Homogeneous Functions Economics: Euler’s Theorem
Homogeneous functions economics explains how Euler’s theorem links returns to scale, marginal products, and factor payments in production theory.
Mathematical Economics
Discover key mathematical methods used in economic analysis, including calculus, matrices, and optimization.
Total Differential Economics: Small Model Changes
Total differential economics explains how small changes in several variables combine through marginal effects to change an economic model’s outcome.
Implicit Function Theorem Economics: Comparative Statics
Implicit function theorem economics explains how equilibrium comparative statics can be derived locally without solving models explicitly.
Jacobian Matrix Economics: Comparative Statics and Stability
Jacobian matrix economics explains how first-derivative matrices support comparative statics, local solvability, and stability analysis in economic systems.
Hessian Matrix Economics: Curvature and Concavity Tests
Hessian matrix economics explains how second derivatives test curvature, concavity, convexity, and local optima in multivariable economic models.
Bordered Hessian: Second-Order Conditions
Bordered Hessian analysis checks second-order conditions in constrained optimization by testing curvature along feasible directions, not across all possible movements.
Roy’s Identity and Shephard’s Lemma: Recovering Demand from Utility and Cost
Roy's Identity and Shephard's Lemma are the duality results that recover Marshallian and Hicksian demand from indirect utility and expenditure...
Kuhn-Tucker Conditions: Optimisation with Inequality Constraints
The Kuhn-Tucker Conditions extend Lagrangian optimisation to inequality constraints through complementary slackness, the principle that supports modern microeconomics, finance, and...
Envelope Theorem: A Shortcut for Optimisation Problems
The Envelope Theorem simplifies comparative statics: the total derivative of a maximised objective equals the partial derivative at the optimum,...
Bond Duration and Convexity: How Maths Prices Interest-Rate Risk
Bond duration and convexity are the mathematical tools fixed-income markets use to measure how bond prices respond to interest-rate changes,...