There are many important situations in which prices, income or preferences are not known with certainty. For example, the waterfowl hunter of Chapter 9 cannot know for sure the number of waterfowl he will kill and bag during the next hunting season. Similarly, the recreationist of Chapter 8 may be uncertain as regards travel costs, entrance fees, and the weather at the site. In such cases it may seem reasonable to distinguish between risk, that refers to situations where probabilities are knowable, and uncertainty proper, which applies to situations where probabilities cannot even be defined. In this book, we will deal exclusively with the former class of situations, although the terms risk and uncertainty are used interchangeably.

Ordinary or compensated demand functions, obtained under certainty, imply very little about a household's attitudes towards risk. This is because the form of demand functions is an ordinal property, while risk aversion is a cardinal property of preferences. Moreover, while conventional demand theory begins with a quasi-concave direct utility function, risk analysis hinges on the stronger assumption of concavity or convexity. The first section of this chapter is devoted to exploring these different concepts.

In Section 2, the welfare change measures derived in previous chapters are modified so as to be able to cope with cases of uncertainty where some decisions must be made before prices are known.