REFERENCES
Alhadeff, D.A., (1982), "Microeconomics and human behavior: Towards a new
synthesis of economics and psychology," University of California
Press, Berkeley, London
Allen, R., Hicks, J., (1934), "A Reconsideration of the Theorie of Value,"
Economica 1
Arrow, K.J.; Debreu, G., (1954), "Existence of Equilibrium for a Competitive
Economy," Econometrica, 22, 265-290
Arrow, K.J.; Hahn, F.H., (1971), "General Competitive Analysis," Holden-Day,
San Francisco
Azariadis, C., (1981), " Self-Fulfilling Prophecies," Journal of Economic Theory,
25,380-396
Azariadis, C.; Guesnerie, R., (1986), "Sunspot and Cycles," Review of Economic
Studies, 53, 725-738
Baumol, W J.; Quandt, R.E., (1985), "Chaos Models and the Implications for
Forecasting," Eastern Economic Journal, 11(1),3-15
Ben-Akiva, M.; Lerman, S.R., (1985), "Discret Choice Analysis: Theory and
Application to Predict Travel Demand," MIT Press, Cambridge,
MA
Benassy, J.P., (1982), "The economics of market disequilibrium," Economic
Theory, Econometrics, and Mathematical Economics Series,
Academic Press, New York
Benassy, J.P, (1984), "Non-Walrasian Model of the Business Cycle," Journal of
Economic Behavior and Organisation, 5(1), 77-89
116
Benettin, G.; Galgani, L.; Strelcyn, J.-M., (1976), "Kolmogorov Entropy and
Numerical Experiments," Physical Review A, 14,2338
Bergstrom, A.R., (1962), "A Model of Technical Progress, the Production Function
and Cyclical Growth," Economica 29
Boland, L.A., (1986), "Methodology for a new microeconomics: The critical
foundations," Allen & Unwin, Boston
Bombach, G.; Ramser, H.J.; Timmermann, M., (eds.), (1984), "Der
Keynesianismus V," Springer Verlag, Berlin
Branson, W. H., (1979), "Macroeconomic Theory and Policy," Harper & Row, New
York
Cass, D.; Shell, K., (1983), "Do Sunspots Matter?," Journal of Political Economy,
Vol. 91, 193-227
Casti, J.L., (1989), "Alternate realities: Mathematical modells of nature and man,"
Wile-Intesience, New York
Chiappori, P.A.; Guesnerie, R., (1988), "Endogenous Fluctuations under Rational
Expectations," European Economic Review, 32, 389-397
Christmann, Albert, (1991), "Anwendungen der Synergetik und Chaostheorie in
der Okonomie"
Clower, R.W., (1965), "The Keynesian Counterrevolution: A Theoretical
Appraisal," in "The Theory ofInterest Rates," ed. by F.H. Hahn
and Brechling, Macmillian, London
Clower, R. W., (1975), "Reflexions on the Keynesian Perplex," Zeitschrift fUr
Nationalokonomie,35
Coddington, A., (1976), "Keynesian Economics: The Search for the First
Principles," Journal of Economic Literature, Vol. 14, 1258-1273
Day, R. H., (1982), "Irregular Growth Cycles," American Economic Review, 72(3),
406-414
117
Day, R. H., (1982), "Dynamical Systems Theory and Complicated Economic
Behavior," MRG working Paper 215, Department of Economics,
University of Southern California
Day, R. H., (1983), "Disequilibrium Economic Dynamics-A Post-Schumpeterian
Contribution," Journal of Economic Behavior and Organization,
Vol. 5,57-76
Day, R. H., (1983), "The Emergency of Chaos from Classical Economic Growth,"
Quarterly Journal of Economics, Vol 98, 201-213
Day, R.H.,; Shafer, W., (1985), "Keynesian Chaos," Journal of Macroeconomics,
Vol. 7,277-295
Day, R. H., (1987), "The General Theory of Disequilibrium Economics and of
Economic Evolution," in: Batten, D.; Casti, J.; Johansson, B.,
(eds.), "Economic Evolution and Structural Adjustment," Lecture
Notes in Economics and Mathematical Systems, Springer, Berlin,
New York
Deutsche Bundesbank, (1960.1990), "Statistische Beihefte zu den Monatsberichten
der Deutschen Bundesbank; Saisonbereinigte Wirtschaftszahlen,
Reihe4"
Dujin, J.J., (1983), "The Long Wave in Economic Life," London
Drazen, A., (1980), "Recent Developments in Macroeconomic Disequilibrium
Theory," Econometrica, Vol. 48 (2), 283-306
Drazen, A. (1988), "Self fulfilling Optimism in a Trade Friction Model of Business
Cycle," American Economic Review, 78(2), 389-397
Earl, P.E., (edt.), (1988), "Psychological Economics: Development, tensions,
prospects," Recent Economic Thought Series, Kluwer Academics
Fischer, M.M.; Haag, G.; Sonis, M.; Weidlich, W., (1988), "Account to Different
Views in Dynamic Choice Processes," Paper presented at the GIU
Working Group on Mathematical Models, Canbera
118
Fisher, F.M., (1983), "Disequilibrium foundations of equilibrium economics,"
Cambridge University Press, Cambridge, MA
Frank, M.Z.; Stengos, T., (1988), "Chaotic Dynamics in Economic Time Series,"
Journal of Economic Survey, 2,103-133
Frydman, R.; Phelps, E.S., (eds.), (1983), "Individual forecasting and aggregate
outcomes: 'Rational Expectations' examined," Cambridge University Press, Cambridge
Froehling, H.; Crutchfield, J.P.; Farmer, D.; Packard, N.H.; Shaw, R., (1981),
"On Determining the Dimension of Chaotic Flows," Physica 3D,
605-617
Gabisch, G.; Lorenz, H. W., (1987), "Business Cycle Theory. A Survey of
Methods and Concepts," Berlin
Georgescu-Roegen, N., (1971), "The Entropy Law and the Economic Process,"
Harvard University Press, Cambridge Mass.
