCheltenhamGlos GL50 1UAUKEdward Elgar Publishing, Inc.136 West StreetSuite 202NorthamptonMassachusetts 01060USAA catalogue record for this bookis available from the British LibraryISBN 1 84376 029 0 (cased)Typeset by Cambrian Typesetters, Frimley, SurreyPrinted and bound in Great Britain by MPG Books Ltd, Bodmin, Cornwall
  4. 4. ContentsList of contributors and their entries xiiiPreface xxviiAdam Smith problem 1Adam Smith’s invisible hand 1Aitken’s theorem 3Akerlof’s ‘lemons’ 3Allais paradox 4Areeda–Turner predation rule 4Arrow’s impossibility theorem 6Arrow’s learning by doing 8Arrow–Debreu general equilibrium model 9Arrow–Pratt’s measure of risk aversion 10Atkinson’s index 11Averch–Johnson effect 12Babbage’s principle 13Bagehot’s principle 13Balassa–Samuelson effect 14Banach’s contractive mapping principle 14Baumol’s contestable markets 15Baumol’s disease 16Baumol–Tobin transactions demand for cash 17Bayes’s theorem 18Bayesian–Nash equilibrium 19Becher’s principle 20Becker’s time allocation model 21Bellman’s principle of optimality and equations 23Bergson’s social indifference curve 23Bernoulli’s paradox 24Berry–Levinsohn–Pakes algorithm 25Bertrand competition model 25Beveridge–Nelson decomposition 27Black–Scholes model 28Bonferroni bound 29Boolean algebras 30Borda’s rule 30Bowley’s law 31Box–Cox transformation 31Box–Jenkins analysis 32Brouwer fixed point theorem 34
  5. 5. vi ContentsBuchanan’s clubs theory 34Buridan’s ass 35Cagan’s hyperinflation model 36Cairnes–Haberler model 36Cantillon effect 37Cantor’s nested intervals theorem 38Cass–Koopmans criterion 38Cauchy distribution 39Cauchy’s sequence 39Cauchy–Schwarz inequality 40Chamberlin’s oligopoly model 41Chipman–Moore–Samuelson compensation criterion 42Chow’s test 43Clark problem 43Clark–Fisher hypothesis 44Clark–Knight paradigm 44Coase conjecture 45Coase theorem 46Cobb–Douglas function 47Cochrane–Orcutt procedure 48Condorcet’s criterion 49Cournot aggregation condition 50Cournot’s oligopoly model 51Cowles Commission 52Cox’s test 53Davenant–King law of demand 54Díaz–Alejandro effect 54Dickey–Fuller test 55Director’s law 56Divisia index 57Dixit–Stiglitz monopolistic competition model 58Dorfman–Steiner condition 60Duesenberry demonstration effect 60Durbin–Watson statistic 61Durbin–Wu–Hausman test 62Edgeworth box 63Edgeworth expansion 65Edgeworth oligopoly model 66Edgeworth taxation paradox 67Ellsberg paradox 68Engel aggregation condition 68Engel curve 69Engel’s law 71
  6. 6. Contents viiEngle–Granger method 72Euclidean spaces 72Euler’s theorem and equations 73Farrell’s technical efficiency measurement 75Faustmann–Ohlin theorem 75Fisher effect 76Fisher–Shiller expectations hypothesis 77Fourier transform 77Friedman’s rule for monetary policy 79Friedman–Savage hypothesis 80Fullarton’s principle 81Fullerton–King’s effective marginal tax rate 82Gale–Nikaido theorem 83Gaussian distribution 84Gauss–Markov theorem 86Genberg–Zecher criterion 87Gerschenkron’s growth hypothesis 87Gibbard–Satterthwaite theorem 88Gibbs sampling 89Gibrat’s law 90Gibson’s paradox 90Giffen goods 91Gini’s coefficient 91Goodhart’s law 92Gorman’s polar form 92Gossen’s laws 93Graham’s demand 94Graham’s paradox 95Granger’s causality test 96Gresham’s law 97Gresham’s law in politics 98Haavelmo balanced budget theorem 99Hamiltonian function and Hamilton–Jacobi equations 100Hansen–Perlof effect 101Harberger’s triangle 101Harris–Todaro model 102Harrod’s technical progress 103Harrod–Domar model 104Harsanyi’s equiprobability model 105Hausman’s test 105Hawkins–Simon theorem 106Hayekian triangle 107Heckman’s two-step method 108
  7. 7. viii ContentsHeckscher–Ohlin theorem 109Herfindahl–Hirschman index 111Hermann–Schmoller definition 111Hessian matrix and determinant 112Hicks compensation criterion 113Hicks composite commodities 113Hicks’s technical progress 113Hicksian demand 114Hicksian perfect stability 115Hicks–Hansen model 116Hodrick–Prescott decomposition 118Hotelling’s model of spatial competition 118Hotelling’s T2 statistic 119Hotelling’s theorem 120Hume’s fork 121Hume’s law 121Itô’s lemma 123Jarque–Bera test 125Johansen’s procedure 125Jones’s magnification effect 126Juglar cycle 126Kakutani’s fixed point theorem 128Kakwani index 128Kalai–Smorodinsky bargaining solution 129Kaldor compensation criterion 129Kaldor paradox 130Kaldor’s growth laws 131Kaldor–Meade expenditure tax 131Kalman filter 132Kelvin’s dictum 133Keynes effect 134Keynes’s demand for money 134Keynes’s plan 136Kitchin cycle 137Kolmogorov’s large numbers law 137Kolmogorov–Smirnov test 138Kondratieff long waves 139Koopman’s efficiency criterion 140Kuhn–Tucker theorem 140Kuznets’s curve 141Kuznets’s swings 142Laffer’s curve 143Lagrange multipliers 143
  8. 8. Contents ixLagrange multiplier test 144Lancaster’s characteristics 146Lancaster–Lipsey’s second best 146Lange–Lerner mechanism 147Laspeyres index 148Lauderdale’s paradox 148Learned Hand formula 149Lebesgue’s measure and integral 149LeChatelier principle 150Ledyard–Clark–Groves mechanism 151Leontief model 152Leontief paradox 153Lerner index 154Lindahl–Samuelson public goods 155Ljung–Box statistics 156Longfield paradox 157Lorenz’s curve 158Lucas critique 158Lyapunov’s central limit theorem 159Lyapunov stability 159Mann–Wald’s theorem 161Markov chain model 161Markov switching autoregressive model 162Markowitz portfolio selection model 163Marshall’s external economies 164Marshall’s stability 165Marshall’s symmetallism 166Marshallian demand 166Marshall–Lerner condition 167Maskin mechanism 168Minkowski’s theorem 169Modigliani–Miller theorem 170Montaigne dogma 171Moore’s law 172Mundell–Fleming model 172Musgrave’s three branches of the budget 173Muth’s rational expectations 175Myerson revelation principle 176Nash bargaining solution 178Nash equilibrium 179Negishi’s stability without recontracting 181von Neumann’s growth model 182von Neumann–Morgenstern expected utility theorem 183von Neumann–Morgenstern stable set 185
  9. 9. x ContentsNewton–Raphson method 185Neyman–Fisher theorem 186Neyman–Pearson test 187Occam’s razor 189Okun’s law and gap 189Paasche index 192Palgrave’s dictionaries 192Palmer’s rule 193Pareto distribution 194Pareto efficiency 194Pasinetti’s paradox 195Patman effect 197Peacock–Wiseman’s displacement effect 197Pearson chi-squared statistics 198Peel’s law 199Perron–Frobenius theorem 199Phillips curve 200Phillips–Perron test 201Pigou effect 203Pigou tax 204Pigou–Dalton progressive transfers 204Poisson’s distribution 205Poisson process 206Pontryagin’s maximun principle 206Ponzi schemes 207Prebisch–Singer hypothesis 208Radner’s turnpike property 210Ramsey model and rule 211Ramsey’s inverse elasticity rule 212Rao–Blackwell’s theorem 213Rawls’s justice criterion 213Reynolds–Smolensky index 214Ricardian equivalence 215Ricardian vice 216Ricardo effect 217Ricardo’s comparative costs 218Ricardo–Viner model 219Robinson–Metzler condition 220Rostow’s model 220Roy’s identity 222Rubinstein’s model 222Rybczynski theorem 223
  10. 10. Contents xiSamuelson condition 225Sard’s theorem 225Sargan test 226Sargant effect 227Say’s law 227Schmeidler’s lemma 229Schumpeter’s vision 230Schumpeterian entrepreneur 230Schwarz criterion 231Scitovsky’s community indifference curve 232Scitovsky’s compensation criterion 232Selten paradox 233Senior’s last hour 234Shapley value 235Shapley–Folkman theorem 236Sharpe’s ratio 236Shephard’s lemma 237Simon’s income tax base 238Slutksky equation 238Slutsky–Yule effect 240Snedecor F-distribution 241Solow’s growth model and residual 242Sonnenschein–Mantel–Debreu theorem 244Spencer’s law 244Sperner’s lemma 245Sraffa’s model 245Stackelberg’s oligopoly model 246Stigler’s law of eponymy 247Stolper–Samuelson theorem 248Student t-distribution 248Suits index 250Swan’s model 251Tanzi–Olivera effect 252Taylor rule 252Taylor’s theorem 253Tchébichef’s inequality 254Theil index 254Thünen’s formula 255Tiebout’s voting with the feet process 256Tinbergen’s rule 257Tobin’s q 257Tobin’s tax 258Tocqueville’s cross 260Tullock’s trapezoid 261Turgot–Smith theorem 262
  11. 11. xii ContentsVeblen effect good 264Verdoorn’s law 264Vickrey auction 265Wagner’s law 266Wald test 266Walras’s auctioneer and tâtonnement 268Walras’s law 268Weber–Fechner law 269Weibull distribution 270Weierstrass extreme value theorem 270White test 271Wicksell effect 271Wicksell’s benefit principle for the distribution of tax burden 273Wicksell’s cumulative process 274Wiener process 275Wiener–Khintchine theorem 276Wieser’s law 276Williams’s fair innings argument 277Wold’s decomposition 277Zellner estimator 279
