This paper uses the familiar, neoclassical theory of capital accumulation to show how complex behavior can emerge from quite simple economic structures. Indeed, when sufficient nonlinearities and a production lag are present, the interaction alone of the propensity to save and the productivity of capital can lead to growth cycles that exhibit a wandering, sawtooth pattern not unlike those observed in reality. These fluctuations need not converge to a cycle of any regular periodicity so they are not quasi periodic. Because such trajectories are unstable, errors of estimation in parameters or initial conditions, however tiny, will accumulate rapidly into substantial errors of forecast. Moreover, periods of erratic cycling can be interspersed with periods of more or less stable growth. Evidently, the future behavior of a model solution cannot be anticipated from its patterns in the past, a situation that seems to mimic experience. Apparent structural change and unpredictability is explained in the present theory by a deterministic, single equation model. Random shocks play no role. So the reader can visualize just what it is we are are talking about, a noteworthy simulation is presented in Figure 1 for GNP in a growth model that is described below in Section III. A period of relatively rapid growth is followed by a period of cycles. Then, remarkably, for a considerable time (about twenty periods) apparently steady-state growth occurs. Wandering cycles, however, emerge. Another brief period close to the steady state appears again toward the end of the series. I establish conditions of savings and productivity that lead to results of this kind. This analysis makes use of the mathematical theory of which, in the form exploited here, originated in the work of Edward Lorenz. A formal definition of chaos and sufficient conditions for chaotic trajectories were provided in a seminal paper by T-Y Li and James Yorke. A survey of these related contributions is found in Yorke and Evelyn Yorke. This theory was introduced into economics by Jess Benhabib and myself (1981), where we showed that sequences of rational choices can be erratic when preferences depend on experience in a certain way; by Michael Stutzer, who provides a detailed analysis of Trygve Haavelmo's growth model; by Benhabib and myself (1980) in an application of the overlapping generations model; and in my forthcoming study of the classical growth model.

It has been argued by William Baumol and Richard Quandt (1964) and Day (1967) that rules of thumb can be efficient economic strategies when decision making is costly and when decision makers have imperfect information. The present paper augments this literature and analyzes an industrial growth model in which firms determine production and investment levels by solving a single period optimizing problem. The solution is carried out period after period rather than by making a complete lifetime plan involving forecasts of the future. We portray the firm as myopically groping toward an unknown equilibrium through successive one-period movements made by a simple linear programming allocation of the firm's cash budget.' Cash availability is the channel through which market feedback, operating through the demand function, modifies behavior. Our model can be thought of as a dynamic, rule of thumb, approximation to an intertemporally optimal investment and production path for the firm and industry. It is shown that, under certain conditions of demand and cost, an industry whose firms use our myopic investment rules will converge asymptotically to a perpetually maintainable capital stock. This solution is the long-run equilibrium of the perfectly competitive industry in which price just covers total costs of the marginal firm. In other words, a shortsighted optimization based on complete ignorance of demand can lead to equilibrium in the sense of theories based on perfect knowledge and polyperiodic time horizons. This is only one of several possible outcomes, however, for under somewhat different market conditions fluctuations in investment and production levels will eventually occur, perhaps after a protracted period of growth. The model can also generate S-shaped industry growth paths, simultaneous saving and investment, and investment at less than the maximum possible rate (excess borrowing capacity). All of these are commonly observed patterns of industry behavior. The possibility of industrial instability suggests the need for a risk-avoiding rule at the firm level. The rule introduced is the safety-first principle (see Andrew Roy, Day, Dennis Aigner and Smith), a device that is easily seen to reduce the likelihood of unstable oscillations about industrial equilibrium.