References

Abraham, R.M./ Marsden, J.E. (1978): Foundations of Mechanics. Reading, Mass.: Benjamin/ Cummings.

Allen, R.G.D. (1963): Mathematical Economics. London: MacMillan.

Allen, R.G.D. (1967): Macroeconomic Theory. London: MacMillan.

Alexander, J.C./ Yorke, J.A. (1978): Global Bifurcation of Periodic Orbits. Amer­ican Journal of Mathematics, 100, pp. 263-292.

Alexander, S.S. (1958): Rate of Change Approaches to Forecasting-Diffusion Indexes and First Differences. Economic Journal, 68; reprinted in: Readings in Busi­ness Cycles (1966), pp. 626-640.

Andronov, A.A./Chaikin, C.E. (1949): Theory of Oscillations. Princeton: Prince­ton University Press.

Arneodo, A./ Coullet, P.I Tresser, C. (1982): Oscillations with Chaotic Behavior: An Illustration of a Theorem by Shil'nikov. Journal of Statistical Physics, 27, pp. 171-182.

Arnold, V.1. (1984): Catastrophe Theory. Berlin - Heidelberg - New York: Springer.

Arrow, K.J./ Hahn, F.H. (1971): General Competitive Analysis. San Francisco: Holden-Day.

Assenmacher, W. (1984): Lehrbuch der Konjunkturtheorie. Miinchen-Wien: Olden­bourg.

Baumol, W.J. (1958): Topology of Second Order Linear Difference Equations With Constant Coefficients. Econometrica, 26, pp. 258-285.

Baumol, W.J. (1970): Economic Dynamics. 3rd ed., New York: MacMillan.

206 References

Begg, D.K.H. (1982): The Rational Expectations Revolution in Macroeconomics. Baltimore: John Hopkins Press.

Begg, D.K.H. (1983): Rational Expectations and Bond Pricing: Modelling the Term Structure with and without Certainty Equivalence. Economic Journal, 94, suppJ., pp. 45-58.

Benassy, J.P. (1982): The Economics of Market Disequilibrium. New York: Academic Press.

Benassy, J.P. (1984): A Non-Walrasian Model of the Business Cycle. Journal of Economic Behavior and Organization, 5, pp. 77-89.

Benhabib, J.I Day, R.H. (1980): Erratic Accumulation. Economic Lett.ers, 6, pp. 113-117.

Benhabib, J.I Day, R.H. (1981): Rational Choice and Erratic Behaviour, Review of Economic Studies, 48, pp. 459-471.

Benhabib, J.I Miyao, T. (1981): Some New Results on the Dynamics of the Gener­alized Tobin Model. International Economic Review, 22, pp. 589- 596.

Benhabib, J.I Nishimura, K. (1979): The Hopf-bifurcation and the Existence of Closed Orbits in Multisector Models of Optimal Economic Growth. Journal of Economic Theory, 21, pp. 421-444.

Bergstrom, A.R. (1972): A Model of Technical Progress, the Production Function and Cyclical Growth. Economica, 29, pp. 357-370.

Black, S. W.I Russel, R.R. (1969): An Alternative Estimate of Potential GNP. Review of Economic Studies, 51, pp. 70-76.

Blad, M.C. (1981): Exchange of Stability in a Disequilibrium Model. Journal of Mathematical Economics, 8, pp. 121-145.

Blad, M.C.I Zeeman, E.C. (1982): Oscillations between Repressed Inflation and Keynesian Equilibria Due to Inertia in Decision Making. Journal of Economic Theory, 28, pp. 165-182.

Blinder, A.S.I Fischer, S. (1981): Inventories, Rational Expectations, and the Busi­ness Cycle. Journal of Monetary Economics, 8, pp. 277-304.

Boldrin, M. (1984): Applying Bifurcation Theory: Some Simple Results on Keynesian Business Cycles. DP 8403 University of Venice.

Boyce, W .E./DiPrima, R.L. (1977): Elementary Differential Equations and Bound­ary Value Problems. 3rd. ed., New York: Wiley.

Branson, W.H. (1979): Macroeconomic Theory and Policy. 2nd. ed., New York: Harper and Row.

Breuss, F. (1982): Potential Output und gesamtwirtschaftliche KapaziHitsauslastung. Monatsberichte des Osterreichischen Instituts fUr Wirtschaftsforschung, 2, 1982, pp. 104-118.

References 207

Broida, A.L. (1955): Diffusion Indexes. The American Statistician, 9, pp. 7-16.

Brunner, K./ Cukierman, A./ Meltzer, A.H. (1980): Stagflation, Persistent Un­employment and the Permanence of Economic Shocks. Journal of Monetary Economics, 6, pp. 467-492.

Brunner, K./ Cukierman, A./ Meltzer, A.H. (1983): Money and Economic Ac­tivity, Inventories and Business Cycles, Journal of Monetary Economics, 11, pp. 281-319.

Burns, A.F. (1954): The Frontiers of Economic Knowledge. Princeton University Press.

Burns, A.F./ Haavelmo, T. (1968): Business Cycles. In: International Encyclopedia of the Social Sciences. Vol. 2, pp. 226-249.

Burns, A.F./ Mitchell, W.C. (1946): Measuring Business Cycles. Studies in Busi­ness Cycles No.2, National Bureau of Economic Research, New York.

Cagan, P. (1956): The Monetary Dynamics of Hyperinflation. In: Friedman, M. (ed.): Studies in the Quantity Theory of Money. Chicago: The University of Chicago Press.

Carter, M./ Maddock, R. (1984): Rational Expectations. Macroeconomics of the 1980s ? London: MacMillan.

Chang, W.W./Smyth, D.J. (1971): The Existence and Persistence of Cycles in a Non-Linear Model: Kaldor's 1940 Model Re-examined. Review of Economic Studies. 38, pp. 37-44.

Christiano, L.J. (1981): A Survey of Measures of Capacity Utilization. IMF Staff Papers, 28, pp. 144-198.

Clark, C.W. (1976): Mathematical Bioeconomics. New York: John Wiley.

Clark, J .M. (1917): Business Acceleration and the Law of Demand: A Technical Factor in Economic Cycles. Journal of Political Economy, 25, pp. 217- 235.

Clower, R.W. (1965): The Keynesian Counterrevolution: A Theoretical Appraisal. In: Hahn, F.H/BrechIing, F.P.R. (eds.): The Theory of Interest Rates. London: Macmillan.

Coddington, E.A./ Levinson, N. (1955): Theory of Ordinary Differential Equations. New York: MacGraw-Hill.

Collet, P./ Eckmann, J.-P. (1980): Iterated Maps on the Interval as Dynamical Systems. Basel - Boston: Birkhaeuser.

Cugno, F./ Montrucchio, L. (1982a): Stability and Instability in a Two Dimensional Dynamical System: a Mathematical Approach to Kaldor's Theory of the Trade Cycle. In: Szegoe, G.P. (ed.): New Quantitative Techniques for Economic Analysis, New York: Academic Press, pp. 265-278.

208 References

Cugno, F.I Montrucchio, L. (1982b): Cyclical Growth and Inflation: a Qualitative Approach to Goodwin's Model with Money Prices. Economic Notes, 11, pp. 93-107.

Cugno, F.I Montrucchio, L. (1984): Some New Techniques for Modelling Non­Linear Economic Fluctuations: A Brief Survey. In: Goodwin, R.M. et al. (1984), pp. 146 - 165.

Dana, R.A.I Malgrange, P. (1984): The Dynamics of a Discrete Version of a Growth Cycle Model. In: Ancot, J.P. (ed.): Analysing the Structure of Economic Models. The Hague: Martinus Nijhoff, pp. 205 -222.

Davidson, P. (1984): Reviving Keynes' Revolution. Journal of Post Keynesian Eco­nomics,6, 1984, pp. 561-575.

Day, R.H. (1978): Cobweb Models with Explicit Suboptimization. In: Day, R.H.I Cigno, A. (eds.): Modelling Economic Change: The Recursive Programming Approach. Amsterdam: North Holland.

Day, R.H. (1982): Irregular Growth Cycles. American Economic Review, 1982,72, pp. 406-414.

Day, R.H. (1983): The Emergence of Chaos from Classical Economic Growth. Quar­terly Journal of Economics, 98, pp. 201-213.

Day, R.H. (1984): Disequilibrium Economic Dynamics. Journal of Economic Be­haviour and Organisation, 5, pp. 57-76.

Day, R.H. (1986): Unscrambling the Concept of Chaos Through Thick and Thin: Reply. Quarterly Journal of Economics, 101, pp. 425-426.

Day, R.H./Shafer, W. (1986): Keynesian Chaos. Journal of Macroeconomics, 7, pp. 277-95.

De Baggis, H.F. (1952): Dynamical Systems with Stable Structures. In: Lefschetz, S. (ed.): Contribution to the Theory of Non-Linear Oscillations. Vol. II., pp. 37-59, Princeton University Press.

Debreu, G. (1959): Theory of Value. New Haven-London: Yale University Press.

De Foville, A. (1888): Essai de Meteorologie Economique et Sociale (I), Journal de la Societe de Statistique de Paris, 29, pp. 243-249.

Dernburg, T.F.I Dernburg, J.D. (1969): Macroeconomic Analysis. Reading, Mass.: Addison-Wesley.

