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Equilibrium, Stability and GrowthA Multi-Sectoral Analysis$

Michio Morishima

Print publication date: 1963

Print ISBN-13: 9780198281450

Published to Oxford Scholarship Online: November 2003

DOI: 10.1093/0198281455.001.0001

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(p.216) References

(p.216) References

Source:
Equilibrium, Stability and Growth
Publisher:
Oxford University Press

Bibliography references:

Arrow, K. J.

[1] ‘Alternative Proof of the Substitution Theorem for Leontief Models in the General Case’, Activity Analysis of Production and Allocation, ed. T. C. Koopmans (New York: Wiley, 1951), 155–64.

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[1] ‘On the Stability of Competitive Equilibrium, II’, Econometrica, xxvii (January 1959), 82–109.

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[1] ‘Existence of an Equilibrium for a Competitive Economy’, Econometrica, xxii (July 1954), 265–90.

Arrow, K. J., and L. Hurwicz

[1] ‘Gradient Method for Concave Programming, I: Local Results’, Studies in Linear and Non‐Linear Programming, ed. K. J. Arrow, L. Hurwicz, and H. Uzawa (Stanford: Stanford University Press, 1958), 117–26.

[2] ‘On the Stability of Competitive Equilibrium, I’, Econometrica, xxvi (October 1958), 522–52.

[3] ‘Competitive Stability under Weak Gross Substitutability: The “Euclidean Distance” Approach’, International Economic Review, i (January 1960), 38–49.

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[1] ‘A Generalized Comparative Statics in Linear Programming’, Review of Economic Studies, xxiii (1955–6), 236–40.

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[1] ‘Comparative Statics in Linear Programming and the Giffen Paradox’, Review of Economic Studies, xxiii (1955–6), 232–5.

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See Arrow, Block, and Hurwicz.

Champernowne, D. G.

[1] ‘A Note on J. v. Neumann's Article on “A Model of Economic Equilibrium” ’, Review of Economic Studies, xiii (1945–6), 10–18.

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[1] An Introduction to Linear Programming (New York: Wiley, 1953).

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[1] ‘The Multi‐Sector Multiplier’, Econometrica, xviii (October 1950), 355–74. (p.217)

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See Charnes, Cooper, and Henderson.

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[1] ‘Market Equilibrium’, Proceedings of the National Academy of Sciences, 42 (November 1956), 876–8.

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See Arrow and Debreu.

Debreu, G., and I. N. Herstein

[1] ‘Nonnegative Square Matrices’, Econometrica, xxi (October 1953), 597–607.

Dorfman, R., P. A. Samuelson, and R. M. Solow

[1] Linear Programming and Economic Analysis (New York: McGraw‐Hill, 1958).

Eilenberg, S., and D. Montgomery

[1] ‘Fixed Point Theorems for Multi‐valued Transformations’, American Journal of Mathematics, lxviii (1946), 214–22.

Fisher, F. M.

[1] ‘Balanced Growth and Intertemporal Efficiency in Capital Accumulation: Comment’, International Economic Review, iv (May 1963), 232–4.

Frobenius, G.

[1] ‘Über Matrizen aus positiven Elementen I’, Sitzungsberichte der königlich preussischen Akademie der Wissenschaften (1908), 471–6.

[2] ‘Über Matrizen aus positiven Elementen II’, Sitzungsberichte (1909), 514–18.

[3] ‘Über Matrizen aus nicht negativen Elementen’, Sitzungsberichte (1912), 456–77.

Fukuoka, M., and A. Koyama

[1] ‘Cassel Ippan Kinko Taikei no Sai‐Kento’ (The Casselian System Re‐examined), Riron Keizaigaku, ix (1959), 44–51.

Furuya, H., and K. Inada

[1] ‘Balanced Growth and Intertemporal Efficiency in Capital Accumulation’, International Economic Review, iii (January 1962), 94–107.

Gale, D.

[1] ‘Convex Polyhedral Cones and Linear Inequalities’, Activity Analysis of Production and Allocation, ed. T. C. Koopmans (New York: Wiley, 1951), 287–97.

[2] ‘The Law of Supply and Demand’, Mathematica Scandinavica, iii (1955), 155–69.

