Functions & Economic Relationships
Functions, domains, ranges, linear and nonlinear relationships, and the geometry of economic models.
y = f(x)
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Go beyond intuition. Use calculus, optimisation, linear algebra and mathematical modelling to understand how consumers choose, firms produce and economic systems reach equilibrium.
Mathematical economics expresses economic relationships through equations, functions, inequalities and systems of constraints. It allows us to formulate precise hypotheses and derive conclusions logically.
The objective is not mathematics for its own sake. It is to understand the structure of economic decisions: why an optimum occurs, how an equilibrium is determined, and what changes when an underlying parameter changes.
Each pathway connects a mathematical tool with its economic interpretation, helping learners progress from foundational calculus to advanced optimisation and economic modelling.
A structured curriculum from functions and calculus to constrained optimisation, duality and equilibrium.
Functions, domains, ranges, linear and nonlinear relationships, and the geometry of economic models.
First derivatives, marginal cost, marginal revenue, elasticities and economic rates of change.
Antiderivatives, definite integrals, total functions and accumulation from marginal relationships.
First- and second-order conditions, maxima, minima, curvature and economic applications.
Lagrange multipliers, budget constraints, cost minimisation and constrained utility maximisation.
Implicit differentiation, equilibrium responses, parameter changes and sensitivity analysis.
Matrix operations, determinants, inverses and solving simultaneous economic equations.
Primal and dual problems, expenditure and cost functions, shadow prices and economic envelopes.
Convex sets, separating hyperplanes, concavity, convexity and equilibrium existence foundations.
Consider a simple utility function with a budget constraint. The laboratory calculates the utility-maximising quantities using the first-order conditions for a Cobb–Douglas utility function.
This is an illustrative model with positive prices and Cobb–Douglas preferences. It is not financial advice.
Equal prices and equal exponents produce equal optimal spending on both goods.
Progress from mathematical foundations to rigorous economic analysis and advanced theory.
Functions, equations, inequalities, graphs and elementary algebra.
Derivatives, integration, extrema, constraints and Lagrange multipliers.
Consumer choice, producer decisions, cost functions and comparative statics.
Duality, matrix methods, convex analysis and equilibrium theory.
Use the checklist to monitor your journey through the mathematical foundations of economics.
This version tracks progress during the current page session. Persistent progress can be implemented with a student account.
Learn the mathematical language that transforms economic questions into structured, testable models.