  12. 12. Contributors and their entriesAlbarrán, Pedro, Universidad Carlos III, Madrid, SpainPigou taxAlbert López-Ibor, Rocío, Universidad Complutense, Madrid, SpainLearned Hand formulaAlbi, Emilio, Universidad Complutense, Madrid, SpainSimons’s income tax baseAlmenar, Salvador, Universidad de Valencia, Valencia, SpainEngel’s lawAlmodovar, António, Universidade do Porto, Porto, PortugalWeber–Fechner lawAlonso, Aurora, Universidad del País Vasco-EHU, Bilbao, SpainLucas critiqueAlonso Neira, Miguel Ángel, Universidad Rey Juan Carlos, Madrid, SpainHayekian triangleAndrés, Javier, Universidad de Valencia, Valencia, SpainPigou effectAparicio-Acosta, Felipe M., Universidad Carlos III, Madrid, SpainFourier transformAragonés, Enriqueta, Universitat Autònoma de Barcelona, Barcelona, SpainRawls justice criterionArellano, Manuel, CEMFI, Madrid, SpainLagrange multiplier testArgemí, Lluís, Universitat de Barcelona, Barcelona, SpainGossen’s lawsArruñada, Benito, Universitat Pompeu Fabra, Barcelona, SpainBaumol’s diseaseArtés Caselles, Joaquín, Universidad Complutense, Madrid, SpainLeontief paradoxAstigarraga, Jesús, Universidad de Deusto, Bilbao, SpainPalgrave’s dictionariesAvedillo, Milagros, Comisión Nacional de Energía, Madrid, SpainDivisia indexAyala, Luis, Universidad Rey Juan Carlos, Madrid, SpainAtkinson index
  13. 13. xiv Contributors and their entriesAyuso, Juan, Banco de España, Madrid, SpainAllais paradox; Ellsberg paradoxAznar, Antonio, Universidad de Zaragoza, Zaragoza, SpainDurbin–Wu–Hausman testBacaria, Jordi, Universitat Autònoma de Barcelona, Barcelona, SpainBuchanan’s clubs theoryBadenes Plá, Nuria, Universidad Complutense, Madrid, SpainKaldor–Meade expenditure tax; Tiebout’s voting with the feet process; Tullock’s trapezoidBarberá, Salvador, Universitat Autònoma de Barcelona, Barcelona, SpainArrow’s impossibility theoremBel, Germà, Universitat de Barcelona, Barcelona, SpainClark problem; Clark–Knight paradigmBentolila, Samuel, CEMFI, Madrid, SpainHicks–Hansen modelBergantiños, Gustavo, Universidad de Vigo, Vigo, Pontevedra, SpainBrouwer fixed point theorem; Kakutani’s fixed point theoremBerganza, Juan Carlos, Banco de España, Madrid, SpainLerner indexBerrendero, José R., Universidad Autónoma, Madrid, SpainKolmogorov–Smirnov testBlanco González, María, Universidad San Pablo CEU, Madrid, SpainCowles CommissionBobadilla, Gabriel F., Omega-Capital, Madrid, SpainMarkowitz portfolio selection model; Fisher–Shiller expectations hypothesisBolado, Elsa, Universitat de Barcelona, Barcelona, SpainKeynes effectBorrell, Joan-Ramon, Universitat de Barcelona, Barcelona, SpainBerry–Levinsohn–Pakes algorithmBover, Olympia, Banco de España, Madrid, SpainGaussian distributionBru, Segundo, Universidad de Valencia, Valencia, SpainSenior’s last hourBurguet, Roberto, Universitat Autònoma de Barcelona, Barcelona, SpainWalras’s auctioneer and tâtonnementCabrillo, Francisco, Universidad Complutense, Madrid, SpainCoase theoremCalderón Cuadrado, Reyes, Universidad de Navarra, Pamplona, SpainHermann–Schmoller definition
  14. 14. Contributors and their entries xvCallealta, Francisco J., Universidad de Alcalá de Henares, Alcalá de Henares, Madrid,SpainNeyman–Fisher theoremCalsamiglia, Xavier, Universitat Pompeu Fabra, Barcelona, SpainGale–Nikaido theoremCalzada, Joan, Universitat de Barcelona, Barcelona, SpainStolper–Samuelson theoremCandeal, Jan Carlos, Universidad de Zaragoza, Zaragoza, SpainCantor’s nested intervals theorem; Cauchy’s sequenceCarbajo, Alfonso, Confederación Española de Cajas de Ahorro, Madrid, SpainDirector’s lawCardoso, José Luís, Universidad Técnica de Lisboa, Lisboa, PortugalGresham’s lawCarnero, M. Angeles, Universidad Carlos III, Madrid, SpainMann–Wald’s theoremCarrasco, Nicolás, Universidad Carlos III, Madrid, SpainCox’s test; White testCarrasco, Raquel, Universidad Carlos III, Madrid, SpainCournot aggregation condition; Engel aggregation conditionCarrera, Carmen, Universidad Complutense, Madrid, SpainSlutsky equationCaruana, Guillermo, CEMFI, Madrid, SpainHicks composite commoditiesCastillo, Ignacio del, Ministerio de Hacienda, Madrid, SpainFullarton’s principleCastillo Franquet, Joan, Universitat Autònoma de Barcelona, Barcelona, SpainTchébichef’s inequalityCastro, Ana Esther, Universidad de Vigo, Vigo, Pontevedra, SpainPonzi schemesCerdá, Emilio, Universidad Complutense, Madrid, SpainBellman’s principle of optimality and equations; Euler’s theorem and equationsComín, Diego, New York University, New York, USAHarrod–Domar modelCorchón, Luis, Universidad Carlos III, Madrid, SpainMaskin mechanismCostas, Antón, Universitat de Barcelona, Barcelona, SpainPalmer’s Rule; Peel’s Law
  15. 15. xvi Contributors and their entriesDíaz-Emparanza, Ignacio, Instituto de Economía Aplicada, Universidad del País Vasco-EHU, Bilbao, SpainCochrane–Orcutt procedureDolado, Juan J., Universidad Carlos III, Madrid, SpainBonferroni bound; Markov switching autoregressive modelDomenech, Rafael, Universidad de Valencia, Valencia, SpainSolow’s growth model and residualEchevarría, Cruz Angel, Universidad del País Vasco-EHU, Bilbao, SpainOkun’s law and gapEscribano, Alvaro, Universidad Carlos III, Madrid, SpainEngle–Granger method; Hodrick–Prescott decompositionEspasa, Antoni, Universidad Carlos III, Madrid, SpainBox–Jenkins analysisEspiga, David, La Caixa-S.I. Gestión Global de Riesgos, Barcelona, SpainEdgeworth oligopoly modelEsteban, Joan M., Universitat Autònoma de Barcelona, Barcelona, SpainPigou–Dalton progressive transfersEstrada, Angel, Banco de España, Madrid, SpainHarrod’s technical progress; Hicks’s technical progressEtxebarria Zubeldía, Gorka, Deloitte & Touche, Madrid, SpainMontaigne dogmaFariñas, José C., Universidad Complutense, Madrid, SpainDorfman–Steiner conditionFebrero, Ramón, Universidad Complutense, Madrid, SpainBecker’s time allocation modelFernández, José L., Universidad Autónoma, Madrid, SpainCauchy–Schwarz inequality; Itô’s lemmaFernández Delgado, Rogelio, Universidad Rey Juan Carlos, Madrid, SpainPatman effectFernández-Macho, F. Javier, Universidad del País Vasco-EHU, Bilbao, SpainSlutsky–Yule effectFerreira, Eva, Universidad del País Vasco-EHU, Bilbao, SpainBlack–Scholes model; Pareto distribution; Sharpe’s ratioFlores Parra, Jordi, Servicio de Estudios de Caja Madrid, Madrid, Spain and UniversidadCarlos III, Madrid, SpainSamuelson’s conditionFranco, Yanna G., Universidad Complutense, Madrid, SpainCairnes–Haberler model; Ricardo–Viner model
  16. 16. Contributors and their entries xviiFreire Rubio, Mª Teresa, Escuela Superior de Gestión Comercial y Marketing, Madrid,SpainLange–Lerner mechanismFreixas, Xavier, Universitat Pompeu Fabra, Barcelona, Spain and CEPRFriedman-Savage hypothesisFrutos de, M. Angeles, Universidad Carlos III, Madrid, SpainHotelling’s model of spatial competitionFuente de la, Angel, Universitat Autònoma de Barcelona, Barcelona, SpainSwan’s modelGallastegui, Carmen, Universidad del País Vasco-EHU, Bilbao, SpainPhillip’s curveGallego, Elena, Universidad Complutense, Madrid, SpainRobinson-Metzler conditionGarcía, Jaume, Universitat Pompeu Fabra, Barcelona, SpainHeckman’s two-step methodGarcía-Bermejo, Juan C., Universidad Autónoma, Madrid, SpainHarsanyi’s equiprobability modelGarcía-Jurado, Ignacio, Universidad de Santiago de Compostela, Santiago de Compostela,A Coruña, SpainSelten paradoxGarcía Ferrer, Antonio, Universidad Autónoma, Madrid, SpainZellner estimatorGarcía Lapresta, José Luis, Universidad de Valladolid, Valladolid, SpainBolean algebras; Taylor’s theoremGarcía Pérez, José Ignacio, Fundación CENTRA, Sevilla, SpainScitovsky’s compensation criterionGarcía-Ruiz, José L., Universidad Complutense, Madrid, SpainHarris–Todaro model; Prebisch–Singer hypothesisGimeno, Juan A., Universidad Nacional de Educación a Distancia, Madrid, SpainPeacock–Wiseman’s displacement effect; Wagner’s lawGirón, F. Javier, Universidad de Málaga, Málaga, SpainGauss–Markov theoremGómez Rivas, Léon, Universidad Europea, Madrid, SpainLongfield’s paradoxGraffe, Fritz, Universidad del País Vasco-EHU, Bilbao, SpainLeontief modelGrifell-Tatjé, E., Universitat Autònoma de Barcelona, Barcelona, SpainFarrell’s technical efficiency measurement
