Excessive revenue model of competitive markets

We present an excessive revenue model of a competitive market. Its partial equilibrium is characterized as a saddle point in a convex-concave game. Convex variables (for minimization) represent prices of goods, and concave variables (for maximization) stand for production and consumption bundles. The analysis of the market is crucially based on Convex Analysis. Namely, our market model admits a joint convex potential function. In particular, equilibrium prices have a natural explanation: they minimize the total excessive revenue of the market’s participants. Due to this characterization, existence and efficiency of partial equilibrium are derived. Additionally, we decentralize prices by introducing the trade design. The total excessive revenue preserves its convexity w.r.t. decentralized prices. This feature allows us to suggest a decentralized price dynamics based on subgradient-type information. We show that unique equilibrium prices can be approached as limiting points of this price dynamics. From the technical point of view, the most unusual feature of our approach is the absence of the budget constraint in its classical form. As a consequence, some consumers may get bankrupt and eventually leave the market. In order to incorporate wealth effects into our model, we make further assumptions on consumers’ behavior. Namely, the consumers are assumed to be responsible and long-term behaved.