Richard M. Goodwin

A Growth Cycle

Presented here is a starkly schematised and hence quite unrealistic model of cycles in growth rates. This type of formulation now seems to me to have better prospects than the more usual treatment of growth theory or of cycle theory, separately or in combination. Many of the bits of reasoning are common to both, but in the present paper they are put together in a different way.

Dynamical Coupling with Especial Reference to Markets Having Production Lags

There is widespread agreement that it is necessary to introduce into economics both dynamical relations and general interdependence. This is not a counsel of perfection or a manifestation of the desire for theoretical elegance and completeness. The most concrete, practical analysis is often vitiated by restrictive assumptions which ignore or ‘eliminate’ the elements of change and of interconnectedness. When two sectors of an economy are interdependent in some way (coupled, we may say), and when we have another than the null or trivial solution of no change, then it is quite inadmissible to discuss the one sector assuming the other unchanged. For, if the one does not remain constant, the other cannot either, by virtue of the coupling. Therefore to allow one sector to vary and keep the other constant would be to hold contradictory assumptions.

John Von Neumann and Modern Economics

Part 1 Von Neumanns growth model in historical perspective: von Neumann and the existence theorem for general equilibrium, Kenneth J.Arrow von Neumann and Karl Mengers mathematical colloquium, Lionello F.Punzo. Part 2 Von Neumanns growth model - the central questions: John von Neumanns model of an expanding economy - an essay in interpretation, Sukhamoy Chakravarty the legacy of John von Neumann, Mohammed H.I.Dore a revisionist view of von Neumanns growth model, Paul A.Samuelson. Part 3 Von Neumanns growth model and dynamics: swinging along the Autostrada - cyclical fluctuations along the von Neumann ray, Richard M.Goodwin economics and thermodynamics, Andrew Brody. Part 4 Von Neumanns growth model and game theory: game theoretic growth - a numerical illustration, Mohammed H.I.Dore an equilibrium-point interpretation of the von Neumann-Morgenstern solution and a proposed alternative definition, John C.Harsanyi. Part 5 Von Neumanns growth model - retrospective and reformulation: von Neumanns economic model, Sidney N.Afriat John von Neumanns contributions to mathematical programming economics, Gerald L.Thompson.

The Economy as an Evolutionary Pulsator

Abstract The problem of Long Waves is formalized as one of the dynamical coupling of a relatively steady flow of new techniques and goods along with the endemic tendency of capitalism to evolve in a cyclical fashion. This implies a strong exogenous influence which renders any precise periodicity unlikely. The model is illustrated by a hypothetical, historically determined potential which controls the path in time of the economy.

Schumpeter, Keynes and the Theory of Economic Evolution

The contribution deals with a nonlinear dynamic macro-economic model which is used for simulation runs. Conditions and model specifications allowing for global stability are investigated and tested. Based on this some well-known facts as Schumpeterian long-wave phenomena, Keynesian unemployment, productivity growth effects are simulated. Moreover specifying an instrumental variable for state interventions policy issues are also discussed. With this runs it is shown that minor changes of parameters may provide totally different outcomes and different economic developments.

Non-Linear Dynamics and Economic Evolution

Since I am to be dealing with an aspect of evolution, I hope I may be forgiven for approaching the topic through my own evolution. When I was young I often said There is no bore like an old bore - but now, for some reason or other, I rarely repeat that view (though I have just done so)! So I shall be brief.

Swinging along the Autostrada

The greatest mistake in my career occurred when Schumpeter came to me in 1938 or ’39 and asked me to report on a very important new publication: the von Neumann paper given at the Monger seminar, a repetition of the one he had given in Princeton in 1932. When I got as far as realizing that he was including all remaining plant and equipment in annual output, I rashly judged it to be totally unrealistic, and I still do, though in retrospect I realize the immense simplifying power of the method. In any case, I, alas, reported back to Schumpeter that it was no more than a piece of mathematical ingenuity, failing to see that it contained two aspects close to Schumpeter’s heart — a rigorous solution to Walras’s central problem and a demonstration that the rate of profit arose from growth not quantity of capital. When I came to edit his papers for the final section of his History, I found no reference to what now appears to me to be one of the great, seminal works of this century, the omission being possibly the result of my own blindness. The beautifully spare architecture of its encompassing structure leaves one awestruck. Apparently without antecedents, it sprang full blown from that fertile brain. Demonstrating the existence of a solution to the economic problem wherein all goods could be produced at the lowest price and the greatest possible quantity, with price equal to cost and supply equal to demand for all goods, along with showing the necessity for maximal growth if dynamic equilibrium is to exist. So grandiose an achievement was, of course, achieved at a cost. My purpose here is to suggest how one may, with a modest reformulation, bring it closer to reality, without damaging its essentially robust and clarifying solutions. The von Neumann theory may appropriately be considered the progenitor of contemporary growth theory since it demonstrated that a decentralized, capitalist economy had to grow at a determinate, constant rate to clear its markets. Profoundly true though in some sense it is, this type of theory is painfully unrealistic for the turbulent history of industrial capitalism. Not only that but it contains two quite unacceptable assumptions: there is no technical progress and there is a constant real wage. The maximal growth rate depends vitally on the real wage, but the wage is exogenous instead of being determined by the functioning of the system. My proposal is that the economy first overshoots and then undershoots the von Neumann solution, but that, on the average over a longer period, achieves an analogous solution to his, thus leaving the essential result undamaged.

A Chaotic Reformulation of Multiplier—Accelerator Models

It gives me great pleasure to join in this occasion to honour Bjorn Thalberg. We have known one another for over thirty years, shared an interest in economic dynamics and, in particular, in cycles. He came to Cambridge at a time when I had only recently begun lecturing there and we had a chance to meet outside the formal lecturing periods. Not only that but he sent one of his exceptional students, Kumaraswamy Velupillai, with the instruction to seek out either Nicholas Kaldor or me: happily in the end he became my student.

Towards a Theory of Long Waves

My procedure will be to approach the problem in two stages: first, how a single wave arises from a logistic; second, how and why the completion of each wave leads to a situation which engenders a succeeding wave.

Economic Nonlinear Dynamic Development

The conception of a limit cycle was formulated towards the end of the last century. A practical, usable form was first developed by van der Pol and widely used in the physical sciences. The first qualitative model in economics was proposed by Kalecki in the early thirties but, being linear, was seriously criticized by Frish on the grounds that it was structurally unstable. Then came the dramatic impact of the Keynes General Theory, which led to an altered perception of the problem.