1. Individuals' utility-maximizing choices over time will obviously depend on how they feel about the relative merits of consuming currently or waiting to consume in the future. People may show some impatience in their choices by assuming that the utility from future consumption is implicitly discounted in the individual's mind. For example, we may assume that the utility function for consumption, U(C), is the same in both periods (with U'>0, U''<0), but that period 1's utility is discounted in the individual's mind by a "rate of time preference" of $$\frac{1}{1+\delta}$$ (where $$\delta > 0$$). If the intertemporal utility function is also separable, we can write the following equation:

$$U(C0, C1) = U(C0) + \frac{1}{1+\delta}U(C1),$$

Maximization of the function subject to the intertemporal budget constraint:

$$I = C0 + \frac{C1}{1+r}$$

Where r is the rate of return received on savings and 1 denotes the income.