Mathematical economics

Mathematical economics formulates and analyzes economic relationships with mathematical models, using tools such as optimization, equilibrium analysis, and differential equations.

Optimization: The process of selecting the best feasible choice according to a specified objective. Economic models often represent consumers and firms as optimizing agents.
Economic model: A simplified representation of economic relationships, behavior, or institutions. Mathematical economics gives economic models explicit formal structure.
Consumer theory: The study of how consumers choose among goods under preferences and budget limits. Its models use utility maximization to derive demand and welfare results.
Antoine Augustin Cournot: A French economist whose 1838 work modeled competition and monopoly mathematically. Cournot used equations to analyze firms' output choices and strategic interaction.
Verbal economics: Economic analysis expressed primarily through prose and qualitative argument rather than formal equations. It presents economic reasoning without the explicit mathematical structure emphasized here.
Constrained optimization: Optimization in which choices must satisfy explicit restrictions. Budgets, production limits, and resource scarcity become mathematical constraints.
Comparative statics: The analysis of how an equilibrium changes when an underlying parameter changes. It derives directional predictions without tracing the adjustment process over time.
Production theory: The study of how firms transform inputs into outputs and choose production plans. Mathematical production functions connect technology to costs and output.
Léon Walras: A French economist who developed a mathematical theory of general equilibrium. Walras made simultaneous market-clearing equations central to economic analysis.
Experimental economics: The study of economic behavior through controlled experiments with human participants or institutions. It tests behavior through experiments rather than relying only on formal derivation.

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