The rate of profit as a random variable

Julian Wells, Julian (2007): The rate of profit as a random variable.

Abstract

This thesis is a systematic attempt to investigate two conjectures about the distribution of company rates of profit: that it should be log-normal (Gibrat 1931), and that it should be gamma distributed (Farjoun and Machover 1983).

A large set of company accounts data is analysed, and partial support found for Gibrat and for a generalised version of Farjoun and Machover.

The analysis includes a demonstration of different empirical distributions for different profit rate measures, a demonstration of power law tails in all measures of the profit rate, and a demonstration of size effects (differences in tail weights) in financial ratios. Annual variation in the overall skewness and kurtosis of profit rate distributions is shown to be dominated by variation in the power law tails.

L-moments, a recent innovation in robust methods to deal with extreme values, are used in conjunction with a size-weighted sampling scheme to identify possible models for distributions of the profit rate at the capital level.

Farjoun and Machover derive their hypothesis from a particular conception of the process of capitalist competition. A rival conception, that of Glick (1985), is tested using company accounts data and shown to be vulnerable to criticism concerning the scope of its data set, the test statistic employed, and its choice of profit rate measure. More fundamentally, it is also dependent on doubtful premises about the within-industry distribution of profit rates, as L-moment analysis demonstrates.

• Item Type: MPRA Paper
• Language: English
• Keywords: rate of profit, L-moments, Farjoun, Machover, Laws of Chaos, Marx, transformation problem
• Subjects: B - History of Economic Thought, Methodology, and Heterodox Approaches > B4 - Economic Methodology > B41 - Economic Methodology; B - History of Economic Thought, Methodology, and Heterodox Approaches > B5 - Current Heterodox Approaches > B51 - Socialist ; Marxian ; Sraffian; B - History of Economic Thought, Methodology, and Heterodox Approaches > B5 - Current Heterodox Approaches > B59 - Other; M - Business Administration and Business Economics ; Marketing ; Accounting ; Personnel Economics > M2 - Business Economics > M21 - Business Economics; Y - Miscellaneous Categories > Y4 - Dissertations (unclassified) > Y40 - Dissertations (unclassified)

References

Amoroso, L. (1925) ‘Ricerche intorno alla curva dei redditi’, Annali di Mathematica Pura ed Applicata, Ser. 4-21, pp. 123-159.

Anderson, T.W. and Darling, D.A. (1952) ‘Asymptotic theory of certain “goodness of fit” criteria based on stochastic processes’, Annals of Mathematical Statistics, 23:2, p. 193–212.

Ashley, W.J. (1910) ‘The statistical measurement of profit’, The Economic Journal, 20:80, pp. 530-550.

Axtell, Robert (2005) ‘The complexity of change’, The Economic Journal, 115:June, pp. F193-F210.

Barnett, V. and Lewis, T. (1994) Outliers in statistical data, John Wiley and Sons. Braun, Dieter (2006) ‘Nonequilibrium thermodynamics of wealth condensation’, Physica A: Statistical and Theoretical Physics, 369:2, pp. 714-722.

Bryer, R.A. (1993) ‘The late nineteenth century revolution in financial reporting: accounting for the rise of investor or managerial capitalism?’ Accounting, Organizations and Society, 18:7/8, pp. 649-690.

Bryer, R.A. (1994) ‘Why Marx’s labour theory is superior to the marginalist theory of value: the case from modern financial reporting’, Critical Perspectives on Accounting, 5:4, pp. 313-340.

Bryer, R.A. (1999) ‘Marx and accounting’, Critical Perspectives on Accounting, 10, p. 683–709.

Bryer, R.A. (2000) ‘The history of accounting and the transition to capitalism in England. Part one: theory’, Accounting, Organizations and Society, 25:25, pp. 131-162.

Bureau of Economics (1981) ‘Statistical report: annual line of business report 1974 (interim)’, Federal Trade Commission, Washington DC.

Champernowne, D.G. (1985) ‘Review of Laws of Chaos’, British Journal for the Philosophy of Science, 36:3, pp. 348-352.

