| Sumario: | The article establishes a new duality for an intertemporally optimizing firm, between the firm's technology and its value function, giving the maximum value of the integral of discounted future profits. Demand functions cannot generally be determined explicitly from the technology but they are defined implicitly by first order conditions, which can serve as the basis for estimation, though perhaps requiring complicated simultaneous equations techniques. Explicit solutions for calculus of variations problems are even rarer and the implicit representation of solutions generally involves a second order nonlinear differential equation and non-trivial boundary conditions. Three principal directions for future research are indicated. First, the duality between value functions and production functions should be extended to the case of general non-static price expectations. Second, the duality should be applied to test empirically the validity of the adjustment-cost model. Finally, the basic approach of this paper should be adapted to other intertemporal planning problems such as the consumer's life-cycle problem and a model of the extractive firm.
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