Golledge, R.G.; Timmermans, H., (eds.), (1988), "Behaviourial Modelling in
Geography and Planning," Croom Helm, London, New York,
Sydney
Goodwin, R.M., (1950), "A Non-Linear Theory of the Cycle," Review of
Economics and Statistics, 32
Goodwin, R.M., (1951), "The Nonlinear Accelerator and the Persistence of
Business Cycles," Econometrica, Vol. 19, 1-18
Goodwin, R.M.; Kruger, M.; Vercelli, A. (eds.), (1984), "Nonlinear Models of
Fluctuating Growth," Lecture Notes in Economic and Mathematic,
Springer, Berlin, New York
Grandmont, J.M., (1975), "On Money and Banking," Review of Economic Studies,
42,207-236
Grandmont, J.M.; Laroque, G., (1976), "On Keynesian Temporary Equilibria,"
Review of Economic Studies, 43, 53-67
119
Grandmont, J.M., (1977), "Temporary General Equilibrium Theory,"
Economebica,45,535-573
Grandmont, J.M., (1985), "On Endogenous Competitive Business Cycles,"
Economebica, Vol. 53 (5),995-1045
Grandmont, J.M.; Laroque, G., (1986), "Stability of Cycles and Expectations,"
Journal of Economic Theory, 40(1),138-151
Grandmont, J.M.; Malgrange, P., (1986), "Nonlinear Economic Dynamics:
Introduction," Journal of Economic Theory 40,3-12
Grassberger, P.; Procaccia, L, (1983), "Measuring the Strangeness of Strange
Attractors", Physica D 9, 189
Green, J.R., (1973), "Temporary General Equilibrium in a Sequential Trading
Model with Spot and Future Transactions," Economebica, 41,
1103-1123
Greenwald, B.; Stieglitz, J.E., (1987), "Keynesian, New Keynesian and New
Classical Economics," Oxford Economic Papers, 39, 119-132
Grossman, J., (1982), "Heterogenous Information and the Theory of Business
Cycle," Journal of Political Economics, 90(4), 699-727
Guckenheimer, J.; Holmes, P., (1983), "Nonlinear Oscillations, Dynamical
Systems, and Bifurcation of Vector Fields," Springer, New York
Berlin-Heidelberg
Guesnerie, L.E., (1986), "Stationary Sunspots Equilibria in aN-Commodity
World," Journal of Economic Theory, 40(1), 103-127
Haag, G.; Dendrinos, D.S., (1983), "Towards a Stochastic Theory of Location: A
Nonlinear Migration Process," Geographical Analysis, Vol. 15 (4),
269-286
Haag, G.; Weidlich, W., (1983), " A Stochastic Theory ofInterregional Migration,"
Geographical Analysis, 16,331-357
120
Haag, G.; Weidlich, W.; Mensch, G., (1987), "The Schumpeter Clock," in: Batten,
D.; Casti, J.; Johansson, B., (eds.), "Economic Evolution and
Structural Adjustment," Lecture Notes in Economics and
Mathematical Systems, Springer, Berlin, New York
Haag, G., (1989a), "Dynamic Decision Theory: Application to Urban and Regional
Topics," Kluwer Academics Publishers, Dordrecht
Haag, G., (1989b), "A Master Equation of Aggregate and Disaggregate Economic
Decision-Making," Paper presented at the 29th RSA European
Congress, Cambridge, GB
Hahn, F.H., (1965), "On Some Problems of Proving the Existence of an
Equilibrium in a Monetary Economy" in: "The Theory of Interest
Rates," ed. by F.H. Hahn and Brechling, Macmillian, London
Haken, H., (1977), "Synergetics, an Introduction," 2nd ed. Vol. 1, Springer Series
Haken, H., (1983), "Advanced Synergetics, Instability Hierarchies on Self
Organizing Systems and Devices," Springer Series in Synergetics,
Vol. 20, Springer, Berlin
Hicks, J.R., (1939), "Value and Capital. An Inquiry into some Fundamental
Principles of Economic Theory," Oxford
Hicks, J.R., (1950), "A Contribution to the Theory of the Trade Cycle," Oxford
University Press, London
Hillinger, C; Weser, T. (1988), "Die Aggregationsproblematik in der
Konjunkturtheorie," Jahrbuch fUr Nationalokonomie und Statistik,
204(4), 326-341
Hirsch, M. W.; Smale, S., (1974), "Differential Equations, Dynamical Systems,
and Linear Algebra," Academic Press, New York
Isard, W., (1956), "Location and Space Economy," MIT Press, Cambridge, Mass.
Isard, W., (1960), "Methods of Regional Analysis: an Introduction to Regional
Science," MIT Press, Cambridge, Mass.