[3] ‘The Closed Linear Model of Production’, Linear Inequalities and Related Systems, ed. H. W. Kuhn and A. W. Tucker (Princeton: Princeton University Press, 1956), 285–330. (p.218)

[4] The Theory of Linear Economic Models (New York: McGraw‐Hill, 1960).

Georgescu‐Roegen, N.

[1] ‘Relaxation Phenomena in Linear Dynamic Models’, Activity Analysis of Production and Allocation, ed. T. C. Koopmans (New York: Wiley, 1951), 116–31.

[2] ‘Some Properties of a Generalized Leontief Model’, Activity Analysis of Production and Allocation, ed. T. C. Koopmans (New York: Wiley, 1951), 165–73.

Goodwin, R. M.

[1] ‘The Multiplier as Matrix’, Economic Journal, lix (December 1949), 537–55.

Hahn, F. H.

[1] ‘Gross Substitutes and the Dynamic Stability of General Equilibrium’, Econometrica, xxvi (January 1958), 169–70.

[2] ‘On the Stability of a Pure Exchange Equilibrium,’ International Economic Review, iii (May 1962), 206–13.

Harrod, R. F.

[1] Towards a Dynamic Economics (New York: Macmillan, 1952).

Hawkins, D., and H. A. Simon

[1] ‘Note: Some Conditions of Macroeconomic Stability’, Econometrica, xvii (October 1949), 245–8.

Henderson, A., A. Charnes, and W. W. Cooper

See Charnes, Cooper, and Henderson.

Herstein, I. N., and G. Debreu

See Debreu and Herstein.

Hicks, J. R.

[1] Value and Capital (Oxford: Oxford University Press, 1939).

[2] ‘Linear Theory’, Economic Journal, lxx (December 1960), 671–709.

[3] ‘Prices and the Turnpike (I) The Story of a Mare's Nest’, Review of Economic Studies, xxviii (February 1961), 77–88.

Hurwicz, L., and K. J. Arrow

See Arrow and Hurwicz.

Hurwicz, L., K. J. Arrow, and H. D. Block

See Arrow, Block, and Hurwicz.

Inada, K., and H. Furuya

See Furuya and Inada.

Jorgenson, D. W.

[1] ‘A Dual Stability Theorem’, Econometrica, xxviii (October 1960), 892–9.

[2] ‘The Structure of Multi‐sector Dynamic Models’, International Economic Review, ii (September 1961), 276–93.

Kaldor, N.

[1] ‘Alternative Theories of Distribution’, Review of Economic Studies, xxiii (1955–6), 83–100.

[2] ‘A Model of Economic Growth’, Economic Journal, lxvii (December 1957), 591–624. (p.219)

Karlin, S.

[1] ‘Positive Operators’, Journal of Mathematics and Mechanics, viii (1959), 907–37.

[2] Mathematical Methods and Theory in Games, Programming and Economics, vol. i (Reading, Massachusetts: Addison‐Wesley Publishing Company, Inc., 1959).

Kemeny, J. G., O. Morgenstern, and G. L. Thompson

[1] ‘A Generalization of the von Neumann Model of an Expanding Economy’, Econometrica, xxiv (April 1956), 115–35.

Koopmans, T. C.

[1] ‘Alternative Proof of the Substitution Theorem for Leontief Model in the Case of Three Industries’, Activity Analysis of Production and Allocation, ed. T. C. Koopmans (New York: Wiley, 1951), 147–54.

[2] Three Essays on the State of Economic Sciences (New York: McGraw‐Hill, 1957).

Kose, T.

[1] ‘Solutions of Saddle Value Problems by Differential Equations’, Econometrica, xxiv (January 1956), 59–70.

Koyama, A., and M. Fukuoka

See Fukuoka and Koyama.

Kuhn, H. W.

[1] ‘On a Theorem of Wald’, Linear Inequalities and Related Systems, ed. H. W. Kuhn and A. W. Tucker, Annals of Mathematics Studies No. 38 (Princeton: Princeton University Press, 1956), 265–73.

Lancaster, K.

[1] ‘Balanced Growth and the Turnpike Theorem’, mimeographed.

Lange, O.

