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 economy’s endowments are collinear, its excess demand function will obey the weak axiom when certain mild restrictions are...

Consider a finite data set where each observation consists of a bunde of contingent consumption chosen by an agent from a constraint set of such bundles.  We develop a general procedure for testing the consistency of this data set with a broad class of models of choice under risk and under...

These are additional notes relating to the paper `The Comparative Statics of Constrained Optimization Problems`, which is appearing in Econometrica. It gathers together material present in various earlier versions of the paper, as well as some new material, which are not found in the published...

Certain problems in comparative statics, including (but not exclusively) certain problems in consumer theory, cannot be easily addressed by the methods of lattice programming. One reason for this is that there is no order on the choice space which orders choices in a way which conforms with the...

This paper gives a non-fixed point theoretic proof of equilibrium existence when the excess demand function of an exchange economy obeys the weak axiom. The proof is simple and geometrically intuitive, and it also permits a weakening of the continuity assumption on the excess demand function....

We identify necessary and sufficient conditions under which a finite data set of price vectors and consumption bundles can be rationalized by a weakly separable utility function.  Our result could be understood as a generalization of Afriat's Theorem.

Consider a finite data set of price vectors and consumption bundles; under what conditions will there be a weakly separable utlity function that rationalizes the data?  This paper shows that rationalization in this sense is possible if and only if there exists a preference order on some finite...

We identify a natural way of ordering functions, which we call the interval dominance order and develop a theory of monotone comparative statistics based on this order.  This way of ordering functions is weaker than the standard one based on the single crossing property (Milgrom and Shannon,...

The theoretical literature on (non-random) choice largely follows the route of Richter (1966) by working in abstract environments and by stipulating that we see all choices of an agent from a given feasible set.  On the other hand, empirical work on consumption choice using revealed preference...

This paper examines the operation of an emissions trading scheme (ETS) in a Cournot oligopoly.  We study the impact of the ETS on industry output, price, costs, emissions, and profits.  In particular, we develop formulae for the number of emissions permits that have to be freely allocated to...