121
Kahnemann, D.; Siovic, P.; Tversky, A., (eds.), (1982), "Judgement under
Uncertainty: Heuristics and Biases," Cambridge University Press,
Cambridge
Kaplan, J.L.; Yorke, J.A., (1979), "Functional Differential Equations and
Aproximations of Fixed Points," ed. by H.-O. Peitgen and H.-O Walther, Lecture Notes in Mathematics, 730
Katona, G., (1951), "Psychological Analysis of economic behavior," McGraw-Hill,
New York
Katona, G., (1980), "Essays on behavioral Economics," Ann Arbor
Kelsey, D., (1988), "The Economics of Chaos or the Chaos of Economics," Oxford
Economic Papers, 40, 1-31
Keynes, J.M., (1936), "The General Theory of Employment, Interest and Money,"
HBJ edition 1964, San Diego, New York
King, R.G.; Plosser, C.I., (1984), "Money, Credit, and Prices in a Real Business
Cycle," American Economic Review, Vol.74, 363-383
Koblo, R.B., (1989), "Shares and Flows: A New Approach to an Evolutionary
Business Cycle Theory," Paper presented at the RSA Conference,
Nov., IS-18th., 1989
Kromphardt, J., (1989), "Konjunkturtheorie heute: ein Uberblick," Zeitschrift flir
Wirtschafts- und Sozialwissenschaften, 109, 173- 231
Kydland, F.E.; Prescott, E.C., (1982), "Time to Build and Aggregate
Fluctuations," Econometrica, Vol. 50, 1345-1370
Ledyard, J.O., (1974), "On Sequences of Temporary Equilibria" in: "Essays on
Economic Behavior under Uncertainty, Contributions to Economic Analysis, " ed. by M. Balch; D. McFaddden, and S.W. Yu,
Amsterdam
Leijonhufvud, A., (1968), "On Keynesian Economics and the Economics of
Keynes," Oxford University Press, Oxford
122
Leijonhufvud, A., (1981), "Infonnationand Coordination: Essays in
macroeconomic Theory," Oxford University Press, New York,
Oxford
Long, J.B., Plosser, C.I., (1983), "Real Business Cycles," Journal of Political
Economy, Vol. 91,39-69
Lorenz, H.W., (1987a), "Goodwin's Nonlinear Accelerator and Chaotic Motion,"
Zeitschrift fUr Nationalokonomie und Statistik, 47(4), 413-418
Lorenz, H.W., (1987b), "Strange Attractors in a Multi-Sector Business Cycle
Model," Journal of Economic Behavior and Organisation, 8(3),
397-411
Lorenz, H. W., (1988), "Neuere Entwicklungen in der Theory dynamischer
okonomischer Prozesse," Jahrbiicher fUr Nationalokonomie und
Statistik 204,295-315
Lucas, R.E., (1975), "An Equilibrium Model of the Business Cycle," Journal of
Political Economy, Vol. 83, 1113-1144
Lucas, R.E., (1980), "Methods and Problems in Business Cycle Theory," Journal of
Money, Credit, and Banking, Vol. 12 (4), 696-715
Mankiw, N.G., (1989), "Real Business Cycles: A New Keynesian Perspective,"
Journal of Econoic Perspectives, Vol. 3 (3), 79-90
Mensch, G., (1975), "Das technologische Patt. Innovationen iiberwinden
Depressionen," Umschau Verlag, Frankfurt a.M.
Meyer, U., (1983), "Neue Makrookonomik," Springer Verlag, Berlin
Negishi, Takashi, (1979), "Microeconomic foundation of Keynesian
Macroeconomics," Studies in mathematical and managerial
economics, New York
Nelson, R. R.; Winter, S.G., (1974), "Neoclassical vs. Evolutionary Theories of
Economic Growth: Critique and Prospectus," Economic Journal,
84,886-905
123
Nelson, R. R.; Winter, S.G., (1982), "An Evolutionary Theory of Economic
Change," Cambridge Mass., Harvard University Press
Nicolis, G.; Prigogine, L, (1977), "Self-Organization in Nonlinear Systems: From
Dissipative Structures to Order through Fluctuations," John Wiley
& Sons, New York
Oppenlander, K.H.; Poser, G., (eds.), (1989), "Handbuch der Ifo-Umfragen;
Vierzig Jahre Unternehmensbefragungen des Ifo-Instituts fOr
Wirtschaftsforschung, MUnchen," Duncker & Humblot, Berlin
O'Driscoll, G.P.; Rizzo, M.J., (1985), "The Economics of time and ignorance,"
Blackwell, New York
O'F1aherty, B., (1985), "Rational commitment: A foundation for macroeconomics,"
Duke University Press, Durham
Okun, .A.M., (1980), "Rational-Expectations-with-Misperceptions as a Theory of
the Business Cyle," Journal of Money, Credit, and Banking, Part 2,
12(4),817-825
Pareto, V., (1906), "Manual of political economy," Translated by A.S. Schwier,
edt. by A.S. Schwier and A.N. Page, 1971, Kelley, New York
Patinkin, D., (1965), "Money, Interest and Prices," Harper and Row, New York, 1st
ed. 1956
Phelps, E.S.; et aI., (1970), "Microeconomic Foundation of Employmentand
Inflation Theory," New York
Phillips, A., (1954), "Stabilisation Policy in a closed Economy," Economic Journal
64,291-323
Phillips, A., (1961), "A Simple Model of Employment, Money and Prices,"
Economica 28, 360-370
Pittield, D.E., (1984), "Discrete Choice Models in Regional Science," Pion, London
124
Plosser, C.I., (1989), "Understanding Real Business Cycles," Journal of Economic
Perspectives, Vol.3 (3)" 51-77
Puu, T. (1987), "Complex Dynamics in Continuous Models of the Business Cycle,"
in: Batten, D.; Casti, J.; Johansson, B., (eds.), "Economic
Evolution and Structural Adjustment," Lecture Notes in Economics
and Mathematical Systems, Springer, Berlin, New York
Radner, R., (1975), "Satisficing," Journal of Mathematical Economics, Vol. 2, 253-
