Non-concavity problems in the dynamic macroeconomic models: A note
This note provides a method to convert the dynamic models in Cysne [Cysne, Rubens P., 2006. A note on the non-convexity problem in some shopping-time and human-capital models. Journal of Banking and Finance 30 (10), 2737-2745] and in Cysne [Cysne, Rubens P., 2008. A note on "inflation and welfare". Journal of Banking and Finance 32 (9), 1984-1987] to concave optimization problems. We do this by introducing new control and state variables in the models. Cysne (2006, 2008) restrict attention to continuous time models and derive parametric conditions to use Arrow's sufficiency theorem. When the sufficient conditions presented in Cysne (2006) are satisfied (but not under the sharper sufficient conditions presented in Cysne (2008)) we can rewrite these models as concave optimization problems even if time is discrete.
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- Cysne, Rubens Penha, 2006. "A note on the non-convexity problem in some shopping-time and human-capital models," Journal of Banking & Finance, Elsevier, vol. 30(10), pages 2737-2745, October.
- Robert E. Lucas, Jr., 2000. "Inflation and Welfare," Econometrica, Econometric Society, vol. 68(2), pages 247-274, March.
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