Desai, M. (1973): Growth Cycles and Inflation in a Model of the Class Struggle. Journal of Economic Theory, 6, pp. 527-545.

Deutsche Bundesbank (1973): Das Produktionspotential in der Bundesrepublik Deutschland. Monatsberichte, 25, No. 10, pp. 28-34. English Translation in Deutsche Bundesbank (1973), Monthly Reports.

References 209

Deutsche Bundesbank (1981): Neuberechnung des Produktionspotentials fUr die Bundesrepublik Deutschland. Monatsberichte, 33, pp. 32-38.

Diamond, P.A. (1965): National Debt in a Neoclassical Growth Model. American Economic Review, 55, pp. 1126-1150.

Diamond, Phil (1976): Chaotic Behaviour of Systems of Difference Equations. Inter-national Journal of Systems Science, 7, pp. 953-956.

Dornbusch, R./ Fischer, S. (1978): Macroeconomics. New York: McGraw-Hill.

Downs, A. (1959),: An Economic Theory of Democracy. New York: Harper.

Dumenil, G./ Levy, D. (1985): The Dynamics of Competition: A Restoration of the Classical Analysis. Mimeo: CEPREMAP.

Dumenil, G./ Levy. D. (1986): The Macroeconomics of Disequilibrium: A Classical View. Mimeo: CEPREMAP.

Economic Report of the President together with the Annual Report of the Council of Economic Advisors. Washington, D.C., 1962.

Economic Report of the President together with the Annual Report of the Council of Economic Advisors. Washington, D.C., 1977.

Eigen, M./ Winckler, R. (1975): Das Spiel. Munchen: Piper.

Evans, M.K. (1969): Macroeconomic Activity. New York: Harper and Row.

Fehl, U. (1983): Die Theorie dissipativer Strukturen als Ansatzpunkt fur die Analyse von Innovationsproblemen in alternativen Wirtschaftsordnungen. In: Schul­ler, A. et a1. (eds.): Innovationsproblemein Ost und West. Stuttgart: Fischer.

Feigenbaum, M. (1978): Quantitative Universality for a Class of Non-Linear Trans­formations. Journal of Statistical Physics, 19, pp. 25-52,and 21, pp. 669-706.

Fischer, E.O./Jammernegg, W. (1986): Empirical Investigation of a Catastrophe Extension of the Phillips-curve. Mimeo: University of Graz.

Fischer, S. (ed.) (1980a): Rational Expectations and Economic Policy. Chicago: The University of Chicago Press.

Fischer, S. (1980b): On Activist Monetary Policy with Rational Expectations. In: Fischer, S. (1980a), pp. 211-247.

Flaschel, P. (1984): Some Stability Properties of Goodwin's Growth Cycle. A Critical Elaboration. Zeitschrift fur Nationalokonomie, 44, pp. 63-69.

Flaschel, P. (1985): Macroeconomic Dynamics and Effective Demand. Some Correc­tions. Metroeconomica, 37, pp. 135-56.

Flaschel, P./ Kruger, M. (1984): Endogenous Aspirations in a Model of Cyclical Growth. Richerche Economiche, 38, pp. 598-612.

210 References

Flaschel, P./ Semmler, W. (1985): Classical and Neoclassical Competitive Adjust­ment Processes. Mimeo: University of Bielefeld.

Frey, B.S. (1978): Politico-Economic Models and Cycles. Journal of Public Economics, 9, pp. 203-220.

Frey, B.S./ Garbers, H. (1972): Der EinfluB wirtschaftlicher Variablen auf die Pro­duktivitat der Regierung. Jahrbucher fUr Nationalokonomie und Statistik, 186, pp. 281-295.

Frey, B.S./ Kirchgaessner, G. (1977): A Basic Dilemma in Democracy. DP 95, Department of Economics, University of Konstanz.

Frey, B.S./ Lau, L.Y. (1968): Towards a Mathematical Model of Government Be­haviour. Zeitschrift fUr Nationalokonomie. 28, pp. 355-380.

Frey, B.S./ Ramser, H.-J. (1976): The Political Business Cycle: A Comment. Re­view of Economic Studies, 43, pp. 553-555.

Frey, B.S./ Schneider, F. (1978a): An Empirical Study of Politico-Economic In­teraction in the United States. Review of Economics and Statistics, 60, pp. 174-183. .

Frey, B.S./ Schneider, F. (1978b): A Politico-Economic Model of the United King­dom, Economic Journal, 88, pp. 243-253.

Friedman, B.M. (1979): Optimal Expectations and the Extreme Information Assump­tion of "Rational Expectations" Macromodels. Journal of Monetary Economics, 5, pp. 23-41.

Friedman, M. (1968): The Role of Monetary Policy. American Economic Review, 58, pp. 1-17.

Gabisch, G. (1980): Konjunktur und Wachstum. In: Kompendium der Wirtschaft­stheorie und Wirtschaftspolitik, Band 1, pp. 275-332. 2nd. ed. (1984). Munchen: Vahlen.

Gabisch, G. (1984): Nonlinear Models of Business Cycle Theory. In: Hammer, G./Pallaschke, D. (eds.), (1984): Selected Topics in Operations Research and Mathematical Economics. Berlin-Heidelberg-New York: Springer, pp. 205-222.

Gabisch, G. (1985): Nichtlineare Differenzengleichungen in der Konjunkturtheorie. In: Gabisch, G./v. Trotha, H. (1985), pp. 5-25.

Gabisch, G./ v. Throtha, H. (1985) (eds.): Dynamische Eigenschaften nicht-linearer Differenzengleichungen und ihre Anwendungen in der Oekonomie. GMD - Stu­dien, 97, Sankt Augustin.

Gaertner, W. (1986): Zyklische Konsummuster. Jahrbucher fUr Nationalokonomie und Statistik. 201, pp. 54-65.

Gater, R. (1931): Die Konjunkturprognose des Harvard-Institutes. Zurich: Ginberger.

References 211

General Business Conditions. Review of Economic Statistics and Supplements.

George, D. (1981): Equilibrium and Catastrophes in Economics. Scottish Journal of Political Economy, 28, pp. 43-61.

Georgescu-Roegen, N. (1971): The Entropy Law and Economic Progress. Cam­bridge, Mass.: Harvard University Press

Gerard-Varet, L.A.I Jordan, R.I Kirman, A. (1984): Rational Expectations Equilibria with Stochastic Quantity Rationing. Paper presented at the ESEM, Madrid 1984.

Glansdorff, P./Prigogine, I. (1977): Thermodynamic Theory of Structure, Stability and Fluctuations. London - New York: Wiley.

Goldberg, S. (1958): Introduction to Difference Equations. New York: Wiley.

Goodwin, R.M. (1951): The Non-linear Accelerator and the Persistence of Business Cycles. Econometrica, 19, pp. 1-17.

Goodwin, R.M. (1967): A Growth Cycle. In: Feinstein, C.H. (eq.): Socialism, Capitalism and Economic Growth. Cambridge: Cambridge University Press 1969. Revised version in: Hunt, E.K./Schwarz, J~G. (eds.) (1969): A Critique of Economic Theory, pp. 442-449, Harmondsworth: Pepguin

Goodwin, R.M.I Kriiger, M.I Vercelli, A. (eds.) (1984): Non-linear Models of Fluctuating Growth. Berlin - Heidelberg - New York: Springer.

Gordon, R.A. (1952): Business Fluctuations. New York: Harper & Brothers.

Gordon, R.J. (1973): The Welfare Cost of Higher Unemployment. Brookings Papers on Economic Activity, 1973.1, pp. 133-195.

Grandmont, J .-M. (1985): On Endogenous Competitive Business Cycles. Economet­rica, 53, pp. 995-1045.

Grandmont, J.-M./Laroque, G. (1985): Stability of Cycles and Expectations. CEPREMAP 8519.

Granger, C. W.J.I Hatanaka, M. (1964): Spectral Analysis of Economic Time Se­ries. Princeton University Press.

Guckenheimer, J. (1973): Bifurcation and Catastrophe. In: Peixoto, M.M. (ed.): Dynamical Systems. New York - London: Academic Press, pp. 95-109.

Guckenheimer, J. I Holmes, P. (1983): Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. New York - Berlin - Heidelberg: Springer.

Guckenheimer, J.IOster, G./Ipaktchi, A. (1977): The Dynamics of Density De­pendent Population Models. Journal of Mathematical Biology, 4, pp. 101-147.

Haken, H. (1983a): Synergetics. An Introduction. 3rd ed., Berlin-Heidelberg-New York: Springer.

212 References

Haken, H. (1983b): Advanced Synergetics. Berlin - Heidelberg - New York: Springer.

Herrmann, R. (1986): Vergleich der dynamischen Eigenschaften stetiger und diskreter zweidimensionaler Konjunkturmodelle. Dissertation G6ttingen.

Hicks, J .R. (1950): A Contribution to the Theory of the Trade Cycle. Oxford: Oxford University Press. 2nd. ed. (1965), Oxford: Claredon Press

Hirsch, M. W./ Smale, S. (1974): Differential Equations, Dynamical Systems, and Linear Algebra. New York: Academic Press.

lchimura, S. (1955): Towards a General Non-Linear Macrodynamic Theory of Eco­nomic Fluctuations. In: Kurihara, K. K. (ed.): Post-Keynesian Economics. New Brunswick: Rutgers University Press, pp. 192-226.

