Price Dynamics Via Expectations, and the Role of Money Therein

Beyond its obvious macro-economic relevance, fiat money has important micro-economic implications. They matter for addressing No. 8 in Smale's "Mathematical Problems for the Next Century": extend the mathematical model of general equilibrium theory to include price adjustments. In the canonical Arrow-Debreu framework, equilibrium prices are set by a fictitious auctioneer. Removing that fiction raises the question of how prices are set and adjusted by decentralised actors with incomplete information. We investigate this question through a very basic model where a unique factor of production, labour, produces a single consumption good, called jelly for brevity. The point of the model is to study a price dynamics based on the firm's expectations about jelly demand and labour supply. The system tends towards economic equilibrium, however, depending on the initial conditions it might not get there. In different model versions, different kinds of money are introduced. Compared to the case of no money, the introduction of money as a store of value facilitates the system reaching economic equilibrium. If money is introduced as a third commodity, i.e. there is also a demand for money, the system dynamics in general becomes more complex.