  17. 17. xviii Contributors and their entriesGuisán, M. Cármen, Universidad de Santiago de Compostela, Santiago de Compostela, ACoruña, SpainChow’s test; Granger’s causality testHerce, José A., Universidad Complutense, Madrid, SpainCass–Koopmans criterion; Koopmans’s efficiency criterionHerguera, Iñigo, Universidad Complutense, Madrid, SpainGorman’s polar formHernández Andreu, Juan, Universidad Complutense, Madrid, SpainJuglar cycle; Kitchin cycle; Kondratieff long wavesHerrero, Cármen, Universidad de Alicante, Alicante, SpainPerron–Frobenius theoremHerrero, Teresa, Confederación Española de Cajas de Ahorro, Madrid, SpainHeckscher–Ohlin theorem; Rybczynski theoremHervés-Beloso, Carlos, Universidad de Vigo, Vigo, Pontevedra, SpainSard’s theoremHoyo, Juan del, Universidad Autónoma, Madrid, SpainBox–Cox transformationHuergo, Elena, Universidad Complutense, Madrid, SpainStackelberg’s oligopoly modelHuerta de Soto, Jesús, Universidad Rey Juan Carlos, Madrid, SpainRicardo effectIbarrola, Pilar, Universidad Complutense, Madrid, SpainLjung–Box statisticsIglesia, Jesús de la, Universidad Complutense, Madrid, SpainTocqueville’s crossde la Iglesia Villasol, Mª Covadonga, Universidad Complutense, Madrid, SpainHotelling’s theoremIñarra, Elena, Universidad deli País Vasco-EHU, Bilbao, Spainvon Neumann–Morgenstern stable setInduraín, Esteban, Universidad Pública de Navarra, Pamplona, SpainHawkins–Simon theorem; Weierstrass extreme value theoremJimeno, Juan F., Universidad de Alcalá de Henares, Alcalá de Henares, Madrid, SpainRamsey model and ruleJustel, Ana, Universidad Autónoma, Madrid, SpainGibbs samplingLafuente, Alberto, Universidad de Zaragoza, Zaragoza, SpainHerfindahl–Hirschman index
  18. 18. Contributors and their entries xixLasheras, Miguel A., Grupo CIM, Madrid, SpainBaumol’s contestable markets; Ramsey’s inverse elasticity ruleLlobet, Gerard, CEMFI, Madrid, SpainBertrand competition model; Cournot’s oligopoly modelLlombart, Vicent, Universidad de Valencia, Valencia, SpainTurgot–Smith theoremLlorente Alvarez, J. Guillermo, Universidad Autónoma, Madrid, SpainSchwarz criterionLópez, Salvador, Universitat Autònoma de Barcelona, Barcelona, SpainAverch–Johnson effectLópez Laborda, Julio, Universidad de Zaragoza, Zaragoza, SpainKakwani indexLorences, Joaquín, Universidad de Oviedo, Oviedo, SpainCobb–Douglas functionLoscos Fernández, Javier, Universidad Complutense, Madrid, SpainHansen–Perloff effectLovell, C.A.K., The University of Georgia, Georgia, USAFarrell’s technical efficiency measurementLozano Vivas, Ana, Universidad de Málaga, Málaga, SpainWalras’s lawLucena, Maurici, CDTI, Madrid, SpainLaffer’s curve; Tobin’s taxMacho-Stadler, Inés, Universitat Autònoma de Barcelona, Barcelona, SpainAkerlof’s ‘lemons’Malo de Molina, José Luis, Banco de España, Madrid, SpainFriedman’s rule for monetary policyManresa, Antonio, Universitat de Barcelona, Barcelona, SpainBergson’s social indifference curveMaravall, Agustín, Banco de España, Madrid, SpainKalman filterMarhuenda, Francisco, Universidad Carlos III, Madrid, SpainHamiltonian function and Hamilton–Jacobi equations; Lyapunov stabilityMartín, Carmela, Universidad Complutense, Madrid, SpainArrow’s learning by doingMartín Marcos, Ana, Universidad Nacional de Educación de Distancia, Madrid, SpainScitovsky’s community indifference curveMartín Martín, Victoriano, Universidad Rey Juan Carlos, Madrid, SpainBuridan’s ass; Occam’s razor
  19. 19. xx Contributors and their entriesMartín-Román, Angel, Universidad de Valladolid, Segovia, SpainEdgeworth boxMartínez, Diego, Fundación CENTRA, Sevilla, SpainLindahl–Samuelson public goodsMartinez Giralt, Xavier, Universitat Autònoma de Barcelona, Barcelona, SpainSchmeidler’s lemma; Sperner’s lemmaMartínez-Legaz, Juan E., Universitat Autònoma de Barcelona, Barcelona, SpainLagrange multipliers; Banach’s contractive mapping principleMartínez Parera, Montserrat, Servicio de Estudios del BBVA, Madrid, SpainFisher effectMartínez Turégano, David, AFI, Madrid, SpainBowley’s lawMas-Colell, Andreu, Universitat Pompeu Fabra, Barcelona, SpainArrow–Debreu general equilibrium modelMazón, Cristina, Universidad Complutense, Madrid, SpainRoy’s identity; Shephard’s lemmaMéndez-Ibisate, Fernando, Universidad Complutense, Madrid, SpainCantillon effect; Marshall’s symmetallism; Marshall–Lerner conditionMira, Pedro, CEMFI, Madrid, SpainCauchy distribution; Sargan testMolina, José Alberto, Universidad de Zaragoza, Zaragoza, SpainLancaster’s characteristicsMonasterio, Carlos, Universidad de Oviedo, Oviedo, SpainWicksell’s benefit principle for the distribution of tax burdenMorán, Manuel, Universidad Complutense, Madrid, SpainEuclidean spaces; Hessian matrix and determinantMoreira dos Santos, Pedro, Universidad Complutense, Madrid, SpainGresham’s law in politicsMoreno, Diego, Universidad Carlos III, Madrid, SpainGibbard–Satterthwaite theoremMoreno García, Emma, Universidad de Salamanca, Salamanca, SpainMinkowski’s theoremMoreno Martín, Lourdes, Universidad Complutense, Madrid, SpainChamberlin’s oligopoly modelMulas Granados, Carlos, Universidad Complutense, Madrid, SpainLedyard–Clark–Groves mechanismNaveira, Manuel, BBVA, Madrid, SpainGibrat’s law; Marshall’s external economies
  20. 20. Contributors and their entries xxiNovales, Alfonso, Universidad Complutense, Madrid, SpainRadner’s turnpike propertyNúñez, Carmelo, Universidad Carlos III, Madrid, SpainLebesgue’s measure and integralNúñez, José J., Universitat Autònoma de Barcelona, Barcelona, SpainMarkov chain model; Poisson processNúñez, Oliver, Universidad Carlos III, Madrid, SpainKolmogorov’s large numbers law; Wiener processOlcina, Gonzalo, Universidad de Valencia, Valencia, SpainRubinstein’s modelOntiveros, Emilio, AFI, Madrid, SpainDíaz–Alejandro effect; Tanzi-Olivera effectOrtiz-Villajos, José M., Universidad Complutense, Madrid, SpainKaldor paradox; Kaldor’s growth laws; Ricardo’s comparative costs; Verdoorn’s lawPadilla, Jorge Atilano, Nera and CEPRAreeda–Turner predation rule; Coase conjecturePardo, Leandro, Universidad Complutense, Madrid, SpainPearson’s chi-squared statistic; Rao–Blackwell’s theoremPascual, Jordi, Universitat de Barcelona, Barcelona, SpainBabbage’s principle; Bagehot’s principlePazó, Consuelo, Universidad de Vigo, Vigo, Pontevedra, SpainDixit–Stiglitz monopolistic competition modelPedraja Chaparro, Francisco, Universidad de Extremadura, Badajoz, SpainBorda’s rule; Condorcet’s criterionPeña, Daniel, Universidad Carlos III, Madrid, SpainBayes’s theoremPena Trapero, J.B., Universidad de Alcalá de Henares, Alcalá de Henares, Madrid, SpainBeveridge–Nelson decompositionPerdices de Blas, Luis, Universidad Complutense, Madrid, SpainBecher’s principle; Davenant–King law of demandPérez Quirós, Gabriel, Banco de España, Madrid, SpainSuits indexPérez Villareal, J., Universidad de Cantabria, Santander, SpainHaavelmo balanced budget theoremPérez-Castrillo, David, Universidad Autònoma de Barcelona, Barcelona, SpainVickrey auctionPires Jiménez, Luis Eduardo, Universidad Rey Juan Carlos, Madrid, SpainGibson paradox
  21. 21. xxii Contributors and their entriesPolo, Clemente, Universitat Autònoma de Barcelona, Barcelona, SpainLancaster–Lipsey’s second bestPoncela, Pilar, Universidad Autónoma, Madrid, SpainJohansen’s procedurePons, Aleix, CEMFI, Madrid, SpainGraham’s demandPonsati, Clara, Institut d’Anàlisi Econòmica, CSIC, Barcelona, SpainKalai–Smorodinsky bargaining solutionPrat, Albert, Universidad Politécnica de Cataluña, Barcelona, SpainHotelling’s T2 statistics; Student t-distributionPrieto, Francisco Javier, Universidad Carlos III, Madrid, SpainNewton–Raphson method; Pontryagin’s maximum principlePuch, Luis A., Universidad Complutense, Madrid, SpainChipman–Moore–Samuelson compensation criterion; Hicks compensation criterion; Kaldorcompensation criterionPuig, Pedro, Universitat Autònoma de Barcelona, Barcelona, SpainPoisson’s distributionQuesada Paloma, Vicente, Universidad Complutense, Madrid, SpainEdgeworth expansionRamos Gorostiza, José Luis, Universidad Complutense, Madrid, SpainFaustmann–Ohlin theoremReeder, John, Universidad Complutense, Madrid, SpainAdam Smith problem; Adam Smith’s invisible handRegúlez Castillo, Marta, Universidad del País Vasco-EHU, Bilbao, SpainHausman’s testRepullo, Rafael, CEMFI, Madrid, SpainPareto efficiency; Sonnenschein–Mantel–Debreu theoremRestoy, Fernando, Banco de España, Madrid, SpainRicardian equivalenceRey, José Manuel, Universidad Complutense, Madrid, SpainNegishi’s stability without recontractingRicoy, Carlos J., Universidad de Santiago de Compostela, Santiago de Compostela, ACoruña, SpainWicksell effectRodero-Cosano, Javier, Fundación CENTRA, Sevilla, SpainMyerson revelation principleRodrigo Fernández, Antonio, Universidad Complutense, Madrid, SpainArrow–Pratt’s measure of risk aversion