Intrilligator, M. (1971): Mathematical Optimization and Economic Theory. Engle­wood Cliffs: Prentice Hall.

100ss, G. (1979): Bifurcations of Maps and Applications. Amsterdam: North Holland.

100ss, G./ Joseph, D.D. (1980): Elementary Stability and Bifurcation Theory. New York - Heidelberg - Berlin: Springer.

Jager, K. (1984): Persistenz und zyklische Schwankungen der Unterbeschiiftigung in Gleichgewichtsmodellen mit rationalen Erwartungen. Zeitschrift fur Wirt­schafts- und Sozialwissenschaften, 104, pp. 645-673.

Kaldor, N. (1940): A Model of the Trade Cycle. Economic Journal, 50, pp. 78-92.

Kaldor, N. (1971): A Comment. Review of Economic Studies, 38, pp. 45-46.

Kalecki, M. (1935): A Macroeconomic Theory of the Business Cycle. Econometrica, 3, pp. 327-344.

Kalecki, M. (1937): A Theory of the Business Cycle. Review of Economic Studies, 4, pp. 77-97.

Kalecki, M. (1939): A Theory of the Business Cycle. In: Kalecki, M. (1972): Essays in the Theory of Economic Fluctuation. London: Allen-Unwin.

Kalecki, M. (1943): Studies in Economic Dynamics. London: Allen-Unwin.

Kalecki, M. (1952): Theory of Economic Dynamics. London: Unwin University Books.

Kirchgaessner, G. (1984): Optimale Wirtschaftspolitik und die Erzeugung politisch-6konomischer Konjunkturzyklen. Meisenheim: Hain.

Klein, L.R. (1964): A Post-war Quarterly Model: Description and Application. Mod­els of Income Determination, Conference on Research in Income and Wealth. Princeton.

Klein, L.R./ Preston, R.S. (1967): Some New Results in the Measurement of Ca­pacity Utilization. American Economic Review, '57, pp. 34-58.

References 213

Konig, H.j Wolters, J. (1972): Einfiihrung in die Spektralanalyse okonomischer Zeitreihen. Meisenheim: Anton Hain.

Koopmans, T .C. (1947): Measurement without Theory. The Review of Economic Statistics, 29; reprinted in: Readings (1966), pp. 186 - 203.

Koopmans, T.C. (1949): A Reply. The Review of Economics and Statistics, 31; reprinted in: Readings (1966), pp. 218 - 225.

Krelle, W. (1959): Grundlagen einer stochastischen Konjunkturtheorie. Zeitschrift fur die gesamte Staatswissenschaft, U5, pp. 472-494.

Krengel, R. (1970): Die Berechnung des industriellen Produktionspotentials in der Bundesrepublik Deutschland mit Hilfe von Zeitreihen des Brutto-Anlagever­mogens. Beitriige zur Strukturforschung des DIW, 10, pp. 40-44.

Kromphardt, J. (1977): Wachstum und Konjunktur. Gottingen: Vandenhoeck & Ruprecht.

Kromphardt, J. (1984): Ansiitze der Konjunkturtheorie. In: Bombach, G. et al. (eds.): Perspektiven der Konjunkturforschung. Tubingen: J.C.B. Mohr.

Kuh, E. (1966): Measurement of Potential Output. American Economic Review, 56, pp. 758-776.

Kydland, F.j Prescott, E.C. (1980): A Competitive Theory of Fluctuations and the Feasibility and Desirability of Stabilization Policy. In: Fischer, S. (1980a), pp. 169-187.

Laidler, D.E. W. (1976): An Elementary Monetarist Model of Simultaneous Fluctua­tions in Prices and Output. In: Frisch, H. (ed.): Inflation in Small Countries. Berlin-Heidelberg-New York: Springer, pp. 75-89.

Lefschetz, S. (1948): Lectures on Differential Equations. Princeton University Press.

Leijonhufvud, A. (1973): Effective Demand Failures. Swedish Journal of Economics, 75, pp. 27 - 48.

Levinson, N.j Smith, O.K. (1942): A General Equation for Relaxation Oscillations. Duke Mathematical Journal, 9, pp. 382-403.

Li, T.Y.j Yorke, J.A. (1975): Period Three Implies Chaos. American Mathematical Monthly, 82, pp. 985-992.

Lichtenberg, A.J.j Liebermann, M.A. (1982): Regular and Stochastic Motion. New York - Heidelberg - Berlin: Springer.

Lh'!nard, A. (1928): Etude des oscillations entretenues. Revue Generale de I' Elec­tricite, 23, pp. 901-46.

Lindbeck, A. (1976): Stabilization Policy in Open Economics with Endogenous Politi­cians. American Economic Review, Papers and Proceedings, 66, pp. 1-19.

214 References

Long, J .B. / Plosser, C.I. (1983): Real Business Cycles. Journal of Political Economy, 91, pp. 39-69.

Lorenz, E. N. (1963): Deterministic Non-Period Flows. Journal of Atmospheric Sci­ences, 20, pp. 130-141.

Lorenz, H.-W. (1985a): On Chaos, Business Cycles, and Economic Predictability. In: Gabisch, G./ v.Throtha, H. (1985): pp. 39-58.

Lorenz, H.-W. (1985b): Strange Attractors in a Multisector Business Cycle Model. University of Gottingen. Department of Economics. DP 24.

Lotka, A.Y. (1925): Elements of Physical Biology. Baltimore: Wiliams and Wilkens.

Lucas, R.E. (1973): Some International Evidence on Output-Inflation Tradeoffs. In: Lucas, R.E. (1981), pp. 131-l45.

Lucas, R.E. (1975): An Equilibrium Model of the Business Cycle. In: Lucas, R.E. (1981), pp. 179-214.

Lucas, R.E. (1981): Studies in Business Cycle Theory. Cambridge, Mass.: The MIT Press.

Lucas, R.E./ Prescott, E.C. (1974): Equilibrium Search and Unemployment. In: Lucas, R.E. (1981), pp. 156-178.

Lucas, R.E./ Sargent, T.J. (1979): After Keynesian Macroeconomics. In: Lucas, R.E./ Sargent, T.J. (1981), pp. 295-319.

Lucas, R.E./ Sargent, T.J. (eds.) (1981): Rational Expectations and Econometric Practice. Minneapolis: The University of Minnesota Press.

MacRae, D.C. (1977): A Political Model of the Business Cycle. Journal of Political Economy, 85, pp.239-263.

Malinvaud, E. (1977): The Theory of Unemployment Reconsidered. Oxford: Basil­Blackwell.

Marotto, F.R. (1979): Snap-Back Repellers Imply Chaos in Rn. Journal of Mathe­matical Analysis and Applications, 72, pp. 199-223.

Marsden, J.E. / McCracken, M. (1976): The Hopf-bifurcation and its Applications. New York - Heidelberg - Berlin: Springer.

Matthews, R.C.O. (1959): The Trade Cycle. Cambridge University Press.

May, R.M. (1976): Simple Mathematical Models With Very Complicated Dynamics. Nature, 261, pp. 459-467

McCallum, B. (1980): Rational Expectations and Macroeconomic Stabilization Pol­icy. Journal of Money, Credit and Banking, 12, p. 716-746.

Medio, A. (1980): A Classical Model of Business Cycles. In: Nell, E.J. (ed.): Growth, Profits, and Property. Cambridge: Cambridge University Press.

References 215

Medio, A. (1984): Synergetics and Dynamic Economic Models. In: Goodwin, R.M. et al. (1984), pp. 166 - 191.

Medio, A. (1986): Oscillations in Optimal Growth Models. Mimeo. University of Venice.

Melese, F./ Transue, W. (1986): Unscrambling Chaos Through Thick and Thin. Quarterly Journal of Economics, 101, pp. 419-423.

Mertens, D. (1961): Die kurzfristige Kapazitatsauslastungsrechnung des <ODIW. Vier­telsjahresschrift zur Wirtschaftsforschung. 1, pp. 72-90.

Metzler, L.A. (1941): The Nature and Stability of Inventory Cycles. Review of Eco­nomic Studies, 23, pp. 113-129.

Minford, P./ Peel, D. (1983): Rational Expectations and the New Macroeconomics. Oxford: M. Robertson.

Mitchell, w.e./ Burns, A.F. (1938): Statistical Indicators of Cyclic Revivals. Bulletin 69, National Bureau of Economic Research, New York; reprinted in: Moore, G.H. (1961), Ch. 6.

Moore, G.H. (1950): Statistical Indicators of Cyclic Revivals and Recessions. Occa­sional Paper 31, National Bureau of Economic Research, New York; reprinted in: Moore, G.H. (1961), Ch. 7.

Moore, G.H. (1954): Analysing Business Cycles. The American Statistician, 8, pp. 13-19.

Moore, G.H. (1955): The Diffusion of Business Cycles. In: Solo, R.A. (ed.): Economics and Public Interest. New Brunswick: Rutgers University Press; reprinted in: Moore, G.H. (1961), Ch. 8.

Moore, G.H. (1961): Business Cycle Indicators. Vol. 1, Princeton: Princeton Univer­sity Press.

Moore, G.H. {1979}: The Forty-second Anniversary of the Leading Indicators. In: Fellner, W. (ed.): Contemporary Economic Problems. Washington, D.C.: American Enterprise Institute; reprinted in: Moore, G.H. (1980), Ch. 20.

