COMPARATIVE DYNAMICS IN STOCHASTIC MODELS WITH RESPECT TO THE L∞–L∞ DUALITY: A DIFFERENTIAL APPROACH

Many economic analyses are based on the property that the value of a commodity vector responds continuously to a change in economic environment. As is well known, however, many infinite-dimensional models, such as an infinite–time horizon stochastic growth model, lack this property. In the present paper, we investigate a stochastic growth model in which dual vectors lie in an <italic>L</italic>^∞ space. This result ensures that the value of a stock vector is jointly continuous with respect to the stock vector and its support price vector. The result is based on the differentiation method in Banach spaces that Yano [<italic>Journal of Mathematical Economics</italic> 18 (1989), 169–185] develops for stochastic growth models.