Intertemporal Constraints, Shadow Prices, and Financial Asset Values

The conditions under which the unobserved shadow price of capital can be equated to the financial value of the firm have been developed in an important paper by Hayashi (1982). Employing a more powerful analytic method, this paper reexamines the shadow price- asset value relation in a model with a general set of intertemporal constraints. For a model with one capital good, a general relation between shadow prices and asset values is derived, and restrictive assumptions implicit in previous work are highlighted. Of particular importance is the relation between the marginal and average survival rates of capital, and the critical role of geometric depreciation. The impact of a discrete-time framework in specifying and interpreting econometric models is also explored.