On the Roles of Impatience in Homothetic Growth Paths

This article reexamines the role of long-run endogenous impatience in homothetic growth paths. Using a class of intertemporal preferences assuming a continuous time generator representation, the existence, uniqueness and determinacy properties of a homothetic growth path with endogenous rates of time preference are checked. The argument is based on extensive use of prospective utility. The associated utilities are shown to exhibit a rate of time preference function that becomes invariant to prospective utility along the homothetic growth solution. They also enter in a normal way in the generating function. Finally and at the opposite of earlier conclusions for steady states, the nil rate of time preference case associated with multiplicatively separable generators cannot anymore be discarded