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...

The single crossing property plays a crucial role in monotone comparative statics (Milgrom and Shannon (1994)), yet in some important applications the property cannot be directly assumed or easily derived.  Difficulties often arise because the property cannot be aggregated: the sum of two...

Whether they are financial, economic, or psychological, discount rates affect most economic decisions: investment and savings, hirings and firings, defaults and refinancing, financial and economic reforms, learning and experimentation, and any other decision with long-term consequences, such as...

We consider an observer who makes a finite number of observations of an industry producing a homogeneous good, where each observation consists of the market price and firm specific production quantities.  We develop a revealed preference test (in the form of a linear program) for the hypothesis...

This paper presents a nonparametric, revealed preference analysis of intertemporal consumption with risk. In an experimental setting, subjects allocate tokens over four commodities, consisting of consumption in two contingent states and at two time periods, subject to different budget...

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...

We run an experiment designed to elicit preferences over state contingent, timed payouts. We analyze the data using a new revealed preference method (building on Nishimura, Ok, and Quah (2017)) that can test for consistency with utility functions that increase with a given preorder. Using this...

We run an experiment designed to elicit preferences over state contingent, timed payouts. We analyze the data using a new revealed preference method (building on Nishimura, Ok, and Quah (2017)) that can test for consistency with utility functions that increase with a given preorder. Using this...

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...

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...