[A tractable dynamic general equilibrium model of continuous product innovation is developed. Patents, or any imitation lag, of infinite duration may achieve too much, too little, or the socially optimum level of innovation. Most surprising, finite-life patents may induce undamped oscillations in innovation.]

[The rational expectations hypothesis in a life cycle context asserts that agents seek to keep the marginal utility of discounted expenditure constant across time. In this paper we present estimates of a demand system that takes explicit account of this hypothesis. We show how the restrictions from demand theory enable us to identify the model despite the presence of an unobservable variable that can be interpreted as revisions to the marginal utility of discounted expenditure. This allows us to take explicit account of the different effects of anticipated and unanticipated price changes. An important check on our model is the derivation of expenditure elasticities despite the fact that the demand system does not have expenditure on the right hand side. Our estimates are "sensible" and we find that we can reject the hypothesis that revisions to the marginal utility of discounted money are orthogonal to the past values of our variables. We interpret this to be a rejection of the rational expectations hypothesis.]