262
Ramser, H.J., (1988), "Neuere Beitdtge zur Konjunkturtheorie: ein Uberblick,"
IFO-Studien, 34, 95-115
Reiner, R.; Munz, M.; Weidlich, W., (1988), "Migratory dynamics of interacting
subpopulations: regular and chaotic behavior", System Dynamic
Review, Vol. 4,179-199
Samuelson, P.A., (1938), "A Note on the Pure Theory of Consumers's Behaviour,"
Economica 5, P. 61-71
Samuelson, P.A,. (1939), "Interactions between the Multiplier Analysis and the
Princible of Acceleration," The Review of Economic Statistics,
Cambridge, MA, 21, 75-78
Samuelson, P.A,. (1946), "Foundations of Economic Analysis," Harvard University
Press, Cambridge, MA
Scharfstein, D.S.; Stein, J.C., (1990), "Herd Behavior and Investment," The
American Economic Review, 80 (3), 465-479
Schelling, T.C., (1978), "Micromotives and Macrobehavior," Fels Lecture on Public
Policy Analysis, Norton, New York, London
Schumpeter, J. A., (1934), "Theory of Economic Development," Harvard
University Press
Schumpeter, J. A., (1950), "Capitalism, Socialism and Democracy," 3rd ed., Harper
and Brothers, New York
125
Seitz, H., (1989), "Die Quantifizierung von Tendenzbefragungen: Ein Uberblick,"
Ifo-Studien, Vol.35 (1)
Semmler, G., (1986), "On Nonlinear Theories of Economic Cycles and the
Persistence of Business Cycles," Mathematical Social Sciences,
12(1),47-76
Shaw, R., (1981), "Strange Attractors, Chaotic Behavior, and Information Flow,"
Zeitschrift ffir Naturforschung, 36A, 80
Simon, H. A., (1955), "A Behavioral Model of Rational Choice," Quarterly Journal
of Economics, Vol. 69, 99-118
Simon, H.A., (1979), "Rational Decision Making in Business Organizations,"
American Economic Review, Vol. 69, 493-513
Simon, H.A., (1983), "Reason in Human Affairs," Stanford University Press
Smith, T.R., (1981), "Transition probabilities and Behavior in Master Equation
Descriptions of Population Movements," in: Griffith, D.A.;
MacKinnon, R., (eds.), "Dynamic Spatial Models," Sijthoff and
Noordhoff, Alphen aan den Rijn
Stigum, B., (1969), "Entrepreneurial Choice over Time under Conditions of
Uncertainty," International Economic Review, 10,426-442
Strigel, W.H., (1985), "Das Geschaftsklima als Konjunkturindikator," IFO-Studien,
31(1),29-68
Tobin, J., (1980), "Asset Accumulation and Economic Activity," Yrjo Jahnsson
Lectures, Basil Blackwell, Oxford
Tversky, A., (1972), "Elimination by Aspect: A Theory of Choice," Psychological
Review, Vol. 79, 281-299
VellupiIIai, K., (1986), "From the Fractals of Micro to the Chaos of Macro," Journal
of Economic Dynamic Control, 10, 269-272
126
Weidlich, W., (1971), "The Statistical Description of Polarization Phenomena in
Society," Br. J. math. stat. Psychology, 24, 251-266
Weidlich, W.; Haag, G., (1983), "Concepts and Models of a Quantitative
Sociology," Springer Series in Synergetics, Vol 14, Springer
Weidlich, W., (1987), "Quantitative Social Science," Physica Scripta, Vol. 35,380-
387
Weidlich, W., Haag, G., (eds.), (1988), "Interregional Migration, Dynamic Theory
and Comparative Analysis," Springer, New York
Weintraub, E.R., (1979), "Microfoundations," Cambridge Press, New York
Witt, U., (1987), "Individualistische Grundlagen der evolutorischen Okonomik,"
Mohr, Tiibingen
Wolf, A.; Swift, J. B.; Swinney H. L.; Vastano, J. A., (1985), "Determining
Lyapunov Exponents from a Time Series," Physica 16D, 285-317
Woodford, M. (1987), "Three Questions about Sunspot Equilibria as an Explanation
of Economic Fluctuations," American Economic Review, Vol. 77,
P+P, 93-98
INDEX OF FIGURES AND TABLES
Figure 1.1: Interdependence of signals and actions .............................................. 8
Figure 12: Classification of different dynamic choice model approaches ........... 17
Figure 1.3: The master equation point of view the relationship between the
micro and macrolevel in decision processes ...................................... 18
Figure II. 1 : a) Phase diagram of ySu and I for the case of an undamped
cyclic motion (c = 0.8; a = 1; B = 1; v = 1.2); b) Plot of
dY/dt = 0 [-] and dI/dt = 0 [- - -] .................................................. 37
Figure II.2: Effect of an exogenous disruption of Y = 5 at t = 20 ......................... 38
Figure II.3: Graphical solutions of the functions FI = 0 and F2 = 0: [-1;
(a) FI = 0 for small a2: [ ....... ]; (b) FI = 0 for large a2: [- - -] ........... .49
Figure II.4: Domain Dc with interior boundary Ci and exterior boundary Ce. All trajectories enter Dc and remain in Dc according to the
arrows showing the direction of the flux ........................................... 53
Figure II.5: (a) Trajectories in the Y-x plane approaching the one stable focus at the singular point Po for al = 0.09 ; a2 = 0.1; 1= 1.0;
yo = 100; (b) Paths of x(t) and Y(t) for the parameters of (a) ......... 56
Figure II.6: (a) Trajectories in the Y-x plane for al = 0.11; a2 = 0.1;
1 = 1.0; Yo = 100; (b) Paths of x(t) and Y(t) for the parameters