Cheng, R.C.H. and Iles, T.C. (1987) ‘Corrected maximum likelihood in non-regular problems’, Journal of the Royal Statistical Society, series B, 49:1, pp. 95-101.

Cheng, R.C.H. and Traylor, L. (1995) ‘Non-regular maximum likelihood problems’, Journal of the Royal Statistical Society, series B, 57:1, p. 3–44.

Christodoulopoulos, George (1996) ‘International competition and industrial rates of return: an empirical approach 1970-1990’, IWGVT, Boston.

Cockshott, Paul and Cottrell, Allin (1994) ‘Value price transformation as a real process’, Karl Marx’s third volume of ‘Capital’: 1894-1994, University of Bergamo.

Cockshott, Paul and Cottrell, Allin (1998) ‘Does Marx need to transform?’ in Marxian economics: a reappraisal, Vol. 2 (Ed, Bellofiore, Riccardo) Macmillan, London, pp. 70-85.

Cockshott, Paul and Cottrell, Allin (2003) ‘Robust correlations between prices and labour values: a comment’, Cambridge Journal of Economics, 29, pp. 309-316.

Cockshott, Paul, Cottrell, Allin and Michaelson, Greg (1995) ‘Testing Marx: some new results from UK data’, Capital & Class:55, pp. 103-129.

Creedy, John and Martin, Vance L. (1994) ‘A model of the distribution of prices’, Oxford Bulletin of Mathematics and Statistics, 56, pp. 67-76.

Creedy, John, Lye, Jenny N. and Martin, Vance L. (1994) ‘A labour market equilibrium model of the personal distribution of earnings’, University of Melbourne, Department of Economics, Melbourne.

DeLamarter, Richard Thomas (1987) Big Blue: IBM’s use and abuse of power, Macmillan, London.

Dermietzel (1906) Statistische Untersuchungen uber die Kapitalrente der grosseren Aktiengesellschaften von 1876-1902, Gottingen.

Doodson, Arthur T. (1917) ‘Relation of the mode, median and mean in frequency curves’, Biometrika, 11:4, pp. 425-429.

Duménil, Gérard and Lévy, Dominique (1987a) ‘The dynamics of competition: a restoration of the classical analysis’, Cambridge Journal of Economics, 11:2, pp. 133-164.

Duménil, Gérard and Lévy, Dominique (1987b) ‘The trend of the economic rate of return in the [sic] U.S. manufacturing since the depression’, CEPREMAP, Paris.

Duménil, Gérard and Lévy, Dominique (1990) ‘Post depression trends in the economic rate of return for U.S. manufacturing’, The Review of Economics and Statistics, 72:3, pp. 406-413.

Duménil, Gérard and Lévy, Dominique (1994) ‘Stylized facts about technical progress since the Civil War: a vintage model’, Structural Change and Economic Dynamics, 5:1, pp. 1-23.

Duménil, Gérard and Lévy, Dominique (1999a) ‘The acceleration and slowdown of technical progress in the US since the Civil War: the transition between two paradigms’, CEPREMAP.

Duménil, Gérard and Lévy, Dominique (1999b) ‘Profit rates: gravitation and trends’, CEPREMAP.

Duménil, Gérard and Lévy, Dominique (1999c) ‘The profit rate: where and how much did it fall? Did it recover? (USA 1948-1997)’, CEPREMAP.

Dunne, Paul (1991) ‘An introduction to quantitative Marxism’, in Quantitative Marxism, (Ed, Dunne, Paul) Polity Press in association with Basil Blackwell, Cambridge.

Edgeworth, F.Y. (1883) ‘The method of least squares’, Philosophical Magazine, 16, p. 78–84.

Edwards, Jeremy, Kay, Jon and Mayer, Colin (1987) The economic analysis of accounting profitability, Clarendon Press, Oxford.

Efron, Bradley and Tibshirani, Robert J. (1993) An introduction to the bootstrap, Chapman and Hall, London.

