This paper by Robert E. Lucas, Jr. examines the stochastic behavior of equilibrium asset prices in a one-good, pure exchange economy with identical consumers. The economy is characterized by a single good produced in multiple units, each with stochastic productivity. Lucas develops a general method to construct equilibrium prices and applies it to various examples. The main focus is on deriving and applying a functional equation for equilibrium asset prices, which is a generalization of the Martingale property of stochastic price sequences. The analysis assumes that prices fully reflect all available information, a hypothesis known as rational expectations. The paper also discusses the stability of equilibrium and provides examples to illustrate the concepts. The conclusions replicate those reached by LeRoy, showing that the failure of a price series to possess the Martingale property can be evidence of non-competitive or "irrational" behavior. The paper concludes with methodological insights and suggestions for further research, including the use of non-additive preferences and the introduction of capital accumulation.This paper by Robert E. Lucas, Jr. examines the stochastic behavior of equilibrium asset prices in a one-good, pure exchange economy with identical consumers. The economy is characterized by a single good produced in multiple units, each with stochastic productivity. Lucas develops a general method to construct equilibrium prices and applies it to various examples. The main focus is on deriving and applying a functional equation for equilibrium asset prices, which is a generalization of the Martingale property of stochastic price sequences. The analysis assumes that prices fully reflect all available information, a hypothesis known as rational expectations. The paper also discusses the stability of equilibrium and provides examples to illustrate the concepts. The conclusions replicate those reached by LeRoy, showing that the failure of a price series to possess the Martingale property can be evidence of non-competitive or "irrational" behavior. The paper concludes with methodological insights and suggestions for further research, including the use of non-additive preferences and the introduction of capital accumulation.