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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.
Intended learning outcomes
- Recognise and set up standard economic problems (the consumption decision, the production decision, cost minimization, simple multi-period decision making) as optimization problems
- Solve specific optimization problems such as those involving utility and profit maximization and cost minimization
- Solve market equilibrium problems
- Explain the geometry of constrained optimization, the geometry of Lagrange multipliers;
- Explain the difference between necessary and sufficient conditions, and their application at both interior and corner points;
- Solve matrix algebra problems including those involving quadratic forms and eigenvalues and vectors, and explain the connection between positive definite forms and convexity;
- Solve problems in multivariate calculus, including the calculation of gradients and tangents, and differentiating a function along a curve;
- Set up and solve Khun Tucker problems;
- Explain and interpret Lagrange multipliers as shadow prices;
- Solve problems involving simple comparative statics, both for optimization and equilibrium problems, using the univariate implicit function theorem, single crossing conditions and envelope methods.
High level of development: problem solving; interpretation and analysis; critical thinking.
Moderate level of development: oral communication; written communication; collaborative learning; team work; statistical reasoning; application of theory to practice; receptiveness to alternative ideas.
Some level of development: synthesis of data and other information; evaluation of data and other information; use of computer software; accessing data and other information from a range of sources.
Last updated: 4 August 2022