Engels, Friedrich (1978 [1884]) ‘Preface’, in Capital, Vol. 2 (Ed, Mandel, Ernest) Penguin, Harmondsworth, p. 83–102.

Engels, Friedrich (1981 [1895]) ‘Preface’, in Capital, Vol. 3 (Ed, Mandel, Ernest) Penguin, Harmondsworth, pp. 91-111.

Evans, Merran, Hastings, Nicholas and Peacock, Brian (1993) Statistical distributions, John Wiley & Sons, New York.

Farjoun, Emmanuel (1984) ‘The production of commodities by means of what?’ in Ricardo, Marx, Sraffa, (Eds, Mandel, Ernest and Freeman, Alan) Verso, London, pp. 11-41.

Farjoun, Emmanuel and Machover, Moshé (1983) Laws of chaos: a probabilistic approach to political economy, Verso, London.

Farjoun, Emmanuel and Machover, Moshé (1985) ‘Probability, economics and the labour theory of value’, New Left Review:152, July/August, p. 264.

Fisher, Franklin M. and McGowan, John J. (1983) ‘On the misuse of accounting rates of return to infer monopoly profits’, The American Economic Review, 73:1, pp. 82-97.

Fisher, Franklin M., McGowan, John J. and Greenwood, Joen E. (1983) Folded, spindled, and mutilated: economic analysis and U.S. v. IBM, The MIT Press, Cambridge MA.

Fisher, Irving (1969) ‘Income and capital’, in Readings in the concept and measurement of income, (Eds, Parker, R.H. and Harcourt, Geoffrey C.) Cambridge University Press, Cambridge, pp. 33-53.

Foley, Duncan (1989) ‘Notes on ideology and methodology’, http://cepa.newschool.edu/~foleyd/ideo.pdf: accessed on 31 October, 2006.

Freeman, Alan (1995) ‘Marx without equilibrium’, Capital and Class:56, pp. 49-90.

Freeman, Alan (1998) ‘The transformation of prices into values’, in Marxian economics: a reappraisal, Vol. 2 (Ed, Bellofiore, Riccardo) Macmillan, London, pp. 270-275.

Freeman, Alan (2006) ‘How economies fluctuate: the ambivalent metaphor of ‘centre of gravity’ in recent economic writings’, Association for Heterodox Economics annual conference, London.

Freeman, Alan and Carchedi, Guiglielmo (1996) Marx and non-equilibrium economics, Edward Elgar.

Freeman, Alan, Kliman, Andrew and Wells, Julian (Eds.) (2004) The new value controversy and the foundations of economics, Edward Elgar, Cheltenham.

Fritsche, Stephen R. and Dugan, Michael T. (1997) ‘A simulation-based investigation of errors in accounting-based surrogates for internal rate of return’, Journal of Business Finance and Accounting, 24:6, pp. 781-802.

Fujiwara, Yoshi, Aoyama, Hideaki, Di Guilmi, Corrado, Souma, Wataru and Gallegati, Mauro (2004) ‘Gibrat and Pareto–Zipf revisited with European firms’, Physica A: Statistical Mechanics and its Applications, 344:1–2, p. 112–116.

Fujiwara, Yoshi , Souma, Wataru, Aoyama, Hideaki, Kaizoji, Taisei and Aoki, Masanao (2003) ‘Growth and fluctuations of personal income’, Physica A: Statistical Mechanics and its Applications, 321:3-4, pp. 598-604.

Gale, B. and Branch, B. (1982) ‘Concentration versus market share: which determines performance and why does it matter?’ The Antitrust Bulletin:Spring, pp. 83-105.

Gibrat, Robert Pierre Louis (1930) ‘Une loi des réparations économiques: l’effet proportionnel’, Bulletin Statistique générale Française, 19, p. 469.

Gibrat, Robert Pierre Louis (1931) Les inégalités économiques, Sirey, Paris. Gillman, Joseph M. (1956) The falling rate of profit: Marx’s law and its significance to twentieth-century capitalism, Dennis Dobson, London.

Glaisher, J.W.L. (1872–3) ‘On the rejection of discordant observations’, Monthly Notices of the Royal Astronomical Society, 33:251.

