General competitive analysis

Abstract

The decentralized economy, driven by self-interest and guided by price signals, achieves coherent resource allocation under specific conditions of rationality and market structure. A systematic formalization of general equilibrium theory proves the existence of competitive equilibrium using topological fixed-point theorems and convex analysis. Within this framework, household and firm behaviors are deduced from axiomatic preferences and production possibilities, establishing that price-guided systems can reach Pareto-efficient outcomes. The mathematical requirements for the uniqueness and stability of these equilibria are identified, with particular emphasis on gross substitutability, diagonal dominance, and the convergence properties of the tâtonnement process.

Beyond the idealized model of perfect competition, the theoretical scope includes the analysis of non-convex preferences and the core of market economies, demonstrating that bargaining outcomes converge toward competitive equilibria as the number of agents grows. The analysis further extends to temporary equilibrium and the institutional complexities of monetary exchange, offering a rigorous basis for understanding market failures, speculative behaviors, and the constraints addressed in Keynesian macroeconomic theory. This comprehensive examination clarifies not only how a decentralized system can achieve order but also identifies the specific structural features—such as non-convexities or incomplete markets—that may prevent such coordination. – AI-generated abstract.