5 - Some Remarks on Measures of Risk Aversion and on Their Uses

Abstract

To gain some feeling for the importance of the assumption of expected utility maximization for the analysis of risk aversion, we turn now to an article that explores the same issues, using the state preference approach but not the hypothesis of expected utility maximization.1 Here, consumption in each different state of nature is simply treated as an alternative commodity. As in standard consumer theory, indifference curves in commodity space completely describe the structure of preferences. If the individual's preferences are compatible with the expected utility hypothesis we have the result that one can construct the entire preference map from knowledge of the amount of utility received whenever the individual consumes the same amount independent of the outcome of the random variable and knowledge of the probabilities of the different states of nature. This result allows the inference of general properties of the utility function from the willlingness to take small bets at different levels of wealth. Without the expected utility hypothesis, information about willingness to take large bets does not follow from willingness to take small bets at a safe initial wealth. It is a valuable exercise to develop two different ways of thinking about the same problem, since each approach handles some issues better than the other. The exercise in Chapter 8 asks the reader to convert the analysis of that chapter into this setting. Below we shall use the state preference approach repeatedly.