Necessity of transversality conditions for infinite horizon problems

This paper studies necessity of transversality conditions for the continuou s time, reduced form model. By generalizing Benveniste and Scheinkman's (19 82) "envelope" condition and Michel's (1990) version of the squeezing argum ent, we show a generalization of Michel's (1990, Theorem 1) necessity resul t that does not assume concavity. The generalization enables us to generali ze Ekeland and Scheinkman's (1986) result as well as to establish a new res ult that does not require the objective functional to be finite. The new re sult implies that homogeneity of the return function alone is sufficient fo r the necessity of the most standard transversality condition. Our results are also applied to a nonstationary version of the one-sector growth model. It is shown that bubbles never arise in an equilibrium asset pricing model with a nonlinear constraint.