Monday, January 14, 2013

Time Preference

A staple of both micro- and macroeconomics is the individual time preference. According to this theory, first, goods and services are worth more now than they are later, and second, individuals have different time preferences: some prefer fewer goods and services now rather than more later; others prefer more goods and services later than fewer now. In other words, if I'm entitled to one latte each day, I would never go without a latte today just so I could consume two tomorrow; there's no benefit to foregoing today's latte just so I can drink it tomorrow. But I I can go without a latte today and consume three lattes tomorrow: today's latte, tomorrow's latte, and the "extra" latte I gain by going without today. Some people would rather have their one latte each day; others would rather forego some individual day's lattes so they can get extra in the future.

That there is a time preference is obviously true: some people do not save at interest, and consume everything they're entitled to today; others, in exactly the same situation, consume less than they're entitled to today to consume more tomorrow. However, the question is whether time preference is an intrinsic or a derived element of an individual's utility function.

Let's consider an obviously unrealistic economy. First, we assume the economy is completely stable: there's no per capita economic growth*. We will produce exactly the same amount tomorrow as we do today, and everyone knows and expects economic stability. Second, everyone has exactly the same income, and we assume no individual's income will ever change. Third, we assume that everyone's utility function is constant across some period of time, say a four-week month: every individual will always want to consume exactly the same bundle of goods in any given month.

It seems clear that at least some elements of individuals utility functions still make sense: some people will prefer to consume only lattes and go without yoga lessons; some will consume only yoga lessons and go without lattes, and some will prefer various combinations of lattes yoga lessons. The aggregate of all the utility functions will create a family of indifference curves between lattes and yoga lessons, and the marginal costs of lattes and yoga lessons will create a production possibility frontier, and we know there's one optimal point where the indifference curves and the production possibility frontier intersect, specifying the relative quantities and prices of lattes and yoga lessons. Let's assume that the optimum is that one latte per day for a week is, in aggregate, equivalent to one yoga lesson per week, and people can choose between two lattes per day for a week, two yoga lessons per week, or any combination in between**.

*We can either assume no population growth and no economic growth, or we can assume that per capita production is always constant.

**It doesn't matter here whether or not we can produce and consume fractional lattes and yoga lessons.

We can say, then, that any element of a utility function that makes sense under these restricted conditions is an intrinsic element. Any element that makes sense only when we relax these assumptions is a derived element, derived, that is, from the relaxation of the assumption. For example, if an individual's utility function changes because we allow per capita economic growth, that change is an element derived from the fact of extrinsic economic growth.

Under these assumptions, then, time preference would say different individuals who valued lattes and yoga lessons equally but had different time preferences would choose between the following options:
  1. Neutral: one latte every day (28 per month) and one yoga lesson per week (4 per month) on the one hand, and on the other hand, they might choose
  2. High: two lattes every day for one week (14 per month), two yoga lessons the first week (2 per month), and none at all for the rest of the month.
  3. Low: no lattes or yoga lessons at all for one week, and two lattes and two yoga lessons for the next three weeks (42 lattes and 6 yoga lessons).

The first individual has a neutral time preference, the second has a high time preference, and the third has a low time preference. It's clear that if time preferences are symmetrically distributed, then those with low time preference can trade with those with high time preference, and production and consumption remains constant on a daily basis, with every pair of individuals consuming a total of one latte per day and one yoga lesson per week.

However, it's hard to look at this as specifically a time preference. If we assume that everyone is rational, then every person knows they will have to go without sooner or later. Instead we can look at these kinds of preferences as saying that an individual prefers two lattes a day for a week more than they dislike going without a latte for a week. But in this case, they can trade one-for-one with others with the same preference. They can trade their lattes this week for others' lattes next week, and then switch back and forth. Then, instead of getting two lattes per day (and two yoga lessons) for only one week per month, they get two lattes per day and two yoga lessons per week for two weeks. Thus, a time preference, where more goods later can be substituted for fewer now, seems entirely irrational under conditions of absolute stability.

If we relax the assumptions, then time preference starts to seem more reasonable. If we assume economic growth, or if we assume that income levels change over time (note that the former implies the latter, but not vice versa), or if we assume that fundamental preferences change over time, then a time preference obviously makes sense. Some people will be happy with their one latte a day; those who forego their latte today invest the unused labor to make latte production more efficient tomorrow, and they reap the "extra" lattes not taken from the high time preference consumers but from increased productivity. Indeed, investment and increasing productivity are not the result of time preferences; time preferences are an artifact of economic growth.

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