  22. 22. Contributors and their entries xxiiiRodríguez Braun, Carlos, Universidad Complutense, Madrid, SpainClark–Fisher hypothesis; Genberg-Zecher criterion; Hume’s fork; Kelvin’s dictum; Moore’slaw; Spencer’s law; Stigler’s law of eponymy; Wieser’s lawRodríguez Romero, Luis, Universidad Carlos III, Madrid, SpainEngel curveRodríguez-Gutíerrez, Cesar, Universidad de Oviedo, Oviedo, SpainLaspeyres index; Paasche indexRojo, Luis Ángel, Universidad Complutense, Madrid, SpainKeynes’s demand for moneyRomera, Rosario, Universidad Carlos III, Madrid, SpainWiener–Khintchine theoremRosado, Ana, Universidad Complutense, Madrid, SpainTinbergen’s ruleRosés, Joan R., Universitat Pompeu Fabra, Barcelona, Spain and Universidad Carlos III,Madrid, SpainGerschenkron’s growth hypothesis; Kuznets’s curve; Kuznets’s swingsRuíz Huerta, Jesús, Universidad Rey Juan Carlos, Madrid, SpainEdgeworth taxation paradoxSalas, Rafael, Universidad Complutense, Madrid, SpainGini’s coefficient; Lorenz’s curveSalas, Vicente, Universidad de Zaragoza, Zaragoza, SpainModigliani–Miller theorem; Tobin’s qSan Emeterio Martín, Nieves, Universidad Rey Juan Carlos, Madrid, SpainLauderdale’s paradoxSan Julián, Javier, Universitat de Barcelona, Barcelona, SpainGraham’s paradox; Sargant effectSánchez, Ismael, Universidad Carlos III, Madrid, SpainNeyman–Pearson testSánchez Chóliz, Julio, Universidad de Zaragoza, Zaragoza, SpainSraffa’s modelSánchez Hormigo, Alfonso, Universidad de Zaragoza, Zaragoza, SpainKeynes’s planSánchez Maldonado, José, Universidad de Málaga, Málaga, SpainMusgrave’s three branches of the budgetSancho, Amparo, Universidad de Valencia, Valencia, SpainJarque–Bera testSantacoloma, Jon, Universidad de Deusto, Bilbao, SpainDuesenberry demonstration effect
  23. 23. xxiv Contributors and their entriesSantos-Redondo, Manuel, Universidad Complutense, Madrid, SpainSchumpeterian entrepeneur; Schumpeter’s vision; Veblen effect goodSanz, José F., Instituto de Estudios Fiscales, Ministerio de Hacienda, Madrid, SpainFullerton-King’s effective marginal tax rateSastre, Mercedes, Universidad Complutense, Madrid, SpainReynolds–Smolensky indexSatorra, Albert, Universitat Pompeu Fabra, Barcelona, SpainWald testSaurina Salas, Jesús, Banco de España, Madrid, SpainBernoulli’s paradoxSchwartz, Pedro, Universidad San Pablo CEU, Madrid, SpainSay’s lawSebastián, Carlos, Universidad Complutense, Madrid, SpainMuth’s rational expectationsSebastián, Miguel, Universidad Complutense, Madrid, SpainMundell–Fleming modelSegura, Julio, Universidad Complutense, Madrid, SpainBaumol–Tobin transactions demand for cash; Hicksian perfect stability; LeChatelierprinciple; Marshall’s stability; Shapley–Folkman theorem; Snedecor F-distributionSenra, Eva, Universidad Carlos III, Madrid, SpainWold’s decompositionSosvilla-Rivero, Simón, Universidad Complutense, Madrid, Spain and FEDEA, Madrid,SpainDickey–Fuller test; Phillips–Perron testSuarez, Javier, CEMFI, Madrid, Spainvon Neumann–Morgenstern expected utility theoremSuriñach, Jordi, Universitat de Barcelona, Barcelona, SpainAitken’s theorem; Durbin–Watson statisticsTeixeira, José Francisco, Universidad de Vigo, Vigo, Pontevedra, SpainWicksell’s cumulative processTorres, Xavier, Banco de España, Madrid, SpainHicksian demand; Marshallian demandTortella, Gabriel, Universidad de Alcalá de Henares, Alcalá de Henares, Madrid, SpainRostow’s modelTrincado, Estrella, Universidad Complutense, Madrid, SpainHume’s law; Ricardian viceUrbano Salvador, Amparo, Universidad de Valencia, Valencia, SpainBayesian–Nash equilibrium
  24. 24. Contributors and their entries xxvUrbanos Garrido, Rosa María, Universidad Complutense, Madrid, SpainWilliams’s fair innings argumentValenciano, Federico, Universidad del País Vasco-EHU, Bilbao, SpainNash bargaining solutionVallés, Javier, Banco de España, Madrid, SpainGiffen goodsVarela, Juán, Ministerio de Hacienda, Madrid, SpainJones’s magnification effectVázquez, Jesús, Universidad del País Vasco-EHU, Bilbao, SpainCagan’s hyperinflation modelVázquez Furelos, Mercedes, Universidad Complutense, Madrid, SpainLyapunov’s central limit theoremVega, Juan, Universidad de Extremadura, Badajoz, SpainHarberger’s triangleVega-Redondo, Fernando, Universidad de Alicante, Alicante, SpainNash equilibriumVegara, David, Ministerio de Economià y Hacienda, Madrid, SpainGoodhart’s law; Taylor ruleVegara-Carrió, Josep Ma, Universitat Autònoma de Barcelona, Barcelona, Spainvon Neumann’s growth model; Pasinetti’s paradoxVillagarcía, Teresa, Universidad Carlos III, Madrid, SpainWeibull distributionViñals, José, Banco de España, Madrid, SpainBalassa–Samuelson effectZaratiegui, Jesús M., Universidad de Navarra, Pamplona, SpainThünen’s formulaZarzuelo, José Manuel, Universidad del País Vasco-EHU, Bilbao, SpainKuhn–Tucker theorem; Shapley valueZubiri, Ignacio, Universidad del País Vasco-EHU, Bilbao, SpainTheil index
  25. 25. PrefaceRobert K. Merton defined eponymy as ‘the practice of affixing the name of the scientist to allor part of what he has found’. Eponymy has fascinating features and can be approached fromseveral different angles, but only a few attempts have been made to tackle the subject lexico-graphically in science and art, and the present is the first Eponymous Dictionary ofEconomics. The reader must be warned that this is a modest book, aiming at helpfulness more thanerudition. We realized that economics has expanded in this sense too: there are hundreds ofeponyms, and the average economist will probably be acquainted with, let alone be able tomaster, just a number of them. This is the void that the Dictionary is expected to fill, and ina manageable volume: delving into the problems of the sociology of science, dispelling allMertonian multiple discoveries, and tracing the origins, on so many occasions spurious, ofeach eponym (cf. ‘Stigler’s Law of Eponymy’ infra), would have meant editing another book,or rather books. A dictionary is by definition not complete, and arguably not completable. Perhaps this iseven more so in our case. We fancy that we have listed most of the economic eponyms, andalso some non-economic, albeit used in our profession, but we are aware of the risk of includ-ing non-material or rare entries; in these cases we have tried to select interesting eponyms, oreponyms coined by or referring to interesting thinkers. We hope that the reader will spot fewmistakes in the opposite sense; that is, the exclusion of important and widely used eponyms. The selection has been especially hard in mathematics and econometrics, much moreeponymy-prone than any other field connected with economics. The low risk-aversion readerwho wishes to uphold the conjecture that eponymy has numerically something to do withscientific relevance will find that the number of eponyms tends to dwindle after the 1960s;whether this means that seminal results have dwindled too is a highly debatable and, owingto the critical time dimension of eponymy, a likely unanswerable question. In any case, we hasten to invite criticisms and suggestions in order to improve eventualfuture editions of the dictionary (please find below our e-mail addresses for contacts). We would like particularly to thank all the contributors, and also other colleagues that havehelped us: Emilio Albi, José María Capapé, Toni Espasa, María del Carmen Gallastegui,Cecilia Garcés, Carlos Hervés, Elena Iñarra, Emilio Lamo de Espinosa, Jaime de Salas,Rafael Salas, Vicente Salas Fumás, Cristóbal Torres and Juan Urrutia. We are grateful for thehelp received from Edward Elgar’s staff in all the stages of the book, and especially for BobPickens’ outstanding job as editor. Madrid, December 2003 J.S. [jsegura@bde.es] C.R.B. [crb@ccee.ucm.es]