[1] Price Flexibility and Employment (Bloomington, Indiana: The Principia Press, 1944).

[2] ‘The Output‐Investment Ratio and Input‐Output Analysis’, Econometrica, xxviii (April 1960), 310–24.

Lefschetz, S.

[1] Introduction to Topology (Princeton: Princeton University Press, 1949).

Leontief, W. W.

[1] The Structure of American Economy, 1919–39 (New York: Oxford University Press, 1951).

[2] ‘Structural Change’, Studies in the Structure of the American Economy, by W. W. Leontief and others (New York: Oxford University Press, 1953), 17–52.

[3] ‘Dynamic Analysis’, Studies in the Structure of the American Economy, by W. W. Leontief and others (New York: Oxford University Press, 1953), 53–90.

Levinson, N., and E. A. Coddington

See Coddington and Levinson.

(p.220) McKenzie, L. W.

[1] ‘On the Existence of General Equilibrium for a Competitive Market’, Econometrica, xxvii (January 1959), 54–71.

[2] ‘Stability of Equilibrium and the Value of Positive Excess Demand’, Econometrica, xxviii (July 1960), 606–17.

[3] ‘Price‐Quantity Duality and the Turnpike Theorem’, paper presented to the Econometric Society, December, 1960.

[4] ‘Turnpike Theorems for a Generalized Leontief Model’, Econometrica, xxxi (January–April 1963), 165–80.

[5] ‘The Dorfman–Samuelson–Solow Turnpike Theorem’, International Economic Review, iv (January 1963), 29–43.

[6] ‘The Turnpike Theorem of Morishima’, mimeographed.

McKinsey, J. C. C.

[1] Introduction to the Theory of Games (New York: McGraw‐Hill, 1952).

McManus, M.

[1] ‘Self‐contradiction in Leontief's Dynamic Model’, Yorkshire Bulletin of Economic and Social Research, ix (May 1957), 1–21.

Marx, K.

[1] Capital (Chicago: Charles Kerr and Company, 1933).

Metzler, L. A.

[1] ‘Stability of Multiple Markets: the Hicks Conditions’, Econometrica, xiii (October 1945), 277–92.

[2] ‘A Multiple‐Country Theory of Income Transfers’, Journal of Political Economy, lix (February 1951), 14–29.

[3] ‘Taxes and Subsidies in Leontief's Input‐Output Model’, Quarterly Journal of Economics, lxv (August 1951), 433–8.

Montgomery, D., and S. Eilenberg

See Eilenberg and Montgomery.

Morgenstern, O., and J. von Neumann

See von Neumann and Morgenstern.

Morgenstern, O., G. L. Thompson, and J. G. Kemeny

See Kemeny, Morgenstern, and Thompson.

Morishima, M.

[1] ‘An Analysis of the Capitalist Process of Reproduction’, Metroeconomica, viii (December 1956), 171–85.

[2] ‘Notes on the Theory of Stability of Multiple Exchange’, Review of Economic Studies, xxiv (June 1957), 203–8.

Morishima, M., and F. Seton

[1] ‘Aggregation in Leontief Matrices and the Labour Theory of Value’, Econometrica, xxix (April 1961), 203–20.

Mosak, J. L.

[1] General Equilibrium Theory in International Trade (Bloomington, Indiana: The Principia Press, 1944).

Negishi, T.

[1] ‘A Note on the Stability of an Economy where All Goods are Gross Substitutes’, Econometrica, xxvi (July 1958), 445–7.

[2] ‘On the Formation of Prices’, International Economic Review, ii (January 1961), 122–6. (p.221)

von Neumann, J.

[1] ‘Über ein ökonomisches Gleichungssystem und eine Verallge‐meinerung des Brouwer'schen Fixpunktsatzes’, Ergebnisse eines mathematischen Kolloquiums, viii (1937), 73–83. English translation: ‘A Model of General Economic Equilibrium’, Review of Economic Studies, xiii (1945–6), 1–9.

von Neumann, J., and O. Morgenstern

[1] Theory of Games and Economic Behavior (Princeton: Princeton University Press, 1947).

Newman, P.

[1] ‘Some Notes on Stability Conditions’, Review of Economic Studies, xxvii (October 1959), 1–9.

