we'll ignore all dates after 60 in the calculation of total utility. On the basis of these assumptions, we can calculate the total value of utility at date 0, and then assess the impact of changes in the assumptions on total utility. Our base case total utility value is 135.413. Now we can assess the impact on total utility of changes in the underlying assumptions. Suppose first that we increase the growth rate in consumption, say from 3 percent to 4 percent. Under this assumption, total utility increases from 135.413 to 138.149. Similarly, if we reduce the growth rate in consumption from 3 percent to 2 percent, total utility declines from 135.413 to 132.394. Clearly our utility function is consistent with the idea that investors prefer higher consumption growth rates to lower. Now let's explore the impact of changes in the rate of time preference, and let the discount rate increase by 10 basis points to 1.10 percent. Under this assumption, investors value consumption today more highly than consumption in the future: The total utility value declines to 131.697. To keep utility unchanged from the base case, consumption growth must increase from a 3.0 percent annual growth rate to a 4.44 percent annual growth rate. Thus, higher discount rates (lower discount factors) imply that consumption growth must increase to keep utility unchanged. The final parameter we can change is the risk aversion parameter. Suppose that we increase the risk aversion parameter from 1.25 to 1.30. In this case, consumption growth must increase from 3.0 percent annually to almost 13 percent annually for utility to be unchanged. How do Mehra and Prescott make use of equation (5.2)? They begin by manipulating this equation to derive demand functions for both assets and consumption. To close the system, Mehra and Prescott need to make assumptions about production and equilibrium. They assume that each period a single perishable good is produced, and that production grows, but at a random rate. Although the growth rate in production is random, its distribution is known, with a long-term average growth rate and a known variance. In this simple economy, the long-term average growth rate is assumed to be given exogenously. Factors such as productivity growth that would naturally be expected to influence the long-term average growth rate are not considered in this model. To close the system, they further assume that in equilibrium consumption equals production of the single good at every date. Thus, uncertainty about future consumption-that is, the quantities in equation (5.2)-is effectively uncertainty about future output. Now, what about asset pricing and asset returns? Looking at equation (5.2) more closely, we see that in the abstract, the only unknown quantity at any date in time is consumption, or ct. Mehra and Prescott exploit this point quite explicitly in their analysis. Effectively, they are trying to provide answers to the following questions: What would an investor be willing to pay for an asset whose payoff would look approximately like the path of consumption? What would the return on that asset be over time? And what would give rise to a premium on that asset? Mehra and Prescott's answers to these questions begin from a very fundamental point: If production (and, in this model, consumption) were known with cer-