  26. 26. Mathematical notationA vector is usually denoted by a lower case italic letter such as x or y, and sometimes is repre-sented with an arrow on top of the letter such as → or →. Sometimes a vector is described by x yenumeration of its elements; in these cases subscripts are used to denote individual elementsof a vector and superscripts to denote a specific one: x = (x1, . . ., xn) means a generic n-dimensional vector and x0 = (x 0, . . ., x 0 ) a specific n-dimensional vector. As it is usual, x >> 1 ny means xi > yi (i = 1, . . ., n) and x > y means xi ≥ yi for all i and, for at least one i, xi > yi. A set is denoted by a capital italic letter such as X or Y. If a set is defined by some prop-erty of its members, it is written with brackets which contain in the first place the typicalelement followed by a vertical line and the property: X = (x/x >> 0) is the set of vectors x withpositive elements. In particular, R is the set of real numbers, R+ the set of non-negative realnumbers, R++ the set of positive real numbers and a superscript denotes the dimension of the nset. R+ is the set of n-dimensional vectors whose elements are all real non-negative numbers. Matrices are denoted by capital italic letters such as A or B, or by squared bracketssurrounding their typical element [aij] or [bij]. When necessary, A(qxm) indicates that matrixA has q rows and m columns (is of order qxm). In equations systems expressed in matricial form it is supposed that dimensions of matri-ces and vectors are the right ones, therefore we do not use transposition symbols. For exam-ple, in the system y = Ax + u, with A(nxn), all the three vectors must have n rows and 1 columnbut they are represented ini the text as y = (y1, . . ., yn), x = (x1, . . ., xn) and u = (u1, . . ., un).The only exceptions are when expressing a quadratic form such as xAxЈ or a matricial prod-uct such as (XЈ X)–1. The remaining notation is the standard use for mathematics, and when more specific nota-tion is used it is explained in the text.
  27. 27. AAdam Smith problem work. More recent readings maintain that theIn the third quarter of the nineteenth century, Adam Smith problem is a false one, hingeinga series of economists writing in German on a misinterpretation of such key terms as(Karl Knies, 1853, Lujo Brentano, 1877 and ‘selfishness’ and ‘self-interest’, that is, thatthe Polish aristocrat Witold von Skarzynski, self-interest is not the same as selfishness1878) put forward a hypothesis known as the and does not exclude the possibility of altru-Umschwungstheorie. This suggested that istic behaviour. Nagging doubts, however,Adam Smith’s ideas had undergone a turn- resurface from time to time – Viner, foraround between the publication of his philo- example, expressed in 1927 the view thatsophical work, the Theory of Moral Senti- ‘there are divergences between them [Moralments in 1759 and the writing of the Wealth of Sentiments and Wealth of Nations] which areNations, a turnaround (umschwung) which impossible of reconciliation’ – and althoughhad resulted in the theory of sympathy set out the Umschwungstheorie is highly implaus-in the first work being replaced by a new ible, one cannot fail to be impressed by the‘selfish’ approach in his later economic differences in tone and emphasis between thestudy. Knies, Brentano and Skarzynski two books.argued that this turnaround was to be attrib-uted to the influence of French materialist JOHN REEDERthinkers, above all Helvétius, with whomSmith had come into contact during his long Bibliographystay in France (1763–66). Smith was some- Montes, Leonidas (2003), ‘Das Adam Smith Problem: its origins, the stages of the current debate and onething of a bête noire for the new German implication for our understanding of sympathy’,nationalist economists: previously anti-free Journal of the History of Economic Thought, 25 (1),trade German economists from List to 63–90. Nieli, Russell (1986), ‘Spheres of intimacy and theHildebrand, defenders of Nationalökonomie, Adam Smith problem’, Journal of the History ofhad attacked Smith (and smithianismus) as Ideas, 47 (4), 611–24.an unoriginal prophet of free trade orthodox-ies, which constituted in reality a defence of Adam Smith’s invisible handBritish industrial supremacy. On three separate occasions in his writings, Thus was born what came to be called Adam Smith uses the metaphor of the invis-Das Adam Smith Problem, in its more ible hand, twice to describe how a sponta-sophisticated version, the idea that the theory neously evolved institution, the competitiveof sympathy set out in the Theory of Moral market, both coordinates the various interestsSentiments is in some way incompatible with of the individual economic agents who go tothe self-interested, profit-maximizing ethic make up society and allocates optimally thewhich supposedly underlies the Wealth of different resources in the economy.Nations. Since then there have been repeated The first use of the metaphor by Smith,denials of this incompatibility, on the part of however, does not refer to the market mech-upholders of the consistency thesis, such as anism. It occurs in the context of Smith’sAugustus Oncken in 1897 and the majority early unfinished philosophical essay on Theof twentieth-century interpreters of Smith’s History of Astronomy (1795, III.2, p. 49) in a
  28. 28. 2 Adam Smith’s invisible handdiscussion of the origins of polytheism: ‘in As every individual, therefore, endeavours asall Polytheistic religions, among savages, as much as he can both to employ his capital in the support of domestick industry, and so towell as in the early ages of Heathen antiquity, direct that industry that its produce may be ofit is the irregular events of nature only that the greatest value; every individual necessarilyare ascribed to the agency and power of their labours to render the annual revenue of thegods. Fire burns, and water refreshes; heavy society as great as he can. He generally,bodies descend and lighter substances fly indeed, neither intends to promote the publick interest, nor knows how much he is promotingupwards, by the necessity of their own it. . . . by directing that industry in such anature; nor was the invisible hand of Jupiter manner as its produce may be of the greatestever apprehended to be employed in those value, he intends only his own gain, and he ismatters’. in this, as in many other cases, led by an invis- The second reference to the invisible hand ible hand to promote an end which was no part of his intention. Nor is it always the worse foris to be found in Smith’s major philosophical the society that it was no part of it. By pursu-work, The Theory of Moral Sentiments ing his own interest he frequently promotes(1759, IV.i.10, p. 184), where, in a passage that of the society more effectually than whenredolent of a philosopher’s distaste for he really intends to promote it. I have neverconsumerism, Smith stresses the unintended known much good done by those who affect to trade for the publick good. It is an affectation,consequences of human actions: indeed, not very common among merchants, and very few words need be employed in The produce of the soil maintains at all times dissuading them from it. nearly that number of inhabitants which it is capable of maintaining. The rich only select from the heap what is most precious and agree- More recently, interest in Adam Smith’s able. They consume little more than the poor, invisible hand metaphor has enjoyed a and in spite of their natural selfishness and revival, thanks in part to the resurfacing of rapacity, though they mean only their own philosophical problems concerning the unin- conveniency, though the sole end which they tended social outcomes of conscious and propose from the labours of all the thousands whom they employ, be the gratification of intentional human actions as discussed, for their own vain and insatiable desires, they example, in the works of Karl Popper and divide with the poor the produce of all their Friedrich von Hayek, and in part to the fasci- improvements. They are led by an invisible nation with the concept of the competitive hand to make nearly the same distribution of market as the most efficient means of allo- the necessaries of life, which would have been made, had the earth been divided into equal cating resources expressed by a new genera- portions among all its inhabitants, and thus tion of free-market economists. without intending it, without knowing it, advance the interests of the society, and afford JOHN REEDER means to the multiplication of the species. Bibliography Finally, in the Wealth of Nations (1776, Macfie, A.L. (1971), ‘The invisible hand of Jupiter’, Journal of the History of Ideas, 32 (4), 593–9.IV.ii.9, p. 456), Smith returns to his invisible Smith, Adam (1759), The Theory of Moral Sentiments,hand metaphor to describe explicitly how the reprinted in D.D. Raphael and A.L. Macfie (eds)market mechanism recycles the pursuit of (1982), The Glasgow Edition of the Works and Correspondence of Adam Smith, Indianapolis:individual self-interest to the benefit of soci- Liberty Classics.ety as a whole, and en passant expresses a Smith, Adam (1776), An Inquiry into the Nature anddeep-rooted scepticism concerning those Causes of the Wealth of Nations, reprinted in W.B. Todd (ed.) (1981), The Glasgow Edition of thepeople (generally not merchants) who affect Works and Correspondence of Adam Smith,to ‘trade for the publick good’: Indianapolis: Liberty Classics.
