The Discrete Nerlove-Arrow Model: Explicit Solutions
We use the optimality principle of dynamic programming to formulate a discrete version of the Nerlove-Arrow maximization problem. When the payoff function is concave we derive an explicit solution to the problem. If the time horizon is long enough there is a "transiently stationary" (turnpike) value for the optimal capital after which the capital must decay as the end of the time horizon approaches. If the time horizon is short the capital is left to decay after a first-period increase or decrease depending on the capital's initial value. Results are illustrated with the payoff function ÂµK where K is the capital and 0 0. With this function, the solution is in closed form.
|Date of creation:||Nov 2010|
|Date of revision:||Nov 2010|
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