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Download or read book Dynamic Programming, Maximum Principle and Vintage Capital written by Giorgio Fabbri and published by . This book was released on 2007 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present an application of the Dynamic Programming (DP) and of the Maximum Principle (MP) to solve an optimization over time when the production function is linear in the stock of capital (Ak model). Two views of capital are considered. In one, which is embraced by the great majority of macroeconomic models, capital is homogenous and depreciates at a constant exogenous rate. In the other view each piece of capital has its own amp;finite productive life cycle (vintage capital). The interpretation of the time patterns of macroaggregates is quite different betweeen the two cases. A technological shock generates an oscillatory movement in the time pattern of per capita output when capital has a vintage structure; conversely an instantaneous adjustment with no transitional dynamics occurs when capital is homogenous.From a methodological point of view it emerges that the DP approach delivers sharper results than the MP approach (for instance it delivers a closed form solution for the optimal investment strategy) under slacker parameter restrictions.Cross-time and cross-country data on investments, income, and consumption drawn from the Penn World Table version 6.2 are used to evaluate the vintage and standard Ak model.