Stochastic Non-T\^atonnement Processes and the Attraction Principle

I characterize stochastic non-t\^atonnement processes (SNTP) and argue that they are a natural outcome of General Equilibrium Theory. To do so, I revisit the classical demand theory to define a normalized Walrasian demand and a diffeomorphism that flattens indifference curves. These diffeomorphisms are applied on the three canonical manifolds in the consumption domain (i.e., the indifference and the offer hypersurfaces and the trade hyperplane) to analyze their images in the normalized and the flat domains. In addition, relations to the set of Pareto optimal allocations on Arrow-Debreu and overlapping generations economies are discussed. Then, I derive, for arbitrary non-t\^atonnement processes, an Attraction Principle based on the dynamics of marginal substitution rates seen in the "floor" of the flat domain. This motivates the definition of SNTP and, specifically, of Bayesian ones (BSNTP). When all utility functions are attractive and sharp, these BSNTP are particularly well behaved and lead directly to the calculation of stochastic trade outcomes over the contract curve, which are used to model price stickiness and markets' responses to sustained economic disequilibrium, and to prove a stochastic version of the First Welfare Theorem.