# Lecture Notes for ECON 7020 - MACROECONOMIC THEORY 1 with Boileau at Colorado (CU)

## Notes Information

 Material Type: Class Note Professor: Boileau Class: ECON 7020 - MACROECONOMIC THEORY 1 Subject: Economics University: University of Colorado - Boulder Term: -- Keywords: Economic EnvironmentRepresentativeAssumptionsConsumptionSubstitutingSimilaritiesIndividual DemandPrice SystemSubstitutionAccumulation

## Sample Document Text

ECON7020: MACROECONOMIC THEORY I Martin Boileau II. TWO-PERIOD ECONOMIES: A REVIEW 1. Introduction These notes brie°y review two-period economies. This includes the consumer's problem, the producer's problem, and general equilibrium. In what follows, I borrow freely from Chiang (1984), Farmer (1993), Feeney (1999), Obstfeld and Rogo® (1996), and Smith (1997). 2. Constrained Optimization Throughout, we make extensive use of constrained optimization. That is, we aim to solve problems of the following form: maxf(x1; :::; xn) subject to g(x1; :::; xn) · y: This problem is solved using the Lagrangian: L = f(x1;:: :;xn) + ¸[y ¡ g(x1;: ::; xn)]; where ¸ is a Lagrange multiplier. Assuming an interior solution, the necessary ¯rst-order necessary conditions for a maximum are @L @xj = @f @xj ¡ ¸ @g @xj = 0 for j = 1;:: :;n: The second-order su±cient conditions for a maximum are that the bordered hessian, the matrix of second derivatives of the function f(¢) bordered by the ¯rst derivatives of the ...

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