Glick, Mark (1985) ‘Competition vs. monopoly; profit rate dispersion in U.S. manufacturing industries’, PhD dissertation, New School for Social Reserach, New York NY.

Glick, Mark and Erbar, H. (1988) ‘Profit rate equalization in the U.S. and Europe: an econometric investigation’, European Journal of Political Economy, 4:1, pp. 179-201.

Glick, Mark and Erbar, H. (1990) ‘Long-run equilibrium in the empirical study of monopoly and competition’, Economic Enquiry, 28:1, pp. 151-162.

Glick, Mark and Campbell, D.A. (1995) ‘Comment: Classical competitition and the compatibility of market power and uniform rates of profit’, Review of Radical Political Economy, 27:2, pp. 124-153.

Green, R.F. (1976) ‘Outlier-prone and outlier-resistant distributions’, Journal of the American Statistical Association, 71, p. 502–505.

Greenwood, J.A., Landwehr, J.M., Matalas, N.C. and Wallis, J.R. (1979) ‘Probability-weighted moments: definition and relation to parameters of several distributions expressable in inverse form’, Water Resources Research, 15, p. 1049–1054.

Griffin, P.A. (1982) ‘Usefulness to investors and and creditors of information provided by financial reporting: a review of empirical accounting research’, Financial Accounting Standards Board, Stamford, Connecticut.

Harcourt, G.C. (1969) ‘The accountant in a golden age’, in Readings in the concept and measurement of income, (Eds, Parker, R.H. and Harcourt, Geoffrey C.) Cambridge University Press, Cambridge, pp. 127-131.

Härdle, W. (1991) Smoothing techniques: with implementation in S, Springer, New York.

Higson, C., Holly, Sean and Kattuman, Paul (2002) ‘The cross-sectional dynamics of the US business cycle: 1950-1999’, Journal of Economic Dynamics and Control, 26:9-10, pp. 1539-1555.

Higson, C., Holly, S., Kattuman, P. and Platis, S. (2004) ‘The business cycle, macroeconomic shocks and the cross-section: the growth of UK quoted companies’, Economica, 71:281, p.299–318.

Hirose, H. (1995) ‘Maximum likelihood parameter estimation in the three-parameter gamma distribution’, Computational Statistics and Data Analysis, 20, pp. 343-354.

Hosking, J.R.M. (1990) ‘L-moments: analysis and estimation of distributions using linear combinations of order statistics’, Journal of the Royal Statistical Society Series B, 52:1, pp. 105-124.

Hosking, J.R.M. and Wallis, J.R. (1997) Regional frequency analysis: an approach based on L-moments, Cambridge University Press, Cambridge.

International Institute for Social History (2006) ‘Karl Marx/Friedrich Engels Papers’, http://www.eesg.nl.archives/en/files/m/10760604full.php: accessed on 26 August 2006.

Jalali-Naini, Ahmad R. (1986) ‘Laws of Chaos: a probabilistic approach to political economy, by Emmanuel Farjoun and Moshe Machover’, The Journal of Peasant Studies, 13:4, pp. 275-278.

Jaynes, E.T. (1991) ‘How should we use entropy in economics?’ unpublished MS. Johnson, Norman L., Kotz, Samuel and Balakrishnan, N. (1994) Continuous univariate distributions, Vol. 1, John Wiley & Sons.

Jones, M.C. and Faddy, M.J. (2003) ‘A skew extension of the t distribution, with applications’, Journal of the Royal Statistical Society Series B, 65:1, pp. 179-194.

Julius, A.J. (2005) ‘Stable great ratios and stationary dispersion of profit rates in unbalanced growth’, New School for Social Research, New York.

Kaldor, N. (1969) ‘The concept of income in economic theory’, in Readings in the concept and measurement of income, (Eds, Parker, R.H. and Harcourt, Geoffrey C.) Cambridge University Press, Cambridge, pp. 123-124.

Kapteyn, J.C. (1903) Skew frequency curves in biology and statistics, Nordhoff, Groningen.

