# Microeconomics: Theory Through Applications, v. 1.0

by Russell Cooper and A. Andrew John

## 17.4 Choices over Time

Individuals make decisions that unfold over time. Chapter 4 "Life Decisions" gives several examples. Because individuals choose how to spend income earned over many periods on consumption goods over many periods, they sometimes wish to save or borrow rather than spend all of their income in every period.

Figure 17.3 "Choices over Time" shows examples of these choices over a two-year horizon. The individual earns income this year and next. The combinations of consumption that are affordable and that exhaust all of an individual’s income are shown on the budget line, which in this case is called an intertemporal budget constraint. The slope of the budget line is equal to (1 + real interest rate), which, for convenience, we sometimes call the real interest factor (that is, real interest factor = 1 + real interest rate). The slope is the amount of consumption that can be obtained tomorrow by giving up a unit of consumption today.

The preferred point is indicated in the figure as well. This is the combination of consumption this year and consumption next year that the individual prefers to all the points on the budget line. The individual in part (a) of Figure 17.3 "Choices over Time" is consuming less this year than she is earning: she is saving. Next year she can use her savings and can consume more than her income. The individual in part (b) of Figure 17.3 "Choices over Time" is consuming more this year than he is earning: he is borrowing. Next year, his consumption will be less than his income because he must repay the amount borrowed in the first period.

When the real interest rate increases, individuals will borrow less and (usually) will save more (the effect of interest rate changes on saving is unclear as a matter of theory because income effects and substitution effects act in opposite directions). Thus individual loan supply slopes upward.

Of course, individuals live for many periods and make frequent decisions on consumption and saving. The lifetime budget constraint is obtained using the idea of discounted present value:

discounted present value of lifetime income = discounted present value of lifetime consumption.

The left side is a measure of all the disposable income the individual will receive over his lifetime (disposable means after taking into account taxes paid to the government and transfers received from the government). The right side calculates the value of consumption of all goods and services over an individual’s lifetime.

## Key Insights

• Over a lifetime, an individual’s discounted present value of consumption will equal the discounted present value of income.
• Individuals can borrow or lend to obtain their preferred consumption bundle over their lifetimes.
• The price of borrowing is the real interest rate.

Figure 17.3 Choices over Time