Moore, G.H. (1980): Business Cycles, Inflation and Forecasting. National Bureau of Economic Research: Studies in Business Cycles No.24, Cambridge, Mass.: Ballinger.

Muth, J.F. (1961): Rational Expectations and the Theory of Price Movements. In: Lucas, R.E./ Sargent, T.J. (1981)' pp. 3-22.

Nerlove, M. (1958): Adaptive Expectations and Cobweb Phenomena. Quarterly Jour­nal of Economics, 72, pp. 227-240.

Newhouse, S./ Ruelle, D./ Takens, F. (1978): Occurrence of Strange Axiom A Attractors near Quasi-Periodic Flows on T m , m > 3. Communications in Mathematical Physics, 64, pp. 35-40.

216 References

Nordhaus, W.D. (1975): The Political Business Cycle. Review of Economic Studies, 42, pp. 169-190.

Okun, A.M. (1962): Potential GNP: Its Measurement and Significance. American Statistical Association. Proceedings of the Business and Economic Statistics Section. 98-104. Reprinted in: Okun, A.M. (1970).

Okun, .M. (1970): Political Economy of Prosperity. Washington, D.C.: The Brookings Institution.

Ott, A.E. (1972) (ed.): Wachstumszyklen. Berlin: Duncker & Humblot.

Ott, E. (1981): Strange Attractors and Chaotic Motions of Dynamical Systems. Review of Modern Physics, 53, pp. 655-671.

Pasinetti, L.L (1960): Cyclical Fluctuations and Growth. Oxford Economic Papers, 12, pp. 215-241.

Patinkin, D. (1965): Money, Interest and Prices. 2nd. ed., New York: Harper & Row

Persons, W.M. (1919a): Indices of Business Conditions. Review of Economic Statis­tics, 1, pp. 5-107.

Persons, W.M. (1919b): An Index of General Business Conditions. Review of Eco­nomic Statistics, 1, pp. 111-205.

Persons, W.M. (1919c): General Business Conditions. Review of Economic Statistics, 1, Supplement, August 1919, pp. 2-8.

Phelps, E.S. et a1. (1969): Microeconomic Foundations of Employment and Inflation. New York: Norton

Phillips, A. W. (1954): Stabilisation Policy in a Closed Economy. Economic Journal, 64, pp. 290-323.

Phillips, A. W. (1963): An Appraisal of Measures of Capacity. American Economic Review, 53, pp. 275-292.

Ploeg, F. van der (1983): Predator-Prey and Neoclassical Models of Cyclical Growth. Zeitschrift fur Nationalokonomie, 43, pp. 235-256.

Ploeg, F. van der (1985 a): Optimal Government Policy in a Small Open Economy with Rational Expectations and Uncertain Election Outcomes. Paper presented at the World Congress of the Econometric Society, Boston/Mass., August 1985.

Ploeg, F. van der (1985 b): Rational Expectations, Risk and Chaos in Financial Markets, Mimeo London School of Economics, forthcoming in the Economic Journal.

Ploeg, F. van der (1985 c): Classical Growth Cycles, Metroeconomica, 37, pp. 221-230.

References 217

Pobjola, M.J. (1981): Stable and Chaotic Growth: the Dynamics of a Discrete Version of Goodwin's Growth Cycle Model. Zeitschrift fiir Nationalokonomie, 41, pp. 27-38.

Popper, K. (1934): Die Logik der Forschung. Wien: Springer. 8th ed., (1984), Tiibingen: J.C.B.Mohr. Engl. Transl.: The Logic of Scientific Research. 10th. ed., London: Hutchinson.

Poston, T./Stewart, I. (1978): Catastrophe Theory and its Applications. Boston: Pitman.

Prigogine, I. (1980): From being to becoming. San Francisco: W.H.Freeman.

Ramser, H.J. (1983): Preis-Lohn-Dynamik im Modell der neuen Keynesianischen Makrookonomik. In Bombach, G. et a1. (eds): Makrookonomik heute: Gemeinsamkeiten und Gegensatze. Tiibingen: J.C.B. Mohr.

Ramser, H.J. (1985): Konjunkturtheorie. Mimeo. University of Konstanz. March 85.

Rasche, R.H./Tatom, J.A. (1977): Energy Resources and Potential GNP. Review of the Federal Reserve Bank of St.Louis, 59, pp. 10-21.

Readings in Business Cycle Theory (1966), American Economic Association Series. London: Allen and Unwin.

Reichlin, P. (1985): Equilibrium Cycles and Stabilization Policies in an Overlapping Generations Model with Production. Mimeo. Columbia University, New York.

Rose, H. (1967): On the Non-Linear Theory of the Employment Cycle. Review of Economic Studies, 34, pp. 153-173.

Rossler, D.E. (1977): Continuous Chaos. In: Haken, H. (ed.): Synergetics. A Workshop. Berlin-Heidelberg-New York: Springer.

Ruelle, D. (1979): Strange Attractors. Mathematical Intelligencer, 1979, 2, pp. 126-137.

Ruelle, D. / Takens, F. (1971): On the Nature of Turbulence. Communications in Mathematical Physics, 20, pp. 167 - 192.

Sachverstandigenrat (1970): Jahresgutachten zur Begutachtung der gesamtwirt­schaftlichen Entwicklung. Mainz: Kohlhammer.

Sachverstandigenrat (1980): Jahresgutachten zur Begutachtung der gesamtwirt­schaftlichen Entwicklung. Mainz: Kohlhammer.

Samuelson, P.A. (1939): Interactions Between the Multiplier Analysis and Principle of Acceleration. Review of Economic Statistics, 21, pp. 75 - 78.

Samuelson, P.A. (1947): Foundations of Economic Analysis. Cambridge, Mass.: Har­vard University Press.

218 References

Samuelson, P.A. (1958): An Exact Consumption-Loan Model of Interest with or without the Social Contrivance of Money. Journal of Political Economy, 66, pp. 467-482.

Samuelson, P.A. (1971): Generalized Predator-Prey Oscillations in Ecological and Economic Equilibrium. In: Samuelson, P.A. (1972): The Collected Scientific Papers of P.A. Samuelson, Vol. III, pp. 487-90, Cambridge, Mass.: MIT-Press

Samuelson, P.A. (1972): A Universal Cycle? In: Samuelson, P.A. (1972): The Collected Scientific Papers of P.A. Samuelson, Vol. III, pp. 473-86, Cambridge, Mass.: MIT-Press.

Sato, Y. (1985): Marx-Goodwin Growth Cycles in a Two-Sector Economy. Zeitschrift fur Nationalokonomie. 45, pp. 21-34.

Saunders, P. T. (1980): An Introduction to Catastrophe Theory. Cambridge: Cam­bridge University Press.

Schinasi, G.J. (1981): A Non-Linear Dynamic Model of Short-Run Fluctuations. Review of Economic Studies, 48, pp. 649-656.

Schinasi, G.J. (1982): Fluctuations in a Dynamic, Intermediate-Run IS-LM Model: Applications of the Poincare-Bendixon Theorem. Journal of Economic Theory, 28, pp. 369-375.

Schonfeld, P. (1967): Probleme und Verfahren der Messung der Kapazitat und des Auslastungsgrades, Zeitschrift fur die gesamte Staatswissenschaft, 123, pp. 25-59.

Schroder, R. (1985): Chaotisches Verhalten von Differenzengleichungen. In: Ga­bisch, G./ v. Trotha, H. (1985), pp. 143-155.

Shiller, R.J. (1978): Rational Expectations and the Dynamic Structure of Macroecon­omic Models. Journal of Monetary Economics, 4, pp. 1-44.

Silverberg, G. (1984): Embodied Technical Progress in a Dynamic Economic Model: The Self-Organization Paradigm. In: Goodwin, R.M. et al. (1984), pp. 192 - 208.

Simonivits, A. (1982): Buffer Stocks and Naive Expectations in a Non-Walrasian Dy­namic Macromodel: Stability, Cyclicity and Chaos. The Scandinavian Journal of Economics, 84, pp. 571-581.

Skott, P. (1985): Vicious Circles and Cumulative Causation. Thames Papers in Polit­ical Economy. London: Thames Polytechnic.

Slutzky, E. (1937): The Summation of Random Causes as the Source of Cyclic Pro­cesses. Econometrica, 5, pp. 105-146.

Solow, R.M./Stiglitz, J.E. (1968): Output, Employment, and Wages in the Short Run. Quarterly Journal of Economics, 82, pp. 537-60.

References 219

Stahle, H. (1928): Das Beobachtungsverfahren der wirtschaftlichen Wechsellagen des Harvard-University Committee on Economic Research. Schmollers Jahrbuch, 52, pp. 261 - 310.

Straub, . M.j Wenig, A. (1985): The Interaction of Monetary and Non-Monetary Forces in the Business Cycle: A Simple Neo-Austrian Model. In: Gabisch, G.j v. Throtha, B. (1985), pp.59-84.

Strigel, W.H. (1977) (ed.): In Search for Economic Indicators. Berlin - Heidelberg­New York: Springer.

Stutzer, M. (1980): Chaotic Dynamics and Bifurcation in a Macro-Model. Journal of Economic Dynamics and Control, 2, pp. 253-276.

