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"Comparative Dynamics (Sensitivity Analysis) in Optimal Control Theory," Journal of Economic Theory, Vol. 3, 1973, pp.265-283.

• [Outline]
• [Keywords]
• [Full Text]
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[Outline]

This paper considers an optimal control problem with a parameter and develops a systematic method for comparative dynamics. A sufficient condition for the optimum solution to be differentiable with respect to the parameter is provided. Formulas for computing the derivative of the optimal solution with respect to the parameter are given in the form of initial-value problems of linear differential equations. Possibility of discontinuous optimal controls is fully taken care of. The derivative of the maximized objective function with respect to the parameter is expressed in a simple form by using auxiliary variables. An example of the comparative dynamics is given in terms of a model of optimal capital accumilation.

[Keywords]

comparative dynamics, optimal control, sensitivity analysis, parametric calculus of variations

[Full Text]

The Journal of Economic Theory (June, 1973) [PDF: 550KB]
Data for The Journal of Economic Theory (June, 1973) [DOC: 789KB], [PDF: 105KB]
Harvard University, Project on Efficiency of Decision Making in Economic Systems, Technical Report No.10 (including proofs) (April, 1972) [PDF: 1,659KB]

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