Two-Stage Exchange: Extending a Model of Decentralised Bi-lateral Exchange for a Limited Model of Labour, Profit, and Endogenous Production

Abstract

When a private transaction takes place without publically observable prices, how might that information leak into the public domain and coordinate demand and supply sides of the economy? The Walrasian model of general equilibrium addresses this question by assuming it away, introducing the assumption of a "Walrasian auctioneer" who calls out price vectors that enable all consumers and producers to make consumption and production plans based on universal and costlessly observable relative prices of all goods. Violations of the Law of One Price are commonly observable in the real world even across major chain grocery stores that actively advertise some of their price offers. Gintis' (2006) "The Emergence of a Price System from Decentralized Bi-lateral Exchange" highlighted the importance of this question of how stable prices could emerge from initially private bi-lateral exchange. Gintis used agent-based simulation to model a barter economy with exogenous production. In this thesis, we attempt to replicate Gintis' model with an extension that includes simple labour markets and endogenous production.

In Gintis' model, identical goods can trade at different prices that are determined by private bilateral negotiation, violating the so-called Law of One Price. The empirical probability distributions of private prices follow an "adaptive evolutionary dynamic" in which high-scoring agents imitate low-scoring agents. Through evolutionary adaption modeled by cumulative utility scores which serve as a fitness function, these random distributions of private prices become quasi-public and eventually achieve Walrasian equilibrium (i.e. a price vector at which all goods markets simultaneously clear).

Our extension of Gintis' (2006) model introduces household and producer agents engaged in two-stage exchange in each period. We assume that households make decisions about whether to sell labour which is required by producers when they make production decisions. By augmenting Gintis' barter-exchange economy with labour markets, the model embeds a new constraint on producers' ability to produce, and the resulting model features endogenous consumption, production and prices.

To keep the model as simple as possible while incorporating endogenous production, we treat production and exchange as binary events. Output and labour are assumed to be homogenous with no quantity variation to focus solely on whether Walrasian pricing can be achieved once production is endognized. By adapting the same evolutionary mechanisms from Gintis (2006) we replicate one of his findings and fail to replicate the other.

Under a variety of model specifications, our model replicates the shift from private to quasipublic prices to achieve model stability in the presence of a modified Leontief utility function for households and a simple profit function for producers. Unlike Gintis (2006), however, the stable price vectors that emerge in our model with endogenous production diverge from general equilibrium pricing. Thus, Gintis' result that Walrasian equilibrium can arise in a decentralized economy with bi-lateral trade does not appear to be robust to generalization with endogenous production.