Nikaidô, H.

[1] ‘On the Classical Multilateral Exchange Problem’, Metroeconomica, viii (August 1956), 135–45.

[2] Gendai‐keizaigaku no Sugakuteki‐hoho (Mathematical Methods in Contemporary Economics) (Tokyo: Iwanami, 1960).

[3] ‘Balanced Growth in Multi‐Sectoral Income Propagation under Autonomous Expenditure Schemes’, Review of Economic Studies, xxx (October 1963).

[4] ‘Persistence of Continual Growth near the von Neumann Ray: A Strong Version of the Radner Turnpike Theorem’, Econometrica, forthcoming.

Nikaidô, H., and H. Uzawa

[1] ‘Stability and Non‐negativity in a Walrasian Tâtonnement Process’, International Economic Review, i (January 1960), 50–59.

Nørregaard Rasmussen, P.

[1] Studies in Inter‐Sectoral Relations (Amsterdam: North‐Holland Publishing Company, 1956).

Okishio, N.

[1] ‘Shuren Joken to Working no Mondai’ (The Convergency Conditions and the Problems of Working), Kindai Keizai Riron Kenkyu, i (1950), ii.1–ii.11.

Perron, O.

[1] ‘Zur Theorie der Matrizen’, Mathematische Annalen, lxiv (July 1907), 248–63.

Radner, R.

[1] ‘Paths of Economic Growth that are Optimal with regard only to Final States: A Turnpike Theorem’, Review of Economic Studies, xxviii (February 1961), 98–104.

Robinson, J.

[1] The Accumulation of Capital (London: Macmillan, 1956).

Samuelson, P. A.

[1] Foundations of Economic Analysis (Cambridge, Massachusetts: Harvard University Press, 1948).

[2] ‘Abstract of a Theorem Concerning Substitutability in Open Leontief Models’, Activity Analysis of Production and Allocation, ed. T. C. Koopmans (New York: Wiley, 1951), 142–6. (p.222)

[3] ‘Prices of Factors and Goods in General Equilibrium’, Review of Economic Studies, xxi (1953–4), 1–20.

[4] ‘Wages and Interest: A Modern Dissection of Marxian Economic Models’, American Economic Review, xlvii (December 1957), 884–912.

[5] ‘Efficient Paths of Capital Accumulation in Terms of the Calculus of Variations’, Mathematical Methods in the Social Sciences, 1959, ed. K. J. Arrow, S. Karlin, and P. Suppes, Proceedings of the First Stanford Symposium (Stanford: Stanford University Press, 1960), 77–88.

[6] ‘An Extension of the LeChatelier Principle’, Econometrica, xxviii (April 1960), 368–79.

Samuelson, P. A., and R. M. Solow

See Solow and Samuelson.

Samuelson, P. A., R. M. Solow, and R. Dorfman

See Dorfman, Samuelson, and Solow.

Schlesinger, K.

[1] ‘Über die Produktionsgleichung der ökonomischen Wertlehre’, Ergebnisse eines mathematischen Kolloquiums, vi (Vienna: Deuticke, 1933).

Schwartz, J. T.

[1] Lectures on the Mathematical Method in Analytical Economics (New York: Gordon and Breach, 1961).

Seton, F.

[1] ‘The Transformation Problem’, Review of Economic Studies, xxiv (June 1957), 149–60.

Seton, F., and M. Morishima

See Morishima and Seton.

Simon, H. A.

[1] ‘Effects of Technological Change in a Leontief Model’, Activity Analysis of Production and Allocation, ed. T. C. Koopmans (New York: Wiley, 1951), 260–81.

Simon, H. A., and D. Hawkins

See Hawkins and Simon.

Solow, R. M.

[1] ‘On the Structure of Linear Models’, Econometrica, xx (January 1952), 29–46.

[2] ‘A Contribution to the Theory of Economic Growth’, Quarterly Journal of Economics, lxx (February 1956), 65–94.

[3] ‘Competitive Valuation in a Dynamic Input‐Output System’, Econometrica, xxvii (January 1959), 30–53.

Solow, R. M., R. Dorfman, and P. A. Samuelson

See Dorfman, Samuelson, and Solow.