of (a) ................................................................................................ 56
Figure II.7: (a) Trajectories in the Y-x plane for al = 0.11; a2 = 0.4; 1= 1;
yo = 100; (b) Paths ofx(t) and Y(t) for the parameters of (a) .......... 57
128
Figure 11.8 (a) Trajectories in the Y-x plane for al = 0.11; a2 = 0.4;
Y = 2.0; yo = 100; (b) Paths of x(t) and yet) for the
parameters of (a) .............................................................................. 58
Figure ll.9: (a) Trajectories in the Y-x plane for al = 0.18; a2 = 0.4; Y= 0.5;
yo = 100; (b) Paths of x(t) and yet) for the parameters of (a) ....... .59
Figure ll.10: (a) Trajectories in the Y-x plane for al = 0.17; a2 = 1.3; 'Y= 4.0;
yo = 100; with the initial values Yo = 55, XO = 0.25; (b) Paths
of x(t) and yet) for the parameters of (a) ....................................... 60
Figure 11.11: (a) Trajectories in the Y-x plane for al = 0.17; a2 = 1.3; Y = 4;
yo = 100; with the initial values Yo = 52, Xo = - 0.25; (b) Paths
of x(t) and yet) for the parameters of (a) ......................................... 60
Figure 11.12: Graphical solutions of the functions F} = 0 and F2 = 0: L-J; (a) FI = 0 for small a2: [ ....... ] (one singular point); (b) F} = 0 in the marginal case L _ -1 (3 singular points); (c) FI = 0 for
large a2: [- - - ] (5 singular points) ................................................... 70
Figure ll.13: (a) Trajectories in the q-x plane for al = 0.1; a2 = 1.0; bl=0.07;
b2=1.2; 1-1.0; (b) Paths of x(t) and q(t) for the parameters of
(a) ........................................................•..........•............•................... 74
Figure ll.14: (a) Trajectories in the q-x plane for al = 0.15; a2 = 1.0;
bl=O.07; b2=1.2; 1-1.0; (b) Paths of x(t) and q(t) for the
parameters of (a) .............................................................................. 75
Figure 11.15: (a) Trajectories in the q-x plane for al = 0.1; a2 = 1.0;
bl = 0.12; b2 = 1.2; Y = 1.0; (b) Paths of x(t) and q(t) for the
parameters of (a) .............................................................................. 75
Figure 11.16: (a) Trajectories in the q-x plane for al = 0.1; a2 = 1.1;
bl = 0.07; bl = 1.2; Y =1.0; (b) Paths of x(t) and q(t) for the
parameters of (a) .............................................................................. 76
129
Figure 11.17: (a) Trajectories in the q-x plane for al = 0.1; a2 = 1.0;
bl = 0.07; b2 = 1.3; 'Y =1.0; (b) Paths of x(t) and q(t) for the
parameters of (a) .............................................................................. 76
Figure 11.18: (a) Trajectories in the q-x plane for al = 0.1; a2 = 1.5;
bl = 0.07; b2 = 1.5; y:=1.0; with the initial values qo = - 0.5; Xo = - 0.1; (b) Paths of x(t) and q(t) for the parameters of (a) ........ 77
Figure 11.19: (a) Trajectories in the q-x plane for al = 0.1; a2 = 1.5; b l=O.07;
b2=1.5; y:=1.0; with the initial values qo = 0.5; XQ = 0.1; (b)
Paths ofx(t) and q(t) for the parameters of (a) ................................ 77
Figure 11.20: (a) Paths of x(t), q(t) and wet) for al = 0.04; a2 = 0.8; bl = 0.05;
b2 = 5; ci = 0.005; c2 = 0.5; 'Y = 2; 1<: = 2. (b) Trajectories of
x(t) and q(t) in the x-q plane for the parameters of (a) ...................... 85
Figure 11.21: (a) Paths of x(t), q(t) and wet) for al = 0.06; a2 = 0.8; bl = 0.05;
b2 = 5; ci = 0.005; c2 = 0.5; 'Y = 2; 1<: = 2. (b) Trajectories of
x(t) and q(t) in the x-q plane for the parameters of (a) ...................... 86
Figure 11.22: (a) Paths of x(t), q(t) and wet) for al = 0.04; a2 = 0.8; bl = 0.06;
b2 = 5; cl = 0.005; c2 = 0.5; 'Y = 2; 1<: = 2. (b) Trajectories of
x(t) and q(t) in the x-q plane for the parameters of (a) ...................... 86
Figure 11.23: (a) Paths of x(t), q(t) and wet) for al = 0.04; a2 = 0.8; b l = 0.05;
b2 = 5; CI = 0.0053; c2 = 0.5; 'Y = 2; 1<: = 2. (b) Trajectories of
x(t) and q(t) in the x-q plane for the parameters of (a) ............. : ........ 87
Figure 11.24: (a) Paths of x(t), q(t) and wet) for al = 0.04; a2 = 0.8; bl = 0.05;
b2 = 5; ci = 0.0055; c2 = 0.5; 'Y = 2; 1<: = 2. and an initial excess
demand > 0 (b) Paths of x(t), q(t) and wet) for the same
parameters and an initial excess demand < 0 ..................................... 88
Figure 11.25: The Lorenz attractor as an example for a strange attractor ................ 90
Figure 11.26: (a) Trajectories in the q-x-plane for ci = 0.023; (b) Fourier
spectrum for ci = 0.023; (c) Time evolution of x for ci = 0.023 ....... 93
130
Figure I1.27: (a) Trajectories in the q-x-plane for cl = 0.025; (b) Fourier
spectrum for cl = 0.025; (c) Time evolution of x for cl = 0.025 ....... 94
Figure I1.28: (a) Trajectories in the q-x-plane for cl = 0.0255; (b) Fourier
spectrum for cl = 0.0255; (c) Time evolution of x for
cl = 0.0255 ....................................................................................... 95
Figure I1.29: (a) Trajectories in the q-x-plane for cl = 0.03; (b) Fourier
