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Delay equivalence in capital accumulation models. (English) Zbl 1232.91377

Summary: We study delays in capital accumulation models. Our contribution is threefold. First, we identify a class of models that can be transformed into standard optimal control models without delay. Second, in the single state versions of these models the state trajectory is monotonic in the optimal solution. This is noteworthy given the common belief that adding delays facilitates oscillatory behavior of capital, output and investment. Third, we identify an equivalence result between time-to-install/deliver problems and time-to-build problems.

MSC:

91B38 Production theory, theory of the firm
49N90 Applications of optimal control and differential games
91G50 Corporate finance (dividends, real options, etc.)
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References:

[1] Bambi, M., Fabbri, G., Gozzi, F., 2009. Optimal policy and consumption smoothing effects in the time-to-build AK model. Working Paper.; Bambi, M., Fabbri, G., Gozzi, F., 2009. Optimal policy and consumption smoothing effects in the time-to-build AK model. Working Paper. · Zbl 1246.91082
[2] Benhabib, J.; Rustichini, A., Vintage capital, investment, and growth, Journal of Economic Theory, 55, 323-339 (1991) · Zbl 0754.90007
[3] Hartl, R. F., A simple proof of the monotonicity of the state trajectories in autonomous control problems, Journal of Economic Theory, 41, 211-215 (1987)
[4] Hartl, R.F., Kort, P.M., 2010. Delay in Finite Time Capital Accumulation. Central European Journal of Operations Research, forthcoming; DOI:10.1007/s10100-010-0170-7.; Hartl, R.F., Kort, P.M., 2010. Delay in Finite Time Capital Accumulation. Central European Journal of Operations Research, forthcoming; DOI:10.1007/s10100-010-0170-7. · Zbl 1206.91052
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