Takayama, A. (1974): Mathematical Economics. Hinsdale,IlI.: The Dryden Press.

Thorn, R. (1977): What is Catastrophe Theory about? In: Baken, H. (ed.): Syner­getics. A Workshop. Heidelberg - New York: Springer.

Thurow, L.j Taylor, L. (1966): The Interaction between the Actual and Potential Rates of Growth of the Economy. Review of Economic Studies, 48, pp. 351-360.

Tichy, G. (1982): Neuere Entwicklungen in der Konjunkturtheorie. IFO - Studien, 28, pp. 213 - 238.

Torre, V. (1977): Existence of Limit Cycles and Control in Complete Keynesian Sys­tems by Theory of Bifurcations. Econometrica, 45, pp. 1457-1466.

Ursprung, H. W. (1982): Die elementare Katastrophentheorie: Eine Darstellung aus der Sicht der Oekonomie. Berlin-Heidelberg-New York: Springer.

Varian, H.R. (1979): Catastrophe Theory and the Business Cycle. Economic Inquiry, 17,pp.14-28.

Varian, B.R. (1981): Dynamical Systems with Application to Economics. In: Arrow, K.J.j Intrilligat.or, M.D. (eds.): Handbook of Mathematical Economics, Vol. I, Amsterdam: North Holland, pp. 93-110.

Velupillai, K. (1978): Some Stability Properties of Goodwin's Growth Cycle Model, Zeitschrift fUr Nationalokonomie, 39, pp. 245-257.

Vercelli, A. (1984): Fluctuations and Growth: Keynes, Schumpeter, Marx, and the Structural Instability of Capitalism. In: Goodwin, R.M. et al. (1984), pp. 209 - 231.

Vining, R. (1949a): Koopmans on the Choice of Variables to be Studied and of Meth­ods of Measurement. Review of Economic Studies, 31. Reprinted in Readings (1966), pp. 204-217.

Vining, R. (1949b): A Rejoinder. Review of Economic Studies, 31, Reprinted in Readings (1966), pp.226-230.

220 References

Vogt, W. (1969): Fluktuationen in einer wachsenden Wirtschaft unter klassischen Bedingungen. In: Bombach, G. (ed.): Wachstum, Einkommensverteilung und wirtschaftliches Gleichgewicht. Berlin: Duncker und Humblot, pp. 61-72.

Volterra, V. (1931): Lecons sur la Theorie Mathematique de la Lutte pour la Vie. Paris: Gauthier-Villars.

Vosgerau, H.-J. (1979): Konjunkturtheorie. In: Handworterbuch der Wirtschafts­wissenschaften. Tiibingen: J.C.B. Mohr.

Vosgerau, H.-J. (1984): Einige Problemkomplexe der Konjunkturforschung. In: Bombach, G. et al. (eds.): Perspektiven der Konjunkturforschung. Tiibin­gen: J.C.B. Mohr.

Wagemann, E. (1928): Konjunkturlehre. Berlin: Hobbing.

Wallich, H.C. (1968): The American Council of Economic Advisers and the German Sachverstaendigenrat: A Study in the Economics of Advice. Quarterly Journal of Economics, 82, pp. 349-379.

Wenig, A. (1975): Beschiiftigungsschwankungen, Einkommensverteilung und Inflation. Zeitschrift fUr die gesamte Staatswissenschaft, 131, pp. 1-42.

Wenig, A. (1979): Konjunkturtheorie. In: Beckmann, M. et al. (eds). Handworter­buch der Mathematischen Wirtschaftstheorie. Wiesbaden: Beck. pp. 141 - 154.

Wold, H. (1954) A Study in the Analysis of Stationary Time Series. Stockholm.

Zarnowitz, V. (1985): Recent Work on Business Cycles in Historical Perspective. Journal of Economic Literature, 23, pp. 523-580.

Zeeman, E.C. (1977): Catastrophe Theory. Selected Papers 1972-77. Chapters 1 and 2, Reading, Mass.: Addison-Wesley.

Author Index

A

Abraham, R.M., 203. 205 Allen, R.G.D., 37, 39, 40, 58, 59,61,

205 Alexander, J.C., 154,205 Alexander, S.S., 12, 13,205 Andronov, A.A., 205 Arneodo, A., 187,205 Arnold, V.I., 188, 205 Arrow, K.J., 83, 205 Assenmacher, W., 205

B

Baumol, W.J., 37,56,205 Begg, D.K.H., 82, 86. 98ff., 206 Benassy, J.P., 130, 132ff., 206 Benhabib, J., 155, 159ff., 164,175,

178,206 Bergstrom, A.R., 206 Black, S.W., 27, 206 Blad, M.C., 201, 206 Blinder, A.S., 91, 94, 95, 206 Boldrin, M., 159, 206 Bombach, G., 213 Boyce, W.E., 37, 116ff., 145f., 206 Branson, W.H., 89, 206 Breuss, F, 28, 206 Broida, A.L., 10, 11, 12, 207 Brunner, K., 96f., 207

Burns, A.F., 8, 9, 19,207,215

c

Cagan, P., 85, 207 Carter, M., 86, 89, 207 Chaikin, C.E., 205 Chang, W.W., 119ff., 207 Christiano, L.J., 34, 207 Clark, C.M, 141, 207 Clark, J.M., 38, 207 Clower, R.W., 132, 207 Coddington, E.A., 37, 116, 118,207 Collet, P., 166, 169, 172, 207 Coullet, P., 205 Cukierman, A., 96f., 207 Cugno, F., 152, 164, 207, 208

D

Dana, R.A., 208 Davidson, P., 131, 208 Day, R.H., 166, 175ff., 206, 208 DeBaggis, H.F., 119,208 Debreu, G., 83, 118, 208 DeFoville, A., 19, 208 Dernburg, T.F. (J.D.), 37,40,41,

157, 208 Desai, M., 142, 208 Diamond, P.A., 83, 179, 209 Diamond, P., 166, 179, 209 DiPrima, R.L., 37, 116ff., 145f., 206 Dornbusch, R., 89, 209 Downs, A., 68, 209 Dumenil, G., 144, 209

E

Eckmann, J .-P., 166~ 169, 172, 207 Eigen, M., 143, 209 Evans, M.K., 209

222

F

Fehl, U., 204, 209 Feigenbaum, M., 166, 209 Fischer, E.O., 201,209 Fischer, S., 88f., 91, 95,206,209 Flaschel, P., 116, 142f., 144, 209, 210 Frey, B.S., 68, 72, 210 Friedman, B.M., 91, 210 Friedman, M., 89, 207, 210

G

Gabisch, G., 175, 210 Gaertner, W., 175,210 Garbers, H., 68, 210 Gater, R., 14,210 George, D., 200, 211 Georgescu-Roegen, N., 211 Gerard-Varet, L.A., 87, 211 Glansdorff, P., 203f., 211 Goldberg, S., 41, 58, 211 Goodwin, R,M., 102, 105, 139, 211 Gordon, R.A., 21,211 Grandmont, J .-M., 178ff., 211 Granger, C.W.J., 173,211 Guckenheimer, J., 153ff., 161£., 171,

181, 185ff., 211

H

Haavelmo, T., 207 Hahn, F .H., 83, 205, 207 Haken, H., 187, 190, 203f., 211 Hatanaka, M., 173, 211 Herrmann, R., 184, 212 Hicks, J.R., 43, 54, 212 Hirsch, M.W., 104, 116f., 139, 145f.,

212 Holmes, P., 153ff., 161£., 171, 181,

185ff., 211 Hopf, E., 161

A uthor Index

I

Ichimura, S., 147f., 212 Intrilligator, M., 70, 212 looss, G., 161, 212 Ipaktchi, A., 211

J

Jager, K., 212 Jammernegg, W., 201, 209 Jordan, R., 211 Joseph, D.D., 212

K

Kaldor, N., 102, 109ff, 120, 138, 212 Kalecki, M., 59, 74, 76, 77, 116,212 Kirchgiissner, G., 72, 210, 212 Kirman, A., 210 Klein, L.R., 33, 34, 212 Konig, H., 173, 212 Koopmans, T.C., 19f., 213 Krelle, W., 78ff., 213 Krengel, R., 23, 213 Kromphardt, J., 213 Kruger, M., 209, 211 Kuh, E., 27, 213 Kydland, F., 92, 213

L

Laidler, D.E.W., 51, 213 Lau, L.Y., 68, 210 Laroque, G., 180, 211 Lefschetz, S., 213 Leijonhufvud, A., 164, 213 Levinson, N., 37, 116, 118, 145, 207,

213 Levy, D., 144, 209 Li, T.Y., 165f., 169ff., 213

Lichtenberg, A.J., 185, 213 Liebermann, M.A., 185, 213 Lienard, A., 213 Lindbeck, A., 72, 213 Long, J.B., 97f., 213 Lorenz, E.N., 151, 165, 186,214 Lorenz, H.-W., 187,214 Lotka, A.Y., 139,214 Lucas, R.E., 88, 92, 94, 97f., 214

