Statistical Microeconomics

TL;DR

This paper develops a statistical framework for microeconomics by modeling prices and quantities as stochastic processes, using an action functional and correlation analysis to understand market dynamics.

Contribution

It introduces a novel statistical approach to microeconomics, applying concepts from statistical mechanics and defining a model for market price dynamics.

Findings

Prices and quantities are modeled as stochastic processes.

Correlation functions can be calibrated from market data.

A perturbation expansion for correlation functions is developed.

Abstract

A statistical generalization is made of microeconomics in the spirit of going from classical to statistical mechanics. The price and quantity of every commodity1 traded in the market, at each instant of time, is considered to be an independent random variable: all prices and quantities are considered to be stochastic processes, with the observed market prices being a random sample of the stochastic prices. The dynamics of market prices is determined by an action functional and, for concreteness, a specific model is proposed. The model can be calibrated from the unequal time correlation of the market commodity prices. A perturbation expansion for the correlation functions is defined in powers of the inverse of the total budget of the aggregate consumer and the propagator for the market prices is evaluated.