are interdependent: The effort on the part of investors to select an optimal path for current and future consumption also sets a path for asset demand, and vice versa. An implication of this type of reasoning is that analysts should first write down (explicitly) a function representing asset demands. This demand function will, of course, reflect all features of the investor's utility function. Equilibrium asset prices are found by combining the path of asset demand with a path for asset supply. Asset returns, of course, are simply the changes in asset prices over time, and the equity premium is simply the return on a risky asset relative to a risk-free asset. Thus, Mehra and Prescott's model gives us a very elegant way to relate the equity premium to investor preferences about consumption. To represent investor behavior, Mehra and Prescott use a very standard utility function. They assume that there is a single investor (who is also the single consumer) acting as a stand-in for the entire economy. Again following standard practice, this investor is assumed to want to maximize the following function: Er ZP, t,(1-a)-l 1-cc (5.2) Several important ideas are expressed in equation (5.2). The first interesting parameter is p. This parameter represents the rate at which the investor is willing to substitute current consumption for future consumption. At one level, we can interpret p as the rate at which the investor discounts future consumption. The second interesting parameter is a. This parameter governs the investor's level of risk aversion. More risk-averse investors require higher levels of future consumption to keep well-being (as measured by the utility function) constant. The third interesting part of the equation is the variable cp or consumption at time t. This part of the equation tells us that the investor's current utility depends on the entire stream of consumption. Finally, the E{ } represents the mathematical expectation. This part of the equation tells us that the investor is operating in a world of uncertainty. Since a and P are assumed to be fixed, the uncertainty that the investor faces is about the path of consumption. Thus, equation (5.2) tells us that the investor wants to maximize the expected discounted value of the utility of current and future consumption, where the discount rate is the rate of intertemporal substitution and the utility of consumption depends of the level of risk aversion. To understand the impact of some of the parameters, let's work through a simple example. For simplicity, we'll assume that the path of consumption is known. We'll index consumption to be 100 at date 0, and assume that it grows at a constant rate of 3.0 percent per year: In other words, cQ = 100, c1 = 103, c2 = 106.09, and so on. Now, to calculate total utility, all we need to do is pin down values for a and p. For a, we'll use 1.25 as a starting value. We'll assume that pf = p( for every date. In other words, the rate of time preference is constant across two adjacent periods. For p, let's assume that the real