The most common theoretical defense of the hypothesis that firms maximize profits is that otherwise they will be driven out of the market. The idea is that only those firms which for whatever reason succeed in maximizing profits will able to attract or accumulate enough capital to survive and grow. Although this intuition has been around for a long time (see Alchian (1950), Friedman (1953) and Winter (1964, 1971)) it has not been investigated in a general equilibrium setting. The argument also has its critics. In particular, Koopmans (1957) argued that referencing an external dynamic process to support the validity of a key behavioral assumption is not really a satisfactory way to proceed. In the work leading up to this proposal we have examined this hypothesis in a simple general equilibrium model in which firms fund current operations from retained earnings, without access to external financial capital markets. This dynamic, much like that discussed by Winter, drives the scale of firm operation. We found that among all firms having access to the same technology only those that come closest to maximizing profits survive. But Koopmans is nonetheless right. The tendency to select for profit maximizers does not generate a corresponding selection for aggregate producer efficiency. In the absence of markets for financial capital, the retained earnings dynamic is not able to reallocate funds across firms so as to achieve producer efficient outcomes. The addition of capital markets `solves` the problem in that if all investors have rational expectations, and markets are dynamically complete, then the equilibrium is efficient. But this begs the question. More interesting is what happens if not all investors have rational expectations. In this case the result can be even worse than without financial capital markets. Our research plan can be characterized as taking Koopmans' concern seriously. We are interested in what does happen when firms do not necessarily maximize profits, and investors are not necessarily rational, but the forces of economic natural selection are at work. What characteristics does the sequence of equilibria display? What are the asymptotic properties? Are there any optimality properties for either the sequence of equilibria or for the limit equilibria? We know that profit maximizers are selected for in some settings and not in others, but can the fit decision rules be characterized generally? These questions are particularly interesting when profits are random and firms cannot be valued through arbitrage. In this case it is not clear what objective to attribute to a firm. Our preliminary investigation suggest that there is no tendency to select for expected profit maximization even when that is what capitalists want. Instead we conjecture that there will be selection for firms that act so as to maximize the expected growth rate of their retained earnings. This is not consistent with expected profit maximization, but it is consistent with popular commentary about the objectives of large corporations.