spectrum for cl = 0.03 (c) Time evolution of x for cl = 0.03 ............ 96
Figure I1.30: Strange attractor of the present system in the q-x-w state with
the parameters of Figure I1.29 .......................................................... 97
Figure 11.31: Distance of two initially closed trajectories on the strange
attractor from Figure I1.29 and I1.30 ................................................. 99
Figure I1.32: Determination of the correlation dimension Dc of the strange
attractor from Figure I1.29 and I1.30 ............................................... 1 00
Figure m.1: Plot of the basic time series. BSPR: total volume of real production; CPR: real consumption; IAR: real investment.. ............ 103
Figure I11.2: Plot of the trend corrected and smoothed basic time series ............. 103
Figure I11.3: Plot of the trend corrected, smoothed and normalized basic time
series .............................................................................................. 105
Figure III.4: The business climate as an early indicator for investment
demand ........................................................................................... 109
Figure III.5: Time series of the business climate and the planned production
as indicators for the microeconomic investment and the
production climate .......................................................................... 110
Table I1.1: Lyapunov spectrum for the system of Chapter ITA ........................... 98
131
Table ill. 1: Parameters for the empirical macroeconomic time series
according to Equations II.72 and 11.73 ............................................ 105
Table III.2: Parameters for the empirical macroeconomic time series
according to Equations II.74 and II.75 ............................................ 105
Table ill.3: Parameters for the empirical microeconomic time series
according to Equations II.72 and II.73 ............................................ 110
Table IlIA: Parameters for the empirical microeconomic time series
according to Equations II.74 and II.75 ............................................ 111
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-Ciassical Theory of Distribution and Wealth. V, 146 pages. 1966.
Vol. 263: M. Schafer, Resource Extraction and Market Structure. XI, 154 pages. 1966. '
Vol. 264: Models of Economic Dynamics. Proceedings, 1963, Edited by H.F, Sonnenschein. VII, 212 pages. 1986.
Vol. 265: Dynamic Games and Applications in Economics, Edited by T. Bqar, IX, 288 pages. 1986.
Vol. 288: Muki-Stage Production Planning and Inventory Control. Edited by S. Axsiiter, Ch. Schneeweiss and E. Silver. V, 264 pages. 1986.
Vol, 267: R. Bemelmans, The Capacity Aepect of Inventories, IX, 165 pages. 1986.
Vol, 288: V. Fircheu, Information Evaluation in Capital Markets. VII, 103 pages, 1966,
Vol. 269: A, Borglin, H. Keiding, Optimality in Infinite Horizon Economies. VI, 180 pages. 1986.
Vol . 270: Technological Change, Employment an<j Spatial Dynamics. Proceedings 1965. Edited by P. Nijkamp. VII, 466 pages, 1966.
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, 1965. Edited by G. Fandel, M, Grauer, A. Kurzhanski and A. p, Wierzbicki. VII, 363 pages, 1966.
Vol. 274: W. K. Klein Haneveld, Duality in Stochastic Linear and Dynamic Programming. VII, 295 pages. 1988.
Vol, 275: Competition, Instability, and Non~near Cycles. Proceedings, 1985. Edited by W. Semmler, XII, 340 pages, 1966.
Vol. 276: M,R. Baye, O.A. Black, Consumer Beflavior, 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.
I Vol, 278: W. E. Oiewert, The Measurement of the Economic Benefits of Infrastructure Services. V, 202 pages. 1986,
Vol. 279: H.-J. Bumer, G. Frei and B. Schips, Estimation of Oisequi~rium 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. 2,63: G. Gabisch, H.-W. lorenz, Business Cycle Theory. VII, 229 pages. 1987.
Vol. 264: H. Lii1kepohl, Forecasting Aggregated Vector ARMA Prcx;esaes. X, 323 pages. 1987.
Vol. 285: T award Interactive and Intelligent Decision Support . Systems. Volume 1. Proceedings, 1986. Edited by Y. Sawaragi, K. lnoue and H. Nakayama. XII, 445 pages. 1987.
Vol. 288: Toward Interactive and Intelligent Decision Support Systems. Volume 2. Proceedings, 1986. Edited by Y. Sawaragi, K. Inoue and H. Nakayama. XII, 450 pages. 1987.
Vol. 287: Dynamical Syetems. Proceedings, 1965. Edited by A.B. Kurzhanski and K. Sigmund. VI, 215 pages. 1987.
Vol. 288: G. O. Rudebuach, The Estimation of Macroeconomic Disequilibrium Models with Regime Classification Infomlation. VII, 128 pages. 1987.
Vol. 289: B. R. Meijboom, Planning in Decentralized Firms. X, 166 pages. 1987.
Vol. 290: O.A. Carlson, A. Haurie, Infinite Horizon Optimal Control. XI, 254 pages. 1987.
Vol. 291 : N. Takahashi, Design of Adaptive Organizations, VI, 140 pages. 1987.
Vol . 292: I. Tchijov, L. Tomaszewicz (Eds.), Input-Outpul Modeling. Proceedings, 1985. VI, 195 pages. 1987.
