Three essays in growth theory

This dissertation consists of three essays in the field of growth theory, with particular emphasis--in the first and third essays--on problems in utility theory for growing economies.;In the first essay, I prove two time-additively separable representation theorems for preferences over an infinite horizon without assuming either that feasible consumption streams are bounded or that preferences are continuous in the product topology. The consumption set over which preferences are defined is the collection of all nonnegative sequences of real n-vectors which are dominated by scalar multiples of some fixed reference sequence--i.e., a Riesz ideal. Preferences are assumed to be continuous in the topology under which the program space is a Banach lattice. In the first theorem, the basic independence and stationarity assumptions of Koopmans are augmented by homotheticity of preferences and balanced growth of the reference sequence. The second representation theorem demonstrates the existence of a time-additively separable utility function when preferences satisfy the basic assumptions of Koopmans and are, additionally, monotone and 'impatient' in a particular way.;The second essay provides sufficient conditions for the existence of endogenously growing optimal paths in a multi-sector Ramsey model. A key assumption is the existence of a positive vector of capital stocks which admits expansibility in inverse proportion to the utility discount factor while still allowing strictly positive current consumption. If any scalar multiple of this feasible combination is also feasible, optimal paths grow without bound given standard convexity and interiority assumptions. I also provide conditions for the existence of optimal balanced paths of consumption and capital accumulation.;The third essay is concerned with Koopmans's 'recursive' utility and models of balanced growth. Despite having proven useful in a number of dynamic modelling contexts, recursive utility has not made significant inroads into models of balanced growth, whether 'exogenous' or 'endogenous'. Mainly, this is due to a dearth of interesting recursive utilities which are consistent with balanced growth. In the third essay I provide conditions on the aggregator which guarantee the existence of a recursive utility function which is consistent with balanced growth. The result in turn shows how a family of such utility functions may be constructed. Situating this class of utility functions in the context of a Ramsey capital accumulation model, I give conditions for both the existence of optimal paths and sustained growth of optimal paths.