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We develop a method to characterize the location as well as the time of approach of optimal steady states in single-state, infinite-horizon, autonomous models. The method is based on a simple function of the state variable which is defined in terms of the model's primitives. The actual implementation does not require to solve the underlying dynamic optimization problem (which often does not admit a closed-form solution). Applying the method to a generic class of resource management problems, we show how it identifies the set of candidate steady states and determines, for each steady state, whether the corresponding approach time is finite or infinite.


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