Vol. 293: O. Batten, J. Cssti, B. Johansson (Eds.), Economic Evolution and Structural Adjustment. Proceedings, 1985. VI, 382 pages. 1987.
Vol. 294: J. Jahn, W. Krabs (Eds.), Recent Advances and Historical Osvelopment of Vector Optimization. VII, 405 pages. 1987.
Vol. 295: H' Meister, The Purification Problem for Constrained Games with Incomplete Information. X, 127 pages. 1987.
Vol. 296: A. BOrsch-Supan, Econometric Analysis of Discrete Choice. VIII, 211 pages. 1987.
Vol. 297: V. Fedorov, H. Lii.uter (Eds.), Model-Oriented Data Analysis. Proceedings, 1987. VI, 239 pages. 1988.
Vol. 298: S.H. Chew, O. Zheng, Integral Global Optimization. VII, 179 pages. 1988.
Vol. 299: K. . Marti, Osscent Directions and Efficient Solutions in Discretely Distributed Stochastic Programs. XIV, 178 pages. 1988.
Vol. 300: U. Oerigs, Programming in Networks and Graphs. XI, 315 pages. 1988.
Vol. 301: J. Kacprzyk, M. Roubens (Eds.), Non-Conventional Preference Relations in Decision Making. VII, 155 pages. 1988.
Vol. 302: H.A. Eisen, G. Pederzoli (Eds.), Advances in Optimization and Control. Proceedings, 1966. VIII, 372 pages. 1988.
Vol. 303: F.X. ~iebold, Empirical Modeling of Exchange Rate Dynamics. VII, 143 pages. 1988.
Vol. 304: A. Kurzhanski, K. Neumann, O. Pallaschke (Eds.), Optimization, Parallel Processing and Applicstions. Proceedings, 1987. VI, 292 pages. 1988.
Vol. 305: G,-J .C. Th. van Schijndel, Dynamic Firm and Investor Behaviour under Progressive Personal Taxation. X, 215 pages. 1988.
Vol. 306: Ch. Klein, A Stetic Microeconomic Model of Pure Competition. VIII, 139 pages. 1988.
Vol. 307: T. K. Oijkstra (Ed.), On Model Uncertainty and ~s Statistical Implications. VII, 138 pages. 1988.
Vol. 308: J. R. Oaduna, A. Wren (Eds,), Computer·Aided Trans~ Scheduling. VIII, 339 pages. 1988.
Vol. 309: G. Ricci, K. Velupillai (Eds.), Growth Cycles and'Multisectoral Economics:. the Goodwin Tradition. III, 126 pages. 1988.
Vol. 310: J. Kacprzyk, M. Fedrizzi (Eds.) , Combining Fuzzy Imprecision with Probabilistic Uncertainty in Decision Making. IX, 399 pages. 1988.
Vol. 311 : R. Fare, Fundamentals of Production Theory. IX, 163 pages. 1988.
Vol. 312: J. Krishnakumar, Estimation of Simun&neous Equation Models with Error Components Structure. X, 357 pages. 1988.
Vol, 313: W. Jammemegg, Sequential Binary Investment Decisions. VI, 156 pages. 1988.
Vol. 314: R. Toetz, W. Albers, R. Selten (Eds.), Boun'ded Rational Behavior in Experimental Games and Markets. VI, 366 pages. 1988.
Vol. 315: I. Orishimo, G.J.O. Hewings, P. Nijkamp (Eds.), Information Technology: Social and Spatial Perspectives. Proceedings, 1986. VI, 268 pages. 1988,
Vol. 316: R.L. Basmann, O.J. Slottje, K. Hayes, J.O, Johnson, O.J. Molina, The Generalized Fechner-Thurstone Direct Utility Function and Some of its Uses. VIII, 159 pages. 1988.
Vol. 317: l. Bianco, A. La Bella (Eds.), Freight Transport Planning and Logistics. Proceedings, 1987, X. 568 pages. 1988.
Vol. 318: T. Doup, Simplicial Algorithms on the Simplotope. VIII, 262 pages. 1988.
Vol. 319: D. T. Luc, Theory of Vector Optimization. VIII, 173 pages. 1989.
Vol. 320: D. van der Wijst, Financial Structure in Small Business. VII, 181 pages. 1989.
Vol. 321: M. Di Matteo, R.M. Goodwin, A. Vercelli (Eds.), Technological and Social Factors in Long T arm Fluctuations. Proceedings. IX, 442 pages. 1989.
Vol. 322: T. Kollintzas (Ed.), The Rational Expectations Equilibrium Inventory Model. XI, 269 pages. 1989.
Vel. 323: M. B. M. de Koster, Capacity Oriented Analysis and Design of Production Systems. XII, 245 pages. 1989.
Vol. 324: I.M. Bomze, 8.M. P6tscher, Game Theoretical Foundations of Evolutionary Stability. VI, 145 pages. 1989.
Vol. 325: P. Ferri, E. Greenberg, The Labor Market and Business Cycle Theories. X, 183 pages. 1989.
Vol. 326: Ch. Sauer, Alternative Theories of Output, Unemployment, and Inflation in Germany: 1960-1985. XIII, 206 pages. 1989.
Vol. 327: M. Tawada, Production Structure and International Trade. V, 132 pages. 1989.
Vol. 328: W. Giith, B. Kalkofen, Unique Sclutions for Strategic Games. VII, 200 pages. 1989.
Vol. 329: G. Tillmann, Equity, Incentives, and Taxation. VI, 132 pages. 1989.