  29. 29. Akerlof’s ‘lemons’ 3Smith, Adam (1795), Essays on Philosophical Subjects, 2001 (jointly with A. Michael Spence and reprinted in W.P.D. Wightman and J.C. Bryce (eds) (1982), The Glasgow Edition of the Works and Joseph E. Stiglitz). His main research interest Correspondence of Adam Smith, Indianapolis: has been (and still is) the consequences for Liberty Classics. macroeconomic problems of different micro- economic structures such as asymmetricAitken’s theorem information or staggered contracts. RecentlyNamed after New Zealander mathematician he has been working on the effects of differ-Alexander Craig Aitken (1895–1967), the ent assumptions regarding fairness and socialtheorem that shows that the method that customs on unemployment.provides estimators that are efficient as well The used car market captures the essenceas linear and unbiased (that is, of all the of the ‘Market for “lemons” ’ problem. Carsmethods that provide linear unbiased estima- can be good or bad. When a person buys ators, the one that presents the least variance) new car, he/she has an expectation regardingwhen the disturbance term of the regression its quality. After using the car for a certainmodel is non-spherical, is a generalized least time, the owner has more accurate informa-squares estimation (GLSE). This theory tion on its quality. Owners of bad carsconsiders as a particular case the Gauss– (‘lemons’) will tend to replace them, whileMarkov theorem for the case of regression the owners of good cars will more often keepmodels with spherical disturbance term and them (this is an argument similar to the oneis derived from the definition of a linear underlying the statement: bad money drivesunbiased estimator other than that provided out the good). In addition, in the second-hand ˜by GLSE (b = ((XЈWX)–1 XЈW–1 + C)Y, C market, all sellers will claim that the car theybeing a matrix with (at least) one of its sell is of good quality, while the buyerselements other than zero) and demonstrates cannot distinguish good from bad second-that its variance is given by VAR(b) = ˜ hand cars. Hence the price of cars will reflectVAR(bflGLSE) + s2CWCЈ, where s2CWCЈ is a their expected quality (the average quality) inpositive defined matrix, and therefore that the second-hand market. However, at thisthe variances of the b estimators are greater ˜ price high-quality cars would be underpricedthan those of the b flGLSE estimators. and the seller might prefer not to sell. This leads to the fact that only lemons will be JORDI SURINACH traded. In this paper Akerlof demonstrates howBibliography adverse selection problems may arise whenAitken, A. (1935), ‘On least squares and linear combi- nations of observations’, Proceedings of the Royal sellers have more information than buyers Statistical Society, 55, 42–8. about the quality of the product. When the contract includes a single parameter (theSee also: Gauss–Markov theorem. price) the problem cannot be avoided and markets cannot work. Many goods may notAkerlof’s ‘lemons’ be traded. In order to address an adverseGeorge A. Akerlof (b.1940) got his B.A. at selection problem (to separate the good fromYale University, graduated at MIT in 1966 the bad quality items) it is necessary to addand obtained an assistant professorship at ingredients to the contract. For example, theUniversity of California at Berkeley. In his inclusion of guarantees or certifications onfirst year at Berkeley he wrote the ‘Market the quality may reduce the informationalfor “lemons” ’, the work for which he was problem in the second-hand cars market.cited for the Nobel Prize that he obtained in The approach pioneered by Akerlof has
  30. 30. 4 Allais paradoxbeen extensively applied to the study of dropped, your choices above (as mostmany other economic subjects such as finan- people’s) are perceptibly inconsistent: if thecial markets (how asymmetric information first row was preferred to the second, thebetween borrowers and lenders may explain fourth should have been preferred to thevery high borrowing rates), public econom- third.ics (the difficulty for the elderly of contract- For some authors, this paradox illustratesing private medical insurance), labor that agents tend to neglect small reductionseconomics (the discrimination of minorities) in risk (in the second gamble above, the riskand so on. of nothing is only marginally higher in the first option) unless they completely eliminate INÉS MACHO-STADLER it: in the first option of the first gamble you are offered one million for sure. For others,Bibliography however, it reveals only a sort of ‘opticalAkerlof, G.A. (1970), ‘The market for “lemons”: quality illusion’ without any serious implication for uncertainty and the market mechanism’, Quarterly Journal of Economics, 89, 488–500. economic theory. JUAN AYUSOAllais paradoxOne of the axioms underlying expected util- Bibliographyity theory requires that, if A is preferred to B, Allais, M. (1953), ‘Le Comportement de l’homme rationnel devant la risque: critique des postulats eta lottery assigning a probability p to winning axioms de l’ecole américaine’, Econometrica, 21,A and (1 – p) to C will be preferred to another 269–90.lottery assigning probability p to B and (1 –p) to C, irrespective of what C is. The Allais See also: Ellsberg paradox, von Neumann– Morgenstern expected utility theorem.paradox, due to French economist MauriceAllais (1911–2001, Nobel Prize 1988) chal-lenges this axiom. Areeda–Turner predation rule Given a choice between one million euro In 1975, Phillip Areeda (1930–95) andand a gamble offering a 10 per cent chance of Donald Turner (1921–94), at the time profes-receiving five million, an 89 per cent chance sors at Harvard Law School, published whatof obtaining one million and a 1 per cent now everybody regards as a seminal paper,chance of receiving nothing, you are likely to ‘Predatory pricing and related practicespick the former. Nevertheless, you are also under Section 2 of the Sherman Act’. In thatlikely to prefer a lottery offering a 10 per paper, they provided a rigorous definition ofcent probability of obtaining five million predation and considered how to identify(and 90 per cent of gaining nothing) to prices that should be condemned under theanother with 11 per cent probability of Sherman Act. For Areeda and Turner, preda-obtaining one million and 89 per cent of tion is ‘the deliberate sacrifice of presentwinning nothing. revenues for the purpose of driving rivals out Now write the outcomes of those gambles of the market and then recouping the lossesas a 4 × 3 table with probabilities 10 per cent, through higher profits earned in the absence89 per cent and 1 per cent heading each of competition’.column and the corresponding prizes in each Areeda and Turner advocated the adop-row (that is, 1, 1 and 1; 5, 1 and 0; 5, 0 and tion of a per se prohibition on pricing below0; and 1, 0 and 1, respectively). If the central marginal costs, and robustly defended thiscolumn, which plays the role of C, is suggestion against possible alternatives. The
  31. 31. Areeda–Turner predation rule 5basis of their claim was that companies that The adequacy of average variable costswere maximizing short-run profits would, by as a proxy for marginal costs has receiveddefinition, not be predating. Those compa- considerable attention (Williamson, 1977;nies would not price below marginal cost. Joskow and Klevorick, 1979). In 1996,Given the difficulties of estimating marginal William Baumol made a decisive contribu-costs, Areeda and Turner suggested using tion on this subject in a paper in which heaverage variable costs as a proxy. agreed that the two measures may be differ- The Areeda–Turner rule was quickly ent, but argued that average variable costsadopted by the US courts as early as 1975, in was the more appropriate one. His conclu-International Air Industries v. American sion was based on reformulating theExcelsior Co. The application of the rule had Areeda–Turner rule. The original rule wasdramatic effects on success rates for plain- based on identifying prices below profit-tiffs in predatory pricing cases: after the maximizing ones. Baumol developedpublication of the article, success rates instead a rule based on whether pricesdropped to 8 per cent of cases reported, could exclude equally efficient rivals. Hecompared to 77 per cent in preceding years. argued that the rule which implementedThe number of predatory pricing cases also this was to compare prices to average vari-dropped as a result of the widespread adop- able costs or, more generally, to averagetion of the Areeda–Turner rule by the courts avoidable costs: if a company’s price is(Bolton et al. 2000). above its average avoidable cost, an equally In Europe, the Areeda–Turner rule efficient rival that remains in the marketbecomes firmly established as a central test will earn a price per unit that exceeds thefor predation in 1991, in AKZO v. average costs per unit it would avoid if itCommission. In this case, the court stated ceased production.that prices below average variable cost There has also been debate aboutshould be presumed predatory. However the whether the price–cost test in thecourt added an important second limb to the Areeda–Turner rule is sufficient. On the onerule. Areeda and Turner had argued that hand, the United States Supreme Court hasprices above marginal cost were higher than stated in several cases that plaintiffs mustprofit-maximizing ones and so should be also demonstrate that the predator has aconsidered legal, ‘even if they were below reasonable prospect of recouping the costsaverage total costs’. The European Court of of predation through market power after theJustice (ECJ) took a different view. It found exit of the prey. This is the so-calledAKZO guilty of predatory pricing when its ‘recoupment test’. In Europe, on the otherprices were between average variable and hand, the ECJ explicitly rejected the needaverage total costs. The court emphasized, for a showing of recoupment in Tetra Pak Ihowever, that such prices could only be (1996 and 1997).found predatory if there was independent None of these debates, however, over-evidence that they formed part of a plan to shadows Areeda and Turner’s achievement.exclude rivals, that is, evidence of exclu- They brought discipline to the legal analysissionary intent. This is consistent with the of predation, and the comparison of pricesemphasis of Areeda and Turner that preda- with some measure of costs, which theytory prices are different from those that the introduced, remains the cornerstone of prac-company would set if it were maximizing tice on both sides of the Atlantic.short-run profits without exclusionaryintent. JORGE ATILANO PADILLA