M

MacRae, D.C.;72, 214 Maddock, R., 86, 89, 207 Malgrange, P., 208 Malinvaud, E., 132f., 201, 214 Marotto, F.R., 166, 183ff., 214 Marsden, J.E., 154, 203,205,214 Matthews, R.C.O., 214 May, R.M., 167ff., 175, 214 McCallum, B., 88, 214 McCracken, M., 154, 214 Medio, A., 144, 159, 190, 214, 215 Melese, F., 172, 215 Meltzer, A.H., 96f., 207 Mertens, D., 23, 215 Metzler, L.A., 47, 215 Minford, P., 72, 215

Author Index

Mitchell, W.C., 8,9, 19,207,215 Miyao, T., 155, 160ff., 206 Montrucchio, L., 152, 164,207,208 Moore, G.H., 7ff., 215 ¥uth, J.F., 82, 85f., 215

N

Nerlove, M., 85, 215 Newhouse, S., 187, 215 Nishimura, K., 159, 206 Nordhaus, W.D., 68,72,215

o

Okun, A.M., 22, 23, 216 Oster, G., 211 Ott, A.E., 216 Ott, E., 165, 216

p

Pasinetti, L.L., 216 Patinkin, D., 120, 216 Peel, D., 72, 215 Persons, W.M., 6f., 216 Phelps, E.S., 92, 216 Phillips, A.W., 34,56,216 Ploeg, F. van der, 72, 143, 216 Plosser, J.I., 97f., 213 Pohjola, M.J., 143, 175,216 Popper, K., 20, 217 Poston, T., 188, 195,217 Prescott, E.C., 92, 213, 214 Preston, R.S., 33, 34, 212 Prigogine, I., 203f., 211, 217

R

Ramser, H.J., 88, 210, 217 Rasche, R.H., 24, 30, 32, 217 Reichlin, P., 164, 217 Rose, R., 123ff., 217 Rossler, O.E., 185, 217

223

Ruelle, D., 161, 185, 187, 215, 217 Russel, R.R., 27, 206

224

s

Samuelson, P.A., 37, 58, 83, 143f., 217,218

Sargent, T.J., 88, 94,214 Sato, Y., 143, 218 Saunders, P.T., 188f., 194f., 218 Schinasi, G.J., 138, 147f., 218 Schneider, F., 72, 210 Schonfeld, P, 27, 218 Schroder, R., 182,218 Semmler, W., 144,210 Shafer, W., 175,208 Shiller, R.J., 92,218 Silverberg, G., 204, 218 Simonovits, A., 218 Skott, P., 116, 218 Slutzky, E., 74f., 218 Smale, S., 104, 116f., 139, 145f., 212 Smith, O.K., 145, 213 Smyth, D.J., 119f., 207 Solow, R.M., 129,218 Stiihle, H., 14,218 Stewart, 1.,188,195,217 Stiglitz, J.E., 129, 218 Straub, M., 183, 219 Strigel, W.H., 18, 219 Stutzer, M., 175, 178, 219

T

Takayama, A., 70, 219 Takens, F., 161, 187,215,217 Tatom, J .A., 24, 30, 32, 219 Taylor, L., 27, 219 Thorn, R., 219 Thurow, 1., 27, 219 Tichy, G., 219 Tobin, J., 160 Torre, V., 158f., 219 Transue, W., 172, 215 Tresser, C., 205

Author Index

u Ursprung, H.W., 192, 219

v

Varian, H.R., 116, 196, 219 Velupillai, K., 142, 219 Vercelli, A., 203, 211, 219 Vining, R., 19, 219 Vogt, W., 102,219 Volterra, V., 139,220 Vosgerau, H.-J., 220 v. Trotha, H., 210

w

Wagemann, E., 17, 220 Wallich, H.C., 21,220 Wenig, A., 123, 128ff., 183, 219, 220 Winckler, R., 143, 209 Wold, H., 75, 220 Wolters, J., 173, 212

y

Yorke, J .A, 178, 165f., 169ff., 205, 213

z Zarnowitz, V., 220 Zeeman, E.C., 188, 201, 206, 221

Subject Index

A

ABC-curves, 6, 8 accelerator, 38ff., 43ff., 54f., 105 adiabatic approximation, 190

B

backward dynamics, 179f. barometers, 17 Bendixson-criterion, 119 bifurcation, 152

bifurcation point, 152 bifurcation set, 192 bifurcation value, 152 Hopf, 153ff., 195, 198 subcritical, 154, 162 supercritical, 155f., 162

budget, neutral budget, 5 budget surplus, 5.

Bureau of Census, 13, 34 business activities, 6

c capacity, 20, 25 capacity utilization, 20ff., 51

degree of, 22, 25ff., 51 catastrophe theory, 188ff.

catastrophes, elementary, 190 fold, 190, 192f., 201 cusp, 190, 193ff. swallowtail, 190 butterfly, 190 elliptic umbilic, 190 hyperbolic umbilic, 190 parabolic umbilic, 190

ceiling, 54 certainty equivalence, 86 chaos,

in discrete-time models, 166ff. in continuous-time models, 185ff

characteristic equation, see equation characteristic roots, see roots, charac-

teristic class struggle, 139ff Classical Unemployment, 132 codimension, 189f. coinciders, 6f. conservative system, 144 Cou"neil of Economic Advisers(CEA),

5,20, 27f. coupling of oscillators, 187f.

D

decay rate, 69 demand curve, aggregated, 133f. DeMoivre's theorem, 41 Department of Commerce, 13, 14 depreciation, 54f. depression, 5, 200 Deutsche Bundesbank, 27f., 32 Deutsches Institut fur Wirtschafts-

forschung, 23 diagnosis, 18f. Diamond-criterion, 181£ diffusion index, 9ff. discriminant, 157, 193f. disequilibria, 57, 130ff. dissipative system, 144, 203f. distributed lag, 85, 97

226

E

Economic Report of the President, 5, 20

effective demand, 132 eigenvalues, see roots, characteristic Employment Act, 20 energy, 30f. equation,

characteristic eq., 39, 44 difference eq., 37ff., 53 differential eq., 57 difference-differential eq., 59ff. Lienard eq., 144ff., 151 logistic eq., 167ff., 176 van der Pol eq., 145f., 151

equilibrium surface, 180f. equivalence, 152 expectations, 47

F

adaptive, 52,69, 85, 97, 135 extrapolative, 85 rational, 82, 86ff. static. 69. 84

Federal Reserve Board, 13, 31 Feigenbaum number, 169 finite delay, 60 fixed point, 154

expanding fixed point, 183f. of order k, 168

floor, 54 flow of a dynamical system, 117 frequency, 42, 173f.

G

generations, overlapping, 83, 179 generic, 152 Great Depression, 7, 20 Goodwin-modeL

Subject Index

Goodwin-model (continued): non-linear accelerator, 105ff. predator-prey, 139ff.

gradient systems, 19lf. growth model, 175ff

H

Hamiltonian, dynamics, 203 function, 70

harmonic oscillator, 104 Harvard Barometer, 6ff. Hessian matrix, 191 Hicks-model,

linear, 43ff. non-linear, 54ff.

Hopf-bifurcation, discrete-time, 161ff. continuous-time, 153ff., 195, 198

hysteris cycle, 199

I

IFO-Institute, 29, 35 imaginary axis, 154f. incumbent, 66ff. indicators, 6ff.

NBER,8ff. inflation, 51, 93 inventories, 47ff., 94f.

J

Jacobian matrix, 126, 136, 154, 158f. Jahresgutachten, see Sachverstandi­

genrat

Subject Index

K

Kaldor-model, 109ft'., 139ff., 147ff., 158f., 163

Kalecki-model, 59ft'., 116 Keynesian unemployment, 132

L

laggers,8. leaders, 8. Lienard equation, see equation limit cycle, 117ft'.

uniqueness, 144 stability, see uniqueness

limit point, 117 limit set, 117 LL Yorke theorem, 170ft'. Ljapunov function. 191, 195 Lorenz-attractor, 186 Lotka-Volterra-system, 139

M

macroeconomics, Keynesian, 1, 2 New Classical, 2, 82ff, 144 Non- Walrasian, 130ft'

Malinvaud-model, 132, 201 Markov-process, 93 measurement, 5ff. meteorology, 151 modulus, 41, 53, 152ft'., 162ff. monetarism, 53 monotonic,

damping, 40ff., 45f., 58,63 explosion, 40ff., 46, 63

morphogenesis, 151 moving summation, 75

N

NBER, 8ff., 13 neo-Austrian theory, 183 neo-Keynesian theory, 144 neo-Marxian theory, 144 notional demand. 132

o

Okun's law, 23. 31, orbit,

attracting, 155 closed, 117, 155 homoclinic, 186 repelling, 154

oscillation,

227

damped, 42f., 46, 50, 53, 55f., 61, 63,82

explosive (increasing), 42f., 46, 50, 55f., 61, 63

monotonic (harmonic), 42f., 50, 59, 63

oscillator, harmonic. 104

p

perfect foresight, 86, 179 perturbation, 188 Phillips-curve, 5lf.

linear, 51, 68f, 7lf., 140 non-linear, 125f

Poincare-Bendixson-theorem, 116ft'. , 122, 137, 159

Poincare-map, 181 policy-ineffectiveness, 91 political business cycle, 66 political economy, 144 potential, 191, 201 potential capital productivity, 24 potential output, 6, 20ft'. power spectrum, 173 f.