Vol. 330: P.M. Kort, Optimal Dynamic Investment Policies of a Value Maximizing Firm. VII, 185 pages. 1989.
Vol. 331: A. Lewandowski, A. P. Wierzbicki (Eds.), Aspiration Based Decision Support Systems. X, 400 pages. 1989.
Vol. 332: T.R. Gulledge, Jr., L.A. Litteral (Eds.), Cost Analysis Applications of Economics and Operations Research. Proceedings. VII, 422 pages. 1989.
Vol. 333: N. Dellaert, Production to Order. VII, 158 pages. 1989.
Vol. 334: H.-W, Lorenz, Nonlinear Dynamical Economics and Chaotic Motion. XI, 248 pages. 1989.
Vol. 335: A. G. Lockett, G.lslei (Eds.), Improving Decision Making in Organisations. Proceedings. IX, 606 pages. 1989.
Vol. 336: T. Puu, Nonlinear Economic Dynamics. VII, 119 pages. 1989.
Vol. 337: A. Lewandowski, I. Stanchev (Eds.), Methodology and Software for Interactive Decision Support. VIII, 309 pages. 1989.
Vol. 338: J. K. Ho, R. P. Sundarraj, DECOMP: an Implementation of Dantzig-Wolfe Decomposition for Linear Programming. VI, 206 pages. 1989.
Vol. 339: J. Terceiro Lomba, Estimation of Dynamic Econometric Models with Errors in Variables. VIII, 116 pages. 1990.
Vol. 340: T. Vasko, R. Ayres, L. Fontvieille (Eds.), Life Cycles and Long Waves. XIV, 293 pages. 1990.
Vol. 341: G. R. Uhlich, Descriptive Theories of Bargaining. IX, 165 pages. 1990.
Vol. 342: K. Okuguchi, F. Szidarovszky, The Theory of Oligopoly with MultiProduct Firms. V, 167 pages. 1990.
Vol. 343: C. Chiarella, The Elements of a Nonlinear Theory of Economic Dynamics. IX, 149 pages. 1990.
Vol. 344: K. Neumann, Stochastic Project Networks. XI, 237 pages. 1990.
Vol. 345: A. Cambini, E. Castagnoli, L. Martein, P. Mazzoleni, S. Schaible (Eds.), Generalized Convexity and Fractional Programming with Economic Applications. Proceedings, 1988. VII, 361 pages. 1990.
Vol. 346: R. von Randow (Ed.), Integer Programming and Related Areas. A Classified Bibliography 1984-1987. XIII, 514 pages. 1990.
Vol. 347: D. Rios Insua, Sensitivity Analysis in Multi-objective Decision Making. XI, 193 pages. 1990.
Vol. 348: H. Stormer, Binary Functions and their Applications. VIII, 151 pages. 1990.
Vol. 349: G. A. Pfann, Dynamic Modelling of Stochastic Demand for Manu facturing Employment. VI, 158 pages. 1990.
Vol. 350: W.- B. Zhang, Economic Dynamics. X, 232 pages. 1990.
Vol. 351: A. Lewandowski, V. Volkovich (Eds.), Multiobjective Problems 01 Mathematical Programming. Proceedings, 1988. VII, 315 pages. 1991.
Vol. 352: O. van Hilten, Optimal Firm Behaviour in the Context of Techno logical Progress and a Business Cycle. XII, 229 pages. 1991.
Vol. 353: G. Ricci (Ed.), Decision Processes in Economics. Proceedings 1989. III, 209 pages. 1991.
Vol. 354: M. Ivaldi, A Structural Analysis of Expectation Formation. XII, 23( pages. 1991.
Vol. 355: M. Salomon, Deterministic Lotsizing Models for Production Plan ning. VII, 158 pages. 1991.
Vol. 356: P. Korhonen, A. Lewandowski, J. Wallen ius (Eds.), Multiple Crite ria Decision'Support. Proceedings. 1989. XII, 393 pages. 1991.
Vol. 357: P. Zornig, Degeneracy Graphs and Simplex Cycling. XV, 19~
pages. 1991.
Vol. 358: P. Knottnerus, Linear Models with Correlated Disturbances. VIII 196 pages. 1991.
Vol. 359: E. de Jong, Exchange Rate Determination and Optimal Economic Policy Under Various Exchange Rate Regimes. VII, 270 pages. 1991.
Vol. 360: P. Stalder, Regime Transitions, Spillovers and Buffer Stocks. VI 193 pages. 1991.
Vol. 361: C. F. Da9anzo, Logistics Systems Analysis. X, 321 pages. 1991.
Vol. 362: F. Gehrels, Essays in Macroeconomics of an Open Economy. VII 183 pages. 1991.
Vol. 383: C. Puppe, Distorted Probabilities and Choice under Risk. VIII 100 pages. 1991.
Vol. 364: B. Horvath, Are Policy Variables Exogenous? XII, 162 pages 1991.
Vol. 365: G. A. Heuer, U. Leopold-Wildburger, Balanced Silverman Game~ on General Discrete Sets. V, 140 pages. 1991.
Vol. 366: J. Gruber (Ed.), Econometric Decision Models. Proceedings 1989. VIII, 636 pages. 1991.
Vol. 367: M. Grauer, D. B. Pressmar (Eds.), Parallel Computing and Mathe matical Optimization. Proceedings. V, 208 pages. 1991
Vol. 368: M. Fedrizzi, J. Kacprzyk, M. Roubens (Eds.), Interactive Fuzz O~ti",.",tion. VII, 216 pages. 1991.
Vol. 369: R. Koblo, T~pVisible Hand. VIII, 131 pages. 1991.