  32. 32. 6 Arrow’s impossibility theoremBibliography formal framework. Consider a society of nAreeda, Phillip and Donald F. Turner (1975), ‘Predatory agents, which has to express preferences pricing and related practices under Section 2 of the Sherman Act’, Harvard Law Review, 88, 697–733. regarding the alternatives in a set A. TheBaumol, William J. (1996), ‘Predation and the logic of preferences of agents are given by complete, the average variable cost test’, Journal of Law and reflexive, transitive binary relations on A. Economics, 39, 49–72.Bolton, Patrick, Joseph F. Brodley and Michael H. Each list of n such relations can be inter- Riordan (2000), ‘Predatory pricing: strategic theory preted as the expression of a state of opinion and legal policy’, Georgetown Law Journal, 88, within society. Rules that assign a complete, 2239–330.Joskow, A. and Alvin Klevorick (1979): ‘A framework reflexive, transitive binary relation (a social for analyzing predatory pricing policy’, Yale Law preference) to each admissible state of opin- Journal, 89, 213. ion are called ‘social welfare functions’.Williamson, Oliver (1977), ‘Predatory pricing: a stra- tegic and welfare analysis’, Yale Law Journal, 87, Specifically, Arrow proposes a list of 384. properties, in the form of axioms, and discusses whether or not they may be satis-Arrow’s impossibility theorem fied by a social welfare function. In his 1963Kenneth J. Arrow (b.1921, Nobel Prize in edition, he puts forward the followingEconomics 1972) is the author of this cele- axioms:brated result which first appeared in ChapterV of Social Choice and Individual Values • Universal domain (U): the domain of(1951). Paradoxically, Arrow called it the function must include all possibleinitially the ‘general possibility theorem’, but combinations of individual prefer-it is always referred to as an impossibility ences;theorem, given its essentially negative char- • Pareto (P): whenever all agents agreeacter. The theorem establishes the incompati- that an alternative x is better thanbility among several axioms that might be another alternative y, at a given state ofsatisfied (or not) by methods to aggregate opinion, then the corresponding socialindividual preferences into social prefer- preference must rank x as better than y;ences. I will express it in formal terms, and • Independence of irrelevant alternativeswill then comment on its interpretations and (I): the social ordering of any two alter-on its impact in the development of econom- natives, for any state of opinion, mustics and other disciplines. only depend on the ordering of these In fact, the best known and most repro- two alternatives by individuals;duced version of the theorem is not the one in • Non-dictatorship (D): no single agentthe original version, but the one that Arrow must be able to determine the strictformulated in Chapter VIII of the 1963 social preference at all states of opin-second edition of Social Choice and ion.Individual Values. This chapter, entitled‘Notes on the theory of social choice’, was Arrow’s impossibility theorem (1963)added to the original text and constitutes the tells that, when society faces three or moreonly change between the two editions. The alternatives, no social welfare function canreformulation of the theorem was partly simultaneously meet U, P, I and D.justified by the simplicity of the new version, By Arrow’s own account, the need toand also because Julian Blau (1957) had formulate a result in this vein arose whenpointed out that there was a difficulty with trying to answer a candid question, posed by athe expression of the original result. researcher at RAND Corporation: does it Both formulations start from the same make sense to speak about social preferences?
  33. 33. Arrow’s impossibility theorem 7A first quick answer would be to say that the studied and proposed different methods ofpreferences of society are those of the major- voting, but none of them fully acknowledgedity of its members. But this is not good the pervasive barriers that are so wellenough, since the majority relation generated expressed by Arrow’s theorem: that noby a society of n voters may be cyclical, as method at all can be perfect, because anysoon as there are more than two alternatives, possible one must violate some of the reason-and thus different from individual prefer- able requirements imposed by the impossi-ences, which are usually assumed to be tran- bility theorem. This changes the perspectivesitive. The majority rule (which otherwise in voting theory: if a voting method must besatisfies all of Arrow’s requirements), is not selected over others, it must be on the meritsa social welfare function, when society faces and its defects, taken together; none can bemore than two alternatives. Arrow’s theorem presented as an ideal.generalizes this remark to any other rule: no Another important reading of Arrow’ssocial welfare function can meet his require- theorem is the object of Chapter IV in hisments, and no aggregation method meeting monograph. Arrow’s framework allows us tothem can be a social welfare function. put into perspective the debate among econ- Indeed, some of the essential assumptions omists of the first part of the twentiethunderlying the theorem are not explicitly century, regarding the possibility of a theorystated as axioms. For example, the required of economic welfare that would be devoid oftransitivity of the social preference, which interpersonal comparisons of utility and ofrules out the majority method, is included in any interpretation of utility as a cardinalthe very definition of a social welfare func- magnitude. Kaldor, Hicks, Scitovsky,tion. Testing the robustness of Arrow’s the- Bergson and Samuelson, among other greatorem to alternative versions of its implicit economists of the period, were involved in aand explicit conditions has been a major discussion regarding this possibility, whileactivity of social choice theory for more than using conventional tools of economic analy-half a century. Kelly’s updated bibliography sis. Arrow provided a general frameworkcontains thousands of references inspired by within which he could identify the sharedArrow’s impossibility theorem. values of these economists as partial require- The impact of the theorem is due to the ments on the characteristics of a method torichness and variety of its possible interpre- aggregate individual preferences into socialtations, and the consequences it has on each orderings. By showing the impossibility ofof its possible readings. meeting all these requirements simultane- A first interpretation of Arrow’s formal ously, Arrow’s theorem provided a newframework is as a representation of voting focus to the controversies: no one was closermethods. Though he was not fully aware of it to success than anyone else. Everyone wasin 1951, Arrow’s analysis of voting systems looking for the impossible. No perfect aggre-falls within a centuries-old tradition of gation method was worth looking for, as itauthors who discussed the properties of did not exist. Trade-offs between the proper-voting systems, including Plinius the Young, ties of possible methods had to be the mainRamón Llull, Borda, Condorcet, Laplace and concern.Dodgson, among others. Arrow added histori- Arrow’s theorem received immediatecal notes on some of these authors in his attention, both as a methodological criticism1963 edition, and the interested reader can of the ‘new welfare economics’ and becausefind more details on this tradition in McLean of its voting theory interpretation. But notand Urken (1995). Each of these authors everyone accepted that it was relevant. In