Kliman, Andrew J. (2002) ‘The law of value and laws of statistics: sectoral values and prices in the US economy, 1977-97’, Cambridge Journal of Economics, 26, pp. 299-311.

Kliman, Andrew J. (2003) ‘Reply to Cockshott and Cottrell’, Cambridge Journal of Economics, 29, pp.317-323.

Kolmogorov, Andrei Nikolaevich (1992) ‘On the empirical determination of a distribution law’, in Selected works of A.N. Kolmogorov, Vol. Two (Eds, Prokhorov, Yu. V. and Shiryaev, A.N.) Kluwer, Dordrecht, p. 139–146.

Langston, Robert (1984) ‘A new approach to the relation between prices and values’, in Ricardo, Marx, Sraffa, (Eds, Mandel, Ernest and Freeman, Alan) Verso, London, pp. 1-10.

Lévy, Dominique (1984) ‘A method of dispersion measurement’, CEPREMAP, Paris.

Lianos, Theodore P. and Droucopoulos, Vassilis (1993) ‘Convergence and hierarchy of industrial profit rates: the case of Greek manufacturing’, Review of Radical Political Economics, 25:2, pp. 67-80.

Lienhard, John H. and Meyer, Paul L. (1967) ‘A physical basis for the generalized gamma distribution’, Quarterly Journal of Applied Mathematics, 5:3, pp. 330-334.

Lukacs, Eugene (1955) ‘A characterization of the gamma distribution’, Annals of Mathematical Statistics, 26, pp. 319-324.

Mage, Shane Henry (1963) ‘The ‘law of the falling tendency of the rate of profit’: its place in the Marxian theoretical system and relevance to the U.S. economy’, PhD, Columbia, New York NY.

Maldonado-Filho, Eduardo (1998) ‘Competition and equalization of inter-industry profit rates: the evidence for the Brazilian economy, 1973-85’, International Working Group on Value Theory miniconference at the Eastern Economic Association, New York, N.Y.

Mantegna, Rosario N. and Stanley, H. Eugene (2000) An introduction to econophysics: correlations and complexity in finance, Cambridge University Press, Cambridge.

Markose, Sheri M. (2005) ‘Computability and evolutionary complexity: markets as complex adaptive systems’, The Economic Journal, 115:June, pp. F159-F192.

Marsaglia, G. (1974) ‘Extension and application of Lukacs’ characterization of the gamma distribution’, Proc. Symposium Statistics & Related Topics, Carleton University, Ottawa.

Marsaglia, G. (1989) ‘The X + Y, X/Y characterization of the gamma distribution’, in Contributions to probability and statistics, (Eds, Bleier, L.J., Perlman, M.D., Press, S.J. and Sampson, A.R.) Springer-Verlag, New York, pp. 91-98.

Martin, Stephen (1984) ‘The misuse of accounting rates of return: comment’, The American Economic Review, 74:3, p. 501–506.

Marx, Karl (1952) Wage labour and capital, Progress Publishers, Moscow. Marx, Karl (1969) Theories of surplus value, Vol. 2, Lawrence and Wishart, London.

Marx, Karl (1975a) ‘Excerpts from James Mill’s Elements of political economy’, in Early Writings, (Ed, Colletti, Lucio) Penguin, Harmondsworth, pp. 259-278.

Marx, Karl (1975b) ‘Difference between the Democritean and Epicurean philosophy of nature’, in Marx-Engels collected works, Vol. 1 Lawrence and Wishart, London.

Marx, Karl (1976) Capital, Vol. I, Penguin Books, Harmondsworth.

Marx, Karl (1978) Capital, Vol. II, Penguin Books, Harmondsworth.

Marx, Karl (1981) Capital, Vol. III, Penguin Books, Harmondsworth.

Marx, Karl (n.d.) The poverty of philosophy, Lawrence and Wishart, London. McAlister, D. (1879) ‘The law of the geometric mean’, Proceedings of the Royal Society, 29, p. 367.

McCullagh, P. and Nelder, J.A. (1989) Generalized linear models, Chapman and Hall, London.

