THE TRADING PROCESS used in Case 1 involved a number of markets. In each, the market maker asked Mario and Hue to indicate their reservation prices for a specific security, and then to denote the number of shares they would be willing to buy or sell at an announced price based on those reservation prices. We characterized Mario and Hue's behavior as consistent with downward-sloping demand curves and upward-sloping supply curves. We also represented each of them as having a time preference and a risk aversion. This was, at best, an opaque description of their preferences. In this chapter, we aim to remove most of the mystery. We provide the details of the types of preferences exhibited by Mario and Hue and introduce some alternative types of investor behavior.
Though trading with fish served us well in Chapter 2, it is time to drop that particular conceit. Henceforth we will refer to payoffs as either units of consumption or real dollars (dollars adjusted for changes in purchasing power).
It is not unreasonable to assume that an individual will enter into a trade only if he or she would prefer the result to the status quo. Another way to put this is to say that the goal of an investor is to maximize the expected happiness associated with his or her investments. For decades, economists have operationalized this concept by assuming that an investor seeks to maximize expected utility. As we will see, this is not an innocuous assumption. On the other hand, it need not be as unrealistic as some believe.
In general, a person's expected utility will depend on the consumptions to be obtained in the states (X1, X2, …) and his or her assessment of the probabilities of the states (π1, π2, …) :
EU = f(X1, X2, …, π1, π2, …)
Other things equal, for a state with positive consumption and probability, the higher the consumption the greater its contribution to expected utility; and the higher the probability of the state, the greater its contribution to expected utility.
To actually simulate an equilibrium process we need more specificity. To keep things simple, we assume that each level of consumption in a state provides an