The aggregate weak axiom in a financial economy through dominant substitution effects

Consider a two period financial economy with incomplete markets and with agents having von Neumann-Morgenstern utility functions. It is well known that when the economys endowments are collinear, the excess demand function will obey the weak axiom when certain mild restrictions are imposed on agents coefficient of relative risk aversion. This result is obtained through the application of a theorem on the law of demand (for individual demand) formulated independently by Milleron (1974) and Mitjuschin and Polterovich (1978). In this paper, we develop their arguments further and apply them to economies without collinear endowments. We identify conditions which guarantee that the economys excess demand function obeys the weak axiom near an equilibrium price.

Comparative Statics of the Weak Axiom

This paper examines the comparative statics of Walrasian economies with excess demand functions which obey the weak axiom. We show that in these economies there is a precise sense in which goods that are in excess supply (demand) after some perturbation will experience a fall (rise) in its price. We apply this to an exchange economy with additive utility functions, which can be interpreted as a financial economy with von Neumann-Morgenstern utility functions. We show that when the subjective probabilities which agents attribute to a particular state falls, so will the price of consumption in that state. Another interesting issue is the impact of changes to the endowment on the equilibrium price. We develop conditions under which, for an exchange economy, this equilibrium map - from endowment to equilibrium price - will obey the weak axiom and another stronger, monotonicity property.

Revealed Preference in a Discrete Consumption Space

We show that an agent maximizing some utility function on a discrete (as opposed to continuous) consumption space will obey the generalized axiom of revealed preference (GARP) so long as the agent obeys cost efficiency. Cost efficiency will hold if there is some good, outside the set of goods being studied by the modeler, that can be consumed by the agent in continuous quantities. An application of Afriat's Theorem then guarantees that there is a strictly increasing utility function on the discrete consumption space that rationalizes price and demand observations in that space.Generalized axiom of revealed preference; Afriat's Theorem; discrete demand; utility maximization

Heterotic Models of Aggregate Demand

A common theme in the theory of demand aggregation is that market demand can acquire properties which are not always individually present among the agents who make up that market, a phenomenon we call heterosis in this paper. This paper focusses on the well known result that with a suitable distribution of demand behavior (arising perhaps from the underlying distribution of preferences), market demand can become approximately a linear function of income or even taken an approximate Cobb-Douglas properties. We highlight the mathematical arguments underpinning these models and show that in the right context, it is possible to carry the arguments further and achieve exact rather than just approximate results: exact Cobb-Douglas market demand or exact linearity of market demand with respect to income.heterosis, heterogeneity, Cobb-Douglas, homotheticity, law of demand, aggregation

A nonparametric analysis of the Cournot model

An observer makes a number of observations of an industry producing a homogeneous good. Each observation consists of the market price, the output of individual firms and perhaps information on each firm's production cost. We provide various tests (typically, linear programs) with which the observer can determine if the data set is consistent with the hypothesis that firms in this industry are playing a Cournot game at each observation. When cost information is wholly or partially unavailable, these tests could potentially be used to derive cost information on the firms. This paper is a contribution to the literature that aims to characterize (in various contexts) the restrictions that a data set must satisfy for it to be consistent with Nash outcomes in a game. It is also inspired by the seminal result of Afriat (and the subsequent literature) which addresses similar issues in the context of consumer demand, though one important technical difference from most of these results is that the objective functions of firms in a Cournot game are not necessarily quasiconcave

Discounting and Patience in Optimal Stopping and Control Problems

This paper establishes that the optimal stopping time of virtually any optimal stopping problem is increasing in "patience," understood as a particular partial order on discount rate functions. With Markov dynamics, the result holds in a continuation- domain sense even if stopping is combined with an optimal control problem. Under intuitive additional assumptions, we obtain comparative statics on both the optimal control and optimal stopping time for one-dimensional diusions. We provide a simple example where, without these assumptions, increased patience can precipitate stopping. We also show that, with optimal stopping and control, a project's expected value is decreasing in the interest rate, generalizing analogous results in a deterministic context. All our results are robust to the presence of a salvage value. As an application we show that the internal rate of return of any endogenously-interrupted project is essentially unique, even if the project also involves a management problem until its interruption. We also apply our results to the theory of optimal growth and capital deepening and to optimal bankruptcy decisions.capital growth, comparative statics, discounting, internal rate of return, optimal control, optimal stopping, patience, present value, project valuation

Comparative Statics, Informativeness, and the Interval Dominance Order

We identify a natural way of ordering functions, which we call the interval dominance order and develop a theory of monotone comparative statics based on this order. This way of ordering functions is weaker then the standard one based on the single crossing property (Milgrom and Shannon, 1994) and so our results apply in some settings where the single crossing property does not hold. For example, they are useful when examining the comparative statics of optimal stopping time problems. We also show that certain basic results in statistical decision theory which are important in economics – specifically, the complete class theorem of Karlin and Rubin (1956) and the results connected with Lehmann’s (1988) concept of informativeness – generalize to payoff functions obeying the interval dominance order.single crossing property, interval dominance order, supermodularity, comparative statics, optimal stopping time, complete class theorem, statistical decision theory, informativeness

Law of Demand

We formulate several laws of individual and market demand and describe their relationship to neoclassical demand theory. The laws have implications for comparative statics and stability of competitive equilibrium. We survey results that offer interpretable sufficient conditions for the laws to hold and we refer to related empirical evidence. The laws for market demand are more likely to be satisfied if commodities are more substitutable. Certain kinds of heterogeneity across individuals make the laws more likely to hold in the aggregate even if they are violated by individuals.

A Nonparametric Analysis of the Cournot Model

An observer makes a number of observations of an industry producing a homogeneous good. Each observation consists of the market price, the output of individual rms and perhaps information on each rm's production cost. We provide various tests (typically, linear programs) with which the observer can determine if the data set is consistent with the hypothesis that rms in this industry are playing a Cournot game at each observation. When cost information is wholly or partially unavailable, these tests could potentially be used to derive cost information on the rms. This paper is a contribution to the literature that aims to characterize (in various contexts) the restrictions that a data set must satisfy for it to be consistent with Nash outcomes in a game. It is also inspired by the seminal result of Afriat (and the subsequent literature) which addresses similar issues in the context of consumer demand, though one important technical di erence from most of these results is that the objective functions of rms in a Cournot game are not necessarily quasiconcave. Keywords:

The Law of Demand and Risk Aversion

This note proposes a necessary and sufficient condition on a preference to guarantee that the demand function it generates satisfies the law of demand. It shows that the law of demand may be succinctly characterized by differences in an agent's level of risk aversion when she is confronted with different lotteries composed of commodity bundles.law of demand, monotonicity, preference, risk aversion