Solving macroeconomic models with homogeneous technology and logarithmic preferences

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

In a stylised Robinson Crusoe economy, we illustrate basic dynamic programing techniques. In a first step, we define state-like and control-like variables. In a second step, we introduce the value-function-like function. While the former step reduces the number of variables that have to be considered when solving the model, the latter step reduces the dimensionality of the Bellman equation associated with the optimisation problem. The model's solution is shown to be saddle-path stable, such that the phase diagram associated with the Bellman equation has two solution branches. The simplicity of our model allows us to state both the stable and the unstable branch explicitly. We also explain the usefulness of logarithmic preferences when studying the continuous-time Hamilton-Jacobi-Bellman equation. In this case, the utility maximisation problem can be transformed into an initial value problem for an ordinary differential equation.

Original languageEnglish
Pages (from-to)1-18
Number of pages18
JournalAustralian Economic Papers
Volume52
Issue number1
DOIs
Publication statusPublished - 2013 Mar 1

Fingerprint

Macroeconomic models
Bellman equation
Diagrams
Simplicity
Value function
Usefulness
Hamilton-Jacobi-Bellman equation
Optimization problem
Utility maximization
Dimensionality
Differential equations
Continuous time

ASJC Scopus subject areas

  • Economics, Econometrics and Finance(all)

Cite this

Solving macroeconomic models with homogeneous technology and logarithmic preferences. / Bethmann, Dirk.

In: Australian Economic Papers, Vol. 52, No. 1, 01.03.2013, p. 1-18.

Research output: Contribution to journalArticle

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