McDonald, J.B. (1984) ‘Some generalized functions for the size distribution of income’, Econometrica, 52, pp. 647-663.

McLellan, David (1980) Marx before marxism, Macmillan, London.

Mitzenmacher, Michael (2003) ‘A brief history of generative models for power law and lognormal distributions’, Internet Mathematics, 1:2, pp. 226-251.

Moseley, Fred (1991) The falling rate of profit in the postwar United States economy, Macmillan.

Moseley, Fred (1992) ‘Unproductive labour and the rate of profit in the postwar US economy’, in International perspectives on profitability and accumulation, (Eds, Moseley, Fred and Wolff), pp. 66-90.

Mosselmans, Bert (2005) ‘Adolphe Quetelet, the average man and the development of economic methodology’, Antwerp, pp. 25.

Parker, R.H. and Harcourt, Geoff C. (1969a) ‘Introduction’, in Readings in the concept and measurement of income, Cambridge University Press, Cambridge, p. 402.

Parker, R.H. and Harcourt, Geoff C. (Eds.) (1969b) Readings in the concept and measurement of income, Cambridge University Press, Cambridge.

Perroux, Francois (1926 [1996]) Le probleme du profit, Presses Universitaires de Grenoble.

Puty, Cláudio Castelo Branco (n.d.) ‘A simulation model of the general rate of profit with capital accumulation’, Belém, Brasil.

Quetelet, Lambert Adolphe Jacques (1842 [1969]) A treatise on man and the development of his faculties, Scholars’ Facsimiles and Reprints, Gainesville, Florida.

Ravenscraft, David J. (1983) ‘Structure-profit relationships at the line of business and industry level’, The Review of Economics and Statistics, 65, pp. 22-31.

Ricardo, David (1951) On the principles of political economy and taxation, Vol. I, Cambridge University Press, Cambridge.

Rider, P.R. (1933) ‘Criteria for rejection of observations’, Washington University Studies – New Series, Science and Technology, 8, p. 3–23.

Russo, Alberto, Delli Gatti, Domenico and Gallegati, Mauro (2006) ‘Technological innovation, financial fragility and complex dynamics’, in Economic growth and distribution: on the nature and causes of the wealth of nations, (Ed, Salvadori, Neri) Edward Elgar, Cheltenham.

Salamon, G.L. (1982) ‘Cash recovery rates and measures of firm profitability’, Accounting Review, 57:April, pp. 292-302.

Salamon, G.L. (1985) ‘Accounting rates of return’, American Economic Review, 75:June, pp. 495-504.

Salem, A.B.Z. and Mount, T.D. (1974) ‘A convenient descriptive model of income distribution: the gamma density’, Econometrica, 42:6, pp. 1115-1128.

Serrano Cinca, C., Mar Molinero, C. and Gillizo Larraz, J.L. (2001) ‘Country and size effects in financial ratios: a European perspective’, University of Southampton, Southampton.

Shaikh, Anwar (1978) ‘National income accounts and marxian categories’, New School for Social Research, New York.

Shapiro, S.S. and Chen, L. (2001) ‘Composite tests for the gamma distribution’, Journal of Quality Technology, 33:1, pp. 47-59.

Sheppard, Eric and Barnes, Trevor J. (1986) ‘Instabilities in the geography of capitalist production: collective vs. individual profit maxmization’, Annals of the Association of American Geographers, 76, pp. 493-507.

Sheppard, Eric and Barnes, Trevor J. (1990) The capitalist space economy: geographical analysis after Ricardo, Marx and Sraffa, Unwin Hyman, London.

Sherman, Howard J. (1968) Profits in the United States, Cornell University Press, Ithaca.

Silverman, Bernard W. (1986) Density estimation for statistics and data analysis, Chapman and Hall, London.

Simons, H.C. (1969) ‘The definition of income’, in Readings in the concept and measurement of income, (Eds, Parker, R.H. and Harcourt, Geoffrey C.) Cambridge University Press, Cambridge, pp. 63-73.

