2008/04/25 by Lawrence E. Blume · 2 citations
Economics, Econometrics and Finance · #Economic theories and models
paper · doi:10.1057/9780230226203.0315
openalex publication_date 2008/04/25 · openalex created_date 2022/05/12 · openalex updated_date 2026/04/15
Convexity is the modern expression of the classical law of diminishing returns, which was prominent in political economy from Malthus and Ricardo through the neoclassical revolution. Its importance today rests less on any utilitarian or behavioural psychological rationale or physical principle than on its utility as a tool of mathematical analysis. In general equilibrium and game theory, proofs of the existence of equilibrium, competitive and Nash, respectively, rely on the application of a fixed-point theorem to a set-valued, convex-valued map from a convex set to itself. Welfare economics provides another example: The second theorem of welfare economics, which asserts that optimal allocations can be supported by competitive prices, relies on an application of the supporting hyperplane theorem to an appropriate convex set.