228

predator-prey-systems, 139ff, 164 principal minors, 157 prognosis, 18f

Q

quasi,

R

non-linear, 105 periodic, 187

random-numbers. 75f. rationality, 83ff rationing, 130ff recession, 200 re-election, 69 Repressed Inflation, 132 Robertson-lag, 37 Robinson-Crusoe-economy,97 roots,

characteristic, 40, 49f., 58, 120, 154 complex, 40, 46, 50, 58, 61, 154ff. dominant, 40, 162 real, 39f., 44f., 49, 58, 154

Routh-Hurwitz-criterion, 157 Runge-K utta-algorithm, 166

s

Sachverstiindigenrat, 6, 17, 21, 24 saddle-point, 99, 156 Samuelson-model, 37ff. Sarkovskii-theorem, 171£. Schur-criterion, 40 self-organization, 204 set,

bifurcation set, 152, 192 connected set, 118 singularity set, 191 uncountable, 171

Subject Index

shock, -dependent models, 36ff. erratic (random), 73 exogenous, 53, 56, 61, 63 -independent models, 100ff. permanent, 97 transitory, 97

snap-back repeller, 184 spectral analysis, 173f. stability,

global,ll0 structural, 105, 119, 152, 189f.,

202ff. Stability Law, 21 stochastics, 75f., 78 strange attractor, 166, 185 subcritical, see bifurcation supercritical, see bifurcation surveys, 34 supply curve, aggregated, 89, 133f. synergetics, 203

T

Taylor-expansion, 155, 162 toleration, 17f. torus, 187 transversality, 187 turbulences, 151

u

Underconsumption, 132 unemployment, 22f. unfolding, universal, 189f.

v

van der Pol oscillator, 145, 149, 187, 195

variables,

variables (continued): fast, 190 slow, 190

vector field, 117 vintage model, 102 voting function, 69

w

Wharton School Index. 33f. wealth, 120, 196f.

Subject Index 229

Vol. 184: R. E. Burkard and U. Derigs, Assignment and Matching Problems: Solution Methods with FORTRAN-Programs. VIII, 148 pages. 1980.

Vol. 185: C. C. von Weizsacker, Barriers to Entry. VI, 220 pages. 1980.

Vol. 186: Ch.-L. Hwang and K. Yoon, Multiple Attribute Decision Making - Methods and Applications. A State-of-the-Art-Survey. XI, 259 pages. 1981.

Vol. 187: W. Hock, K. Schittkowski, Test Examples for Nonlinear Programming Codes. V. 178 pages. 1981.

Vol. 188: D. Bos, Economic Theory of Public Enterprise. VII, 142 pages. 1981.

Vol. 189: A. P. Lothi, Messung wirtschaftlicher Ungleichheit. IX, 287 pages. 1981.

Vol. 190: J. N. Morse, Organizations: M~ltiple Agents with Multiple Criteria. Proceedings, 1980. VI, 509 pages. 1981.

Vol. 191: H. R. Sneessens, Theory and Estimation of Macroeconomic Rationing Models. VII, 138 pages. 1981.

Vol. 192: H. J. Bierens: Robust Methods and Asymptotic Theory in Nonlinear Econometrics. IX, 198 pages. 1981.

Vol. 193: J. K. Sengupta, Optimal Decisions under Uncertainty. VII, 156 pages. 1981.

Vol. 194: R. W. Shephard, Cost and Production Functions. XI, 104 pages. 1981.

Vol. 195: H. W. Ursprung, Die elementare Katastrophentheorie. Eine Darstellung aus der Sicht der Okonomie. VII, 332 pages. 1982.

Vol. 196: M. Nermuth, Information Structures in Economics. VIII, 236 pages. 1982.

Vol. 197: Integer Programming and Related Areas. A Classified Bibliography. 1978 - 1981. Edited by R. von Randow. XIV, 338 pages. 1982.

Vol. 198: P. Zweifel, Ein okonomisches Modell des Arztverhaltens. XIX, 392 Seiten. 1982.

Vol. 199: Evaluating Mathematical Programming Techniques. Pro­ceedings, 1981. Edited by J.M. MUlvey. XI, 379 pages. 1982.

Vol. 200: The Resource Sector in an Open Economy. Edited by H. Siebert. IX, 161 pages. 1984.

Vol. 201: P. M. C. de Boer, Price Effects in Input-Qutput-Relations: A Theoretical and Empirical Study for the Netherlands 1949-1967. X, 140 pages. 1982.

Vol. 202: U. Witt, J. Perske, SMS - A Program Package for Simulation and Gaming of Stochastic Market Processes and Learning Behavior. VII. 266 pages. 1982.

Vol. 203: Compilation of Input-Output Tables. Proceedings, 1981. Edited by J. V. Skolka. VII, 307 pages. 1982.

Vol. 204: K. C. Mosler, Entscheidungsregeln bei Risiko: Multivariate stochastische Dominanz. VII, 172 Seiten. 1982.

Vol. 205: R. Ramanathan, Introduction to the Theory of Economic Growth. IX, 347 pages. 1982.

Vol. 206: M. H. Karwan, V. Lotli, J. Teigen, and S. Zionts, Redundancy in Mathematical Programming. VII, 286 pages. 1983.

Vol. 207: Y. Fujimori, Modern Analysis of Value Theory. X, 165 pages. 1982.

Vol. 208: Econometric Decision Models. Proceedings, 1981. Edited by J. Gruber. VI, 364 pages. 1983.

Vol. 209: Essays and Surveys on Multiple Criteria Decision Making. Proceedings, 1982. Edited by P. Hansen. VII, 441 pages. 1983.

Vol. 210: Technology, Organization and Economic Structure. Edited by R. Sato and M.J. Beckmann. VIII, 195 pages. 1983.

Vol. 211: P. van den Heuvel, The Stability of a Macroeconomic System with Quantity Constraints. VII, 169 pages. 1983.

Vol. 212: R. Sato and T. NOno, Invariance Principles and the Structure of Technology. V, 94 pages. 1983.

Vol. 213: Aspiration Levels in Bargaining and Economic Decision Making. Proceedings, 1982. Edited by R. Tietz. VIII, 406 pages. 1983.

Vol. 214: M. Faber, H. Niemes und G. Stephan, Entropie, Umwelt­schutz und Rohstoffverbrauch. IX, 181 Seiten. 1983.

Vol. 215: Semi-Infinite P'rogramming and Applications. Proceedings, 1981. Edited by A. V. Fiacco and K.O. Kortanek. XI, 322 pages. 1983.

Vol. 216: H. H. Muller, Fiscal Policies in a General Equilibrium Model with Persistent Unemployment. VI, 92 pages. 1983.

Vol. 217: Ch. Grootaert, The Relation Between Final Demand and Income Distribution. XIV, 105 pages. 1983.

Vol. 218: P. van Loon, A Dynamic Theory of the Firm: Production, Finance and Investment. VII, 191 pages. 1983.

Vol. 219: E. van Damme, Refinements olthe Nash Equilibrium Concept. VI, 151 pages. 1983.

Vol. 220: M. Aoki, Notes on Economic Time Series Analysis: System Theoretic Perspectives. IX, 249 pages. 1983.

Vol. 221: S. Nakamura, An Inter·lndustry Translog Model of Prices and Technical Change for the West German Economy. XIV, 290 pages. 1984.

Vol. 222: P. Meier, Energy Systems Analysis for Developing Countries. VI, 344 pages. 1984.

Vol. 223: W. Trockel, Market Demand. VIII, 205 pages. 1984.

Vol. 224: M. Kiy, Ein disaggregiertes Prognosesystem liir die Bundes· republik Deutschland. XVIII, 276 Seiten. 1984.

Vol. 225: T. R. von Ungern-Sternberg, Zur Analyse von Markten mit unvollstandiger Nachfragerinformation. IX, 125 Seiten. 1984

Vol. 226: Selected Topics in Operations Research and Mathematical Economics. Proceedings, 1983. Edited by G. Hammer and D. Pallaschke. IX, 478 pages. 1984.

Vol. 227: Risk and Capital. Proceedings, 1983. Edited by G. Bam­berg and K. Spremann. VII, 306 pages. 1984.

Vol. 228: NonlinearModels of Fluctuating Growth. Proceedings, 1983. Edited by R. M. Goodwin, M. Kruger and A. Vercelli. XVII, 277 pages. 1984.

Vol. 229: Interactive Decision Analysis. Proceedings, 1983. Edited by M. Grauer and A. P. Wierzbicki. VIII, 269 pages. 1984.

Vol. 230: Macro-Economic Planning with Conflicting Goals. Proceed­ings, 1982. Edited by M. Despontin, P. Nijkamp and J. Spronk. VI, 297 pages. 1984.

Vol. 231: G. F. Newell, The M/M/= Service System with Ranked Ser­vers in Heavy Traffic. XI, 126 pages. 1984.

Vol. 232: L. Bauwens, Bayesian Full Information Analysis of Simultaneous Equation Models Using Integration by Monte Carlo. VI, 114 pages. 1984.

Vol. 233: G. Wagenhals, The World Copper Market. XI, 190 pages. 1984.

Vol. 234: B. C. Eaves, A Course in Triangulations for Solving Equations with Deformations. III, 302 pages. 1984.

Vol. 235: Stochastic Models in ReliabilityTheory. Proceedings, 1984. Edited by S. Osaki and Y. Hatoyama. VII, 212 pages. 1984.

