Mathematical Economics

Set theory, univariate calculus and optimisation are reviewed and applied to the theory of the firm and the theory of consumer demand. Linear algebra concepts including matrix operations, vector spaces and quadratic forms are introduced and applied to problems in economics and econometrics. Applications of multivariate calculus including constrained optimisation, the envelope theorem and Kuhn-Tucker conditions are covered.

• 1Recognise and set up standard economic problems (the consumption decision, the production decision, cost minimization, simple multi-period decision making) as optimization problems;
• 2Solve specific optimization problems such as those involving utility and profit maximization and cost minimization;
• 3Solve market equilibrium problems;
• 4Explain the geometry of constrained optimization, the geometry of Lagrange multipliers;
• 5Explain the difference between necessary and sufficient conditions, and their application at both interior and corner points;
• 6Solve matrix algebra problems including those involving quadratic forms and eigenvalues and vectors, and explain the connection between positive definite forms and convexity;
• 7Solve problems in multivariate calculus, including the calculation of gradients and tangents, and differentiating a function along a curve;
• 8Set up and solve Khun Tucker problems;
• 9Explain and interpret Lagrange multipliers as shadow prices; and
• 10Solve problems involving simple comparative statics, both for optimization and equilibrium problems, using the univariate implicit function theorem, single crossing conditions and envelope methods.