Afriat’s Theorem for General Budget Sets

Afriat (1967) showed the equivalence of the strong axiom of revealed preference and the existence of a solution to a set of linear inequalities. From this solution he constructed a utility function rationalizing the choices of a competitive consumer. We extend Afriat’s theorem to a class of nonlinear budget sets. We thereby obtain testable implications of rational behavior for a wide class of economic environments, and a constructive method to derive individual preferences from observed choices. In an application to market games, we identify a set of observable restrictions characterizing Nash equilibrium outcomes.GARP, rational choice, revealed preferences, market games, SARP, WARP

Shareholder-efficient production plans in a multi-period economy

We propose an objective for the firm in a general model of production economies extending over time under uncertainty and with incomplete markets. Trading in commodities and shares of stock occurs sequentially on spot markets at all date-events. We derive the objective of the firm from the assumption of initial-shareholders efficiency. Each shareholder is assumed to communicate to the firm her marginal valuation of profits all date events (expressed in terms of initial resources). In defining her own marginal valuation of the firm's profits, a shareholder will take two elements into consideration. To evaluate the direct impact of a change in dividends the shareholder uses her own vector of marginal rates of substitution for revenue across date-events. In addition, the shareholder will take into account the impact of future dividends on the firm's stock price when she trades shares. To predict the effect on the stock price, she uses a (possibly different) state price process, her price theory. The only restriction that we impose on consumers' price theories is that they should be compatible with the observed equilibrium : given the equilibrium prices and production plans, a price theory must satisfy a no-arbitrage condition. The firm computes its own shadow prices for profits at all date-events by simply adding up the marginal valuations of all its initial shareholders. We prove existence of an equilibrium.Incomplete markets, shareholders, price theories, firm's objective.

Stock prices, anticipations and investment in general equilibrium

We propose an objective for the firm in a model of production economies extending over time under uncertainty and with incomplete markets. We derive the objective of the firm from the assumption of initial-shareholders efficiency. Each shareholder is assumed to communicate to the firm her marginal valuation of profits at all future events (expressed in terms of initial resources). In defining her own marginal valuation of the firm's profits, a shareholder takes into consideration the direct impact of a change in the value of dividends but also the impact of future dividends on the firm's stock price when she trades shares. To predict the impact on the stock price, she uses a state price process, her price theory. The firm computes its own shadow prices for profits at all date-events by simply adding up the marginal valuations of all its initial shareholders. If no restrictions are placed on individual price theories, the existence of equilibria may require financial constraints on a firm's investment when its shareholders are more optimistic than the market about the profitability of such investment. We then impose that price theories be compatible with the observed equilibrium: they should satisfy a no-arbitrage condition. We show by means of an example that, with incomplete markets and no-short selling constraints, this restriction on price theories is not enough to bring consistency in the individuals' marginal evaluations: a financial constraint on the firm's investment may still be needed to obtain an equilibriumgeneral equilibrium, incomplete markets, stock prices, anticipations, investment constraints, arbitrage

Shareholder-efficient production plans in a multi-period economy

We propose an objective for the firm in a general model of production economies extending over time under uncertainty and with incomplete markets. Trading in commodities and shares of stock occurssequentially on spot markets at all date-events. We derive the objective of the firm from the assumption of initial-shareholders efficiency.Each shareholder is assumed to communicate to the firm her marginal valuation of profits at all date events (expressed in terms of initial resources).In defining her own marginal valuation of the firm’s profits, a shareholder will take two elements into consideration. To evaluatethe direct impact of a change in dividends the shareholder uses her own vector of marginal rates of substitution for revenue across dateevents.In addition, the shareholder will take into account the impact of future dividends on the firm’s stock price when she trades shares. Topredict the effect on the stock price, she uses a (possibly different) state price process, her price theory. The only restriction that we imposeon consumers’ price theories is that they should be compatible with the observed equilibrium: given the equilibrium prices and productionplans, a price theory must satisfy a no-arbitrage condition. The firm computes its own shadow prices for profits at all date-events by simplyadding up the marginal valuations of all its initial shareholders. We prove existence of an equilibrium.