| The Arrow-Pratt analysis of risk aversion offers a cogent explanation of how changes in attitudes towards risk affect the choices of expected utility maximizing agents whose preferences are defined over a single variable, wealth. The restriction of the analysis to utility functions of one argument, however, severely limits its applicability: in many problems of choice we must represent the agent's preferences with a multivariate, not univariate, utility function. The main purpose of this thesis is to extend the Arrow-Pratt analysis to choice problems with more than two commodities and with multiple sources of risk.;Our main comparative statics results are of two types. First we demonstrate necessary and sufficient conditions for any given inverse demand function to increase or decrease in response to increased risk aversion. We then use this result to derive sufficient--and in the two commodity case, necessary--conditions for any demand function to be a monotone function of the agent's attitude towards risk. These conditions generalize the results of Diamond and Stiglitz (1974) and Kihlstrom and Mirman (1974) for a two commodity model with a single source of risk. Of course, if the original n-commodity model can be aggregated into a two commodity model expressible as the expected value of a function of two arguments, then we can dispense with the more restrictive general conditions altogether. We demonstrate, however, that such aggregation is permissible only in rather severe circumstances--hence the need for the disaggregated analysis employed in this thesis.;Finally, we apply these results to some specific models of choice, including a model of uncertain product quality, and a two period disaggregated consumption-savings model in which both the vector of second period prices and the rate of return on savings are uncertain. |