Singh, A. and Whittington, G. (1968) Growth, profitability and valuation, Cambridge University Press, Cambridge.

Stacy, E.W. and Mihram, G.A. (1965) ‘Parameter estimation for a generalized gamma distribution’, Technometrics, 7:3, pp. 349-358.

Stanley, M.H.R., Buldyrev, S.V., Havlin, S., Mantegna, R.N., Salinger, M.A. and Stanley, H.E. (1995) ‘Zipf plots and the size distributions of firm’, Economics Letters, 49, pp. 453-457.

Steedman, Ian (1977) Marx after Sraffa, NLB.

Steedman, Ian (1983) ‘[Review of Laws of Chaos]’, The Economic Journal: December, pp. 1015-1016.

Steibeling, G.C. (1890) Das Werthgesetz und die Profitrate, John Heinrich, New York NY.

Stigler, George J. (1963) Capital and rates of return in manufacturing industries, Princeton University Press, Princeton.

Stigler, S.M. (1973) ‘Simon Newcomb, Percy Daniell, and the history of robust estimation, 1885–1920’, Journal of the American Statistical Association, 68, p. 872–879.

Stigler, Stephen M. (1986) The history of statistics: the measurement of uncertainty before 1900, The Belknap Press of Harvard University Press, Cambridge, Mass.

Stone, E.J. (1873) ‘On the rejection of discordant observations’, Monthly Notices of the Royal Astronomical Society, 34, p. 9–15.

Sutton, J. (1997) ‘Gibrat’s legacy’, Journal of Economic Literature, 35, pp. 40-59.

Taguchi, Tokio (1980) ‘On an interpretation and an estimation of shape parameters of the generalized gamma distribution’, Metron, 38, pp. 27-40.

Tsaliki, Persefoni (1998) ‘Theories of competition and concept of regulating capital: evidence from Greek manufacturing’, IWGVT, New York, N.Y.

van der Borght (1898) ‘Aktiengeselleschaft’, in Dictionnaire d’economie politique, p. 191.

Verso - NLB (Ed.) (1981) The value controversy, Verso.

Webber, M.J. (1986) ‘Survey 9. The theory of prices, profits and values’, Society and Space, 4, pp.109-116.

Webber, Michael (1987) ‘Rates of profit and interregional flows of capital’, Annals of the Association of American Geographers, 77:1.

Webber, Michael J. and Rigby, D.L. (1986) ‘The rate of profit in Canadian manufacturing industry, 1950-1981’, Review of Radical Political Economics, 18:1 & 2, pp. 33-55.

Webber, Michael J. and Rigby, David .L. (1996) The Golden Age illusion: rethinking postwar capitalism.

Weisskopf, Thomas E. (1979) ‘Marxian crisis theory and the rate of profit in the postwar US economy’, Cambridge Journal of Economics, 3:4, pp. 341-378.

Weisskopf, Thomas E. (1981) ‘Wages, salaries, and the profit share: a rejoinder’, Cambridge Journal of Economics:5, pp. 175-182.

Wolff, Edward N. (1979) ‘The rate of surplus value, the organic composition, and the general rate of profit in the U.S. economy, 1947-67’, The American Economic Review, 69:3, pp. 329-341.

Wolff, Edward N. (1986) ‘The productivity slowdown and the fall in the U.S. rate of profit, 1947-76’, Review of Radical Political Economy, 18:1 & 2, pp. 87-109.

Wolff, Edward N. and Dollar, David (1992) ‘Profit and wage convergence and capital accumulation among industrialised countries, 1963-83’, in Profits, deficits and instability, (Ed, Papadimitriou, Dimitri B.) Macmillan, London, pp. 103-138.

Wright, Ian (2005) ‘The social architecture of capitalism’, Physica A: Statistical and Theoretical Physics, 346:3–4, p. 589–620.

Zachariah, Dave (2005) ‘Labor value and equalization of profit rates in Sweden’, Stockholm, Sweden.

Zipf, G. (1932) Selective studies and the principle of relative frequency in language, Harvard University Press, Cambridge MA.