Solow, R. M., and P. A. Samuelson

[1] ‘Balanced Growth under Constant Returns to Scale’, Econometrica, xxi (July 1953), 412–24.

Thompson, G. L., J. G. Kemeny, and O. Morgenstern

See Kemeny, Morgenstern, and Thompson.

(p.223) Tsukui, J.

[1] ‘On a Relative Stability Theorem’, International Economic Review, ii (May 1961), 229–30.

Uzawa, H.

[1] ‘Gradient Method for Concave Programming, II: Global Stability in the Strictly Concave Case’, Studies in Linear and Non‐Linear Programming, ed. K. J. Arrow, L. Hurwicz, and H. Uzawa (Stanford: Stanford University Press, 1958), 127–32.

[2] ‘Walras' Tâtonnement in the Theory of Exchange’, Review of Economic Studies, xxvii (June 1960), 182–94.

[3] ‘The Stability of Dynamic Processes’, Econometrica, xxix (October 1961), 617–31.

[4] ‘On the Stability of Edgeworth's Barter Process’, International Economic Review, iii (May 1962), 218–32.

Uzawa, H., and H. Nikaidô

See Nikaidô and Uzawa.

Wald, A.

[1] ‘Über einige Gleichungssysteme der mathematischen Ökonomie’, Zeitschrift für Nationalökonomie, vii (1936), 637–70. English translation: ‘On Some System of Equations of Mathematical Economics’, Econometrica, xix (October 1951), 368–403.

Walras, L.

[1] Elements of Pure Economics, translated by W. Jaffé (Homewood, Illinois: Richard D. Irwin, Inc., 1954).

Wielandt, H.

[1] ‘Unzerlegbare, nicht negative Matrizen’, Mathematische Zeitschrift, lii (March 1950), 642–8.

Yasui, T.

[1] ‘Walras Taikei no Ichi Kosatsu’ (A Study in the Walrasian System), Keizai no Shimpo to Antei (Economic Progress and Stability: Essays in Honour of Professor Ichiro Nakayama), (Tokyo: Toyo Keizai Shimpo‐sha, 1958), 39–60.

Zarnowitz, V.

[1] ‘Technology and the Price Structure in General Equilibrium System’, Review of Economic Studies, xxiii (1955–6), 109–25.

Zeuthen, F.

[1] ‘Das Prinzip der Knappheit, technische Kombination und ökonomische Qualität’, Zeitschrift für Nationalökonomie, iv (1933), 1–24.

This volume includes the author's following articles with revisions and alterations:

[a] ‘A Dynamic Analysis of Structural Change in a Leontief Model’, Economica, xxv (May 1958), 119–25.

[b] ‘Prices, Interest and Profits in a Dynamic Leontief System’, Econometrica, xxvi (July 1958), 358–80.

[c] ‘Some Properties of a Dynamic Leontief System with a Spectrum of Techniques’, Econometrica, xxvii (October 1959), 626–37. (p.224)

[d] ‘Economic Expansion and the Interest Rate in Generalized von Neumann Models’, Econometrica, xxviii (April 1960), 352–63.

[e] ‘Existence of Solution to the Walrasian System of Capital Formation and Credit’, Zeitschrift für Nationalökonomie, xx (1960), 238–43.

[f] ‘On the Three Hicksian Laws of Comparative Statics’, Review of Economic Studies, xxvii (June 1960), 195–201.

[g] ‘A Reconsideration of the Walras–Cassel–Leontief Model of General Equilibrium’, Mathematical Methods in the Social Sciences 1959, ed. K. J. Arrow, S. Karlin, and P. Suppes, Proceedings of the First Stanford Symposium (Stanford: Stanford University Press, 1960), 63–76.

[h] ‘Generalizations of the Frobenius–Wielandt Theorems for Non‐negative Square Matrices’, Journal of London Mathematical Society, xxxvi (1961), 211–20.

[i] ‘Proof of a Turnpike Theorem: The “No Joint Production Case” ’, Review of Economic Studies, xxviii (February 1961), 89–97.

[j] ‘The Stability of Exchange Equilibrium: An Alternative Approach’, International Economic Review, iii (May 1962), 214–17.