Instrumental Methods of Economic Analysis
- understanding the basic concepts of mathematical analysis and linear algebra
- acquiring skills in solving optimization problems of various types
- Be able to solve unconstrained and constrained optimization problems
- Have an understanding of the envelope theorem and be able to use it in the optimization problems
- Know the necessary and sufficient conditions for concavity/convexity of the function and maximum/minimum.
- Understand the theory of elementary functions, methods of calculus related to the differentiation of single and multiple variable functions.
- Linear algebra: operation with matrices, square matrices, determinant, eigenvalues and eigenvectors
- Functions of one variable: derivative of the function, necessary and sufficient conditions for increasing/decreasing, concavity/convexity, extremum and inflection points.
- Functions of multiple variables: first and second order partial derivatives, Schwarz theorem, necessary and sufficient conditions for concavity/convexity and extremum points
- Unconstrained optimization of multiple variables functions: necessary and sufficient conditions for local/global maximum/minimum, envelope theorem
- Constrained optimization of multiple variable functions. Equality constrains: necessary and sufficient conditions for maximum/minimum, relationship between concavity/convexity of the function with the type of extremum. Inequality constrains: Kuhn-Tucker theorem, relationship between concavity/convexity of the function with the type of extremum
- Sundaram, R. K. (1996). A First Course in Optimization Theory. Cambridge University Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsrep&AN=edsrep.b.cup.cbooks.9780521497701
- Vinogradov, V. V. (2010). Mathematics for Economists. University of Chicago Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsrep&AN=edsrep.b.ucp.bkecon.9788024616575