  34. 34. 8 Arrow’s learning by doingparticular, the condition of independence of Arrow’s learning by doingirrelevant alternatives was not easily This is the key concept in the model developedaccepted as expressing the desiderata of the by Kenneth J. Arrow (b.1921, Nobel Prizenew welfare economics. Even now, it is a 1972) in 1962 with the purpose of explainingdebated axiom. Yet Arrow’s theorem has the changes in technological knowledge whichshown a remarkable robustness over more underlie intertemporal and international shiftsthan 50 years, and has been a paradigm for in production functions. In this respect, Arrowmany other results regarding the general suggests that, according to many psycholo-difficulties in aggregating preferences, and gists, the acquisition of knowledge, what isthe importance of concentrating on trade- usually termed ‘learning’, is the product ofoffs, rather than setting absolute standards. experience (‘doing’). More specifically, he Arrow left some interesting topics out of advances the hypothesis that technical changehis monograph, including issues of aggrega- depends upon experience in the activity oftion and mechanism design. He mentioned, production, which he approaches by cumula-but did not elaborate on, the possibility that tive gross investment, assuming that new capi-voters might strategically misrepresent their tal goods are better than old ones; that is to say,preferences. He did not discuss the reasons if we compare a unit of capital goods producedwhy some alternatives are on the table, and in the time t1 with one produced at time t2, theothers are not, at the time a social decision first requires the cooperation of at least asmust be taken. He did not provide a general much labour as the second, and produces noframework where the possibility of using more product. Capital equipment comes incardinal information and of performing inter- units of equal (infinitesimal) size, and thepersonal comparisons of utility could be productivity achievable using any unit ofexplicitly discussed. These were routes that equipment depends on how much investmentlater authors were to take. But his impossi- had already occurred when this particular unitbility theorem, in all its specificity, provided was produced.a new way to analyze normative issues and Arrow’s view is, therefore, that at leastestablished a research program for genera- part of technological progress does nottions. depend on the passage of time as such, but grows out of ‘experience’ caught by cumula- SALVADOR BARBERÀ tive gross investment; that is, a vehicle for improvements in skill and technical knowl- edge. His model may be considered as aBibliography precursor to the further new or endogenousArrow, K.J. (1951), Social Choice and Individual Values, New York: John Wiley; 2nd definitive edn growth theory. Thus the last paragraph of 1963. Arrow’s paper reads as follows: ‘It has beenBlau, Julian H. (1957), ‘The existence of social welfare functions’, Econometrica, 25, 302–13. assumed that learning takes place only as aKelly, Jerry S., ‘Social choice theory: a bibliography’, by-product of ordinary production. In fact, http://www.maxwell.syr.edu/maxpages/faculty/ society has created institutions, education and jskelly/A.htm.McLean, Ian and Arnold B. Urken (1995), Classics of research, whose purpose is to enable learning Social Choice, The University of Michigan Press. to take place more rapidly. A fuller model would take account of these as additionalSee also: Bergson’s social indifference curve, Borda’s variables.’ Indeed, this is precisely what more rule, Chipman–Moore–Samuelson compensation recent growth literature has been doing. criterion, Condorcet’s criterion, Hicks compensation criterion, Kaldor compensation criterion, Scitovski’s compensation criterion. CARMELA MARTÍN
  35. 35. Arrow–Debreu general equilibrium model 9Bibliography to deliver amounts of a (physical) good if aArrow, K.J. (1962), ‘The economics implications of certain state of the world occurs. Of course, learning by doing’, Review of Economic Studies, 29 (3), 155–73. for this to be possible, information has to be ‘symmetric’. The complete markets hypothe- sis does, in essence, imply that there is noArrow–Debreu general equilibrium cost in opening markets (including those thatmodel at equilibrium will be inactive).Named after K.J. Arrow (b.1921, Nobel In any Walrasian model an equilibrium isPrize 1972) and G. Debreu (b. 1921, Nobel specified by two components. The firstPrize 1983) the model (1954) constitutes a assigns a price to each market. The secondmilestone in the path of formalization and attributes an input–output vector to each firmgeneralization of the general equilibrium and a vector of demands and supplies tomodel of Léon Walras (see Arrow and Hahn, every consumer. Input–output vectors should1971, for both models). An aspect which is be profit-maximizing, given the technology,characteristic of the contribution of Arrow– and each vector of demands–supplies mustDebreu is the introduction of the concept of be affordable and preference-maximizingcontingent commodity. given the budget restriction of the consumer. The fundamentals of Walras’s general Note that, since some of the commoditiesequilibrium theory (McKenzie, 2002) are are contingent, an Arrow–Debreu equilib-consumers, consumers’ preferences and rium determines a pattern of final risk bear-resources, and the technologies available to ing among consumers.society. From this the theory offers an In a context of convexity hypothesis, or inaccount of firms and of the allocation, by one with many (bounded) decision makers,means of markets, of consumers’ resources an equilibrium is guaranteed to exist. Muchamong firms and of final produced commod- more restrictive are the conditions for itsities among consumers. uniqueness. Every Walrasian model distinguishes The Arrow–Debreu equilibrium enjoys aitself by a basic parametric prices hypothe- key property, called the first welfare the-sis: ‘Prices are fixed parameters for every orem: under a minor technical condition (localindividual, consumer or firm decision prob- nonsatiation of preferences) equilibriumlem.’ That is, the terms of trade among allocations are Pareto optimal: it is impossi-commodities are taken as fixed by every ble to reassign inputs, outputs and commodi-individual decision maker (‘absence of ties so that, in the end, no consumer is worsemonopoly power’). There is a variety of off and at least one is better off. To attempt acircumstances that justify the hypothesis, purely verbal justification of this, consider aperhaps approximately: (a) every individual weaker claim: it is impossible to reassigndecision maker is an insignificant part of the inputs, outputs and commodities so that, inoverall market, (b) some trader – an auction- the end, all consumers are better off (for thiseer, a possible entrant, a regulator – guaran- local non-satiation is not required). Definetees by its potential actions the terms of the concept of gross national product (GNP)trade in the market. at equilibrium as the sum of the aggregate The Arrow–Debreu model emphasizes a value (for the equilibrium prices) of initialsecond, market completeness, hypothesis: endowments of society plus the aggregate‘There is a market, hence a price, for every profits of the firms in the economy (that is,conceivable commodity.’ In particular, this the sum over firms of the maximum profitsholds for contingent commodities, promising for the equilibrium prices). The GNP is the
  36. 36. 10 Arrow–Pratt’s measure of risk aversionaggregate amount of income distributed theory is that it constitutes a classificationamong the different consumers. tool for the causes according to which a Consider now any rearrangement of specific market structure may not guaranteeinputs, outputs and commodities. Evaluated final optimality. The causes will fall into twoat equilibrium prices, the aggregate value of categories: those related to the incomplete-the rearrangement cannot be higher than the ness of markets (externalities, insufficientGNP because the total endowments are the insurance opportunities and so on) and thosesame and the individual profits at the related to the possession of market power byrearrangement have to be smaller than or some decision makers.equal to the profit-maximizing value.Therefore the aggregate value (at equilibrium ANDREU MAS-COLELLprices) of the consumptions at the rearrange-ment is not larger than the GNP. Hence there Bibliographyis at least one consumer for which the value Arrow K. and G. Debreu (1954), ‘Existence of an equi- librium for a competitive economy’, Econometrica,of consumption at the rearrangement is not 22, 265–90.higher than income at equilibrium. Because Arrow K. and F. Hahn (1971), General Competitivethe equilibrium consumption for this Analysis, San Francisco, CA: Holden-Day. McKenzie, L. (2002), Classical General Equilibriumconsumer is no worse than any other afford- Theory, Cambridge, MA: The MIT Press.able consumption we conclude that therearrangement is not an improvement for her. See also: Pareto efficiency, Walras’s auctioneer and Under convexity assumptions there is a tâtonnement.converse result, known as the second welfaretheorem: every Pareto optimum can be Arrow–Pratt’s measure of risk aversionsustained as a competitive equilibrium after a The extensively used measure of risk aver-lump-sum transfer of income. sion, known as the Arrow–Pratt coefficient, The theoretical significance of the was developed simultaneously and inde-Arrow–Debreu model is as a benchmark. It pendently by K.J. Arrow (see Arrow, 1970)offers, succinctly and elegantly, a structure and J.W. Pratt (see Pratt, 1964) in theof markets that guarantees the fundamental 1960s. They consider a decision maker,property of Pareto optimality. Incidentally, endowed with wealth x and an increasingin particular contexts it may suffice to utility function u, facing a risky choicedispose of a ‘spanning’ set of markets. Thus, represented by a random variable z within an intertemporal context, it typically distribution F. A risk-averse individual issuffices that in each period there are spot characterized by a concave utility function.markets and markets for the exchange of The extent of his risk aversion is closelycontingent money at the next date. In the related to the degree of concavity of u.modern theory of finance a sufficient market Since uЉ(x) and the curvature of u are notstructure to guarantee optimality obtains, invariant under positive lineal transforma-under some conditions, if there are a few tions of u, they are not meaningfulfinancial assets that can be traded (possibly measures of concavity in utility theory.short) without any special limit. They propose instead what is generally Yet it should be recognized that realism is known as the Arrow–Pratt measure of risknot the strong point of the theory. For exam- aversion, namely r(x) = –uЉ(x)/uЈ(x).ple, much relevant information in economics Assume without loss of generality thatis asymmetric, hence not all contingent Ez = 0 and s2 = Ez2 < ∞. Pratt defines the zmarkets can exist. The advantage of the risk premium p by the equation u(x – p) =

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