Vol. 236: G. Gandolfo, P. C. Padoan, A Disequilibrium Model of Real and Financial Accumulation in an Open Economy. VI, 172 pages. 1984.

Vol. 237: Misspecification Analysis. Proceedings, 1983. Edited by T. K. Dijkstra. V, 129 pages. 1984.

Vol. 238: W. Domschke, A. Drexl, Location and Layout Planning. IV, 134 pages. 1985.

Vol. 239: Microeconomic Models of Housing Markets. Edited by K. Stahl. VII, 197 pages. 1985.

Vol. 240: Contributions to Operations Research. Proceedings, 1984. Edited by K. Neumann and D. Pallaschke. V, 190 pages. 1985.

Vol. 241: U. Wittmann, Das Konzept rationaler Preiserwartungen. XI, 310 Seiten. 1985.

Vol. 242: Decision Making with Multiple Objectives. Proceedings, 1984. Edited by Y. Y. Haimes and V. Chankong. XI, 571 pages. 1985.

Vol. 243: Integer Programming and Related Areas. A Classified Bibliography 1981-1984. Edited by R. von Randow. XX, 386 pages. 1985.

yol. 244: Advances in Equilibrium Theory. Proceedings, 1984. Edited by C. D. Aliprantis, O. Burkinshaw and N.J. Rothman. II, 235 pages. 1985.

Vol. 245: J. E. M. Wilhelm, Arbitrage Theory. VII, 114 pages. 1985.

Vol. 246: P. W. Otter, Dynamic Feature Space Modelling, Filtering and Self-Tuning Control of Stochastic Systems. XIV, 177 pages.1985.

Vol. 247: Optimization and Discrete Choice in Urban Systems. Proceedings, 1983. Edited by B.G. Hutchinson, P. Nijkamp and M. Batty. VI, 371 pages. 1985.

Vol. 248: Plural Rationality and Interactive Decision Processes. Pro­ceedings, 1984. Edited by M. Grauer, M. Thompson and A. P. Wierzbicki. VI, 354 pages. 1985.

Vol. 249: Spatial Price Equilibrium: Advances in Theory, Computation and Application. Proceedings, 1984. Edited by P. T. Harker. VII, 277 pages. 1985.

Vol. 250: M. Roubens, Ph. Vincke, Preference Modelling. VIII, 94 pages. 1985.

Vol. 251: Input-Output Modeling. Proceedings, 1984. Edited by A. Smyshlyaev. VI, 261 pages. 1985.

Vol. 252: A. Birolini, On the Use of Stochastic Processes in Modeling Reliability Problems. VI, 105 pages. 1985.

Vol. 253: C. Withagen, Economic Theory and International Trade in Natural Exhaustible Resources. VI, 172 pages. 1985.

Vol. 254: S. Muller, Arbitrage Pricing of Contingent Claims. VIII, 151 pages. 1985.

Vol. 255: Nondifferentiable Optimization: Motivations and Applica­tions. Proceedings, 1984. Edited by V. F. Demyanov and D. Pallasch­ke. VI, 350 pages. 1985.

Vol. 256: Convexity and Duality in Optimization. Proceedings, 1984. Edited by J. Ponstein. V, 142 pages. 1985.

Vol. 257: Dynamics of Macrosystems. Proceedings, 1984. Edited by J.-P. Aubin, D. Saari and K. Sigmund. VI, 280 pages. 1985.

Vol. 258: H. Funke, Eine allgemeine Theorie der Polypol- und Oligopolpreisbildung. III, 237 pages. 1985.

Vol. 259: Infinite Programming. Proceedings, 1984. Edited by E.J. Anderson and A.B. Philpott. XIV, 244 pages. 1985.

Vol. 260: H.-J. Kruse, Degeneracy Graphs and the Neighbourhood Problem. VIII, 128 pages. 1986.

Vol. 261: Th.R.Gulledge, Jr., N.K. Womer, The Economics of Made­to-Order Production. VI, 134 pages. 1986.

Vol. 262: H. U. Buhl, A Neo-Classical Theory of Distribution and Wealth. V, 146 pages. 1986.

Vol. 263: M. Schafer, Resource Extraction and Market Structure. XI, 154 pages. 1986.

Vol. 264: Models of Economic Dynamics. Proceedings, 1983. Edited by H.F. Sonnenschein. VII, 212 pages. 1986.

Vol. 265: Dynamic Games and Applications in Economics. Edited by T. B8.§ar. IX, 288 pages. 1986.

Vol. 266: Multi-Stage Production Planning and Inventory Control. Edited by S. Axsater, Ch. Schneeweiss and E. Silver. V, 284 pages. 1986.

Vol. 267: R. Bemelmans, The Capacity Aspect of Inventories. IX, 165 pages. 1986.

Vol. 268: V. Firchau, Information Evaluation in Capital Markets. VII, 103 pages. 1986.

Vol. 269: A. Borglin, H. Keiding, Optimality in Infinite Horizon Econo­mies. VI, 180 pages. 1986.

Vol. 270: Technological Change, Employment and Spatial Dynamics. Proceedings 1985. Edited by P. Nijkamp. VII, 466 pages. 1986.

Vol. 271: C. Hildreth, The Cowles Commission in Chicago, 1939-1955. V, 176 pages. 1986.

Vol. 272: G. Clemenz, Credit Markets with Asymmetric Information. VIII, 212 pages. 1986.

Vol. 273: Large-Scale Modelling and Interactive Decision Analysis. Proceedings, 1985. Edited by G. Fandel, M. Grauer, A. Kurzhanski and A. P. Wierzbicki. VII, 363 pages. 1986.

Vol. 274: W. K. Klein Haneveld, Duality in Stochastic Linear and Dynamic Programming. VII, 295 pages. 1986.

Vol. 275: Competition, Instability, and Nonlinear Cycles. Proceedings, 1985. Edited by W. Semmler. XII, 340 pages. 1986.

Vol. 276: M.R. Baye, D.A. Black, Consumer Behavior, Cost of Living Measures, and the Income Tax. VII, 119 pages. 1986.

Vol. 277: Studies in Austrian Capital Theory, Investment and Time. Edited by M. Faber. VI, 317 pages. 1986.

Vol. 278: W. E. Diewert, The Measurement of the Economic Benefits of Infrastructure Services. V, 202 pages. 1986.

Vol. 279: H.-J. Buttler, G. Frei and B. Schips, Estimation of Disequi­librium Models. VI, 114 pages. 1986.

Vol. 280: H. T. Lau, Combinatorial Heuristic Algorithms with FORTRAN. VII, 126 pages. 1986.

Vol. 281: Ch.-L. Hwang, M.-J. Lin, Group Decision Making under Multiple Criteria. XI, 400 pages. 1987.

Vol. 282: K. Schittkowski, More Test Examples for Nonlinear Pro­gramming Codes. V, 261 pages. 1987.

Vol. 283: G. Gabisch, H.-W. Lorenz, Business Cycle Theory. VII, 229 pages. 1987.

Multiple Criteria Decision Methods and Applications Selected Readings of the First International Summer School Acireale, Sicily, September 1983 Editors: G.Fandel, J.Spronk

1985. 56 fIgures, 35 tables. XIV, 402 pages. ISBN 3-540-15596-1

This book provides selected readings of the fIrst international summer school on multiple criteria decision making, held in Acireale Sicily, in September 1983. Its aim is to gi~e a state-of-the-art survey of multiple criteria deci­sion methods, applications and software. It is addressed to interested students, academic researchers beginning in fIelds such as computer science, operational research and management science and staff members in government and industry involved in planning and decision making. The fIrst part of the book is devoted to the philosophy of multiple criter:m decision making and to a survey of solution approaches for discrete problems. The second part is concerened with an evalua­tion of the usefulness of mUltiple criteria deci­sion making in practice.

E.Schlicht

Isolation and Aggregation in Economics 1985. XI, 112 pages. ISBN 3-540-15254-7

Contents: The Setting of the Argument. - On Isolation. - The Moving Equilibrium Method. - Econometric Implications. - The Nature of Macroeconomic Laws. - Epilogue: Economic Imagination. - References. - Author Index. -Subject Index.

M. Sattinger

Unemployment, Choice and Inequality 1985.7 fIgures, 49 tables. XIV, 175 pages. ISBN 3-540-15544-9

This book examines the earnings inequality generated when job search is used to assign workers to jobs. It explains the differences in earnings which are observed among otherwise identical workers and which are a substantial proportion of earnings inequality. Unlike' some previous treatments, it distinguishes between choice and random outcomes as sources of earnings differences. First, a model is developed in which workers search for jobs in a Markov process with two states, employment and unemployment. Firms at the same time search for workers and generate the wage offer distribution. This model is then used to study the costs of unem­ployment, the distribution of unemployment and the distribution of wage rates. Using U.S. census data, costs of unemployment are found to exeed foregone wages. The distribution of accepted wages is shown to differ from the ?istribution of wage offers. Earnings inequality IS then related to the distribution of un employ­ment, wage offers and reservation wages. With data from the U.S. census, estimates are found for the contributions of choice and random outcomes to earnings inequality. The book provides a systematic treatment of a source of inequality that has been neglected in the past, namely the earnings differences that arise for otherwise identical workers. It relates this inequality to the problem solved by job search that of assigning worker to jobs. '

Springer-Verlag Berlin Heidelberg New York Tokyo