Relationships such as the consumption function used above are nec-essarily simplifications, i.e. abstractions of reality. Today’s economists agree that individuals make consumption decisions in the context of a rather intri-cate optimization problem. The approach taken here is that such precise, micro-based consumption behaviour is overly complicated and therefore not practical for many applications. So we will continue to work with simplifica-tions, while trying to foster an understanding of those circumstances under which they break down.
Lifetime patterns of income and consumption
Why is a simplification? First, people evidently do not consume, say, 80% of their income on their weekly or monthly payday. They realize that the pay covers a given period of work and so spread consumption possibilities more or less evenly over that period. But if people are intelligent enough to realize and do that, wouldn’t they apply the same principle if they inherited
€1,000,000 at age 21? Assume that you inherited that sum under the condition that you refrained from any other paid work for the rest of your life. What would your consumption spending plan look like? You would probably try to spread consumption possibilities deriving from the inherited fortune over your expected lifetime. Your consumption during the first year after your twenty-first birthday would be only a very small fraction of the inherited million.
These ideas can be generalized. Utility-maximizing individuals will not ad-just current consumption to every kink in the development of their income. In much the same way as they do over the course of a month, individuals would like to obtain a smooth consumption path over their lifetime. The restriction is, of course, that they usually cannot spend more than they earn. But because
C = cY
C = cY
2.4 An intertemporal view of consumption and investment 53
of the possibility of obtaining loans and to save, this need not apply for each period of time, but only over the total lifetime.
Figure 2.15 shows a stylized but fairly typical income pattern over an indi-vidual’s lifetime (light blue lines). As a rule, income rises during the early stages of a career as the person becomes more productive and experienced. In-come then levels out during the later years of the person’s career. On retire-ment, income drops to some fraction of previous income levels, depending on the retirement plan and the amount of private savings.
Ideally, individuals would like to keep consumption fairly constant along a path like the light grey lines in Figure 2.15. However, this may not always be possible, particularly because of the reluctance of banks to extend loans to young people on the mere expectation of higher future income. But it is what individuals would prefer. So to simplify the argument, if we ignore bequests, rule out that individuals die in debt, and ignore interest payments on savings, total (planned) lifetime consumption equals total (expected) lifetime earnings.
Consumption per period equals expected lifetime income divided by expected remaining lifetime n:
The superscripts e on each Y in parentheses indicate that individuals do not know this value yet, but have to form an expectation of it. is the income expected one period from today in the future. Note that while the series given in parentheses may represent a complicated time profile of income, it is simply all income expected from tomorrow until we die. For the sake of notational convenience, we may denote this sum of all expected future income by to obtain the more compact consumption function:
(2.15) Now let individuals enjoy an income increase in period 40. The first question to ask is whether or not this was expected. If the experienced income rise is
C = 1 n Y + 1
n Ye+
Ye+
Ye+1
C = 1 n Y + 1
n (Ye+1 + Ye+2 + Ye+3 + Á
+ Ye+n - 1)
Figure 2.15 Lifetime patterns of income exhibit rising and falling sections as illustrated by the light-blue line. The grey line is the attached consumption plan. A perceived transitory income rise (panel (a)) increases consumption by very little. A perceived permanent income rise (panel (b)) results in a large consumption response.
Retirement age
(a) 40
Consumption and income
Consumption
Income Transitory income rise
Retirement age
(b) 40
Consumption and income
Consumption
Income Permanent income rise
Large consumption response Small
consumption response
part of the expected lifetime income pattern, there is absolutely no need to re-vise the lifetime consumption plan, and consumption will not respond at all.
Things are different if income increased unexpectedly, way beyond what the lifetime pattern prescribed (blue lines in Figure 2.15). Then a second crucial question must be asked: will the individual be able to sustain this added stream of income in the future? Or is it purely temporary, windfall income that will not have an impact on expected future income streams?
Panel (a) in Figure 2.15 illustrates the case in which the unexpected income bonus is considered to be purely temporary. Then expected lifetime income only increases by a very small percentage and the consumption of this period’s income bonus is spread out over all the remaining periods of one’s life. This is reflected in a very small upwards shift of the consumption path in period 40.
In panel (b), the increase in income is considered to be permanent. This shifts the entire pattern of income upward by the observed change of income and the impact on expected lifetime income is very large. The response to this increase is to consume roughly the full amount of the income increase during this period.
The lesson to be learned from this is that exceptional (or transitory) income, i.e. not expected to accrue regularly, period after period, produces consump-tion reacconsump-tions quite different from those to regular (or permanent) income.
Thus, when we apply our models, it is advisable to ask whether individuals consider an experienced income change permanent or transitory. Only in the first case may we expect to observe a substantial increase in consumption de-mand via multiplier effects.
The above discussion provides a first opportunity to appreciate that eco-nomic decisions are made on the basis of what people expect to happen in the future (will income stay up permanently?) rather than what they observe today. This pivotal role of expectations will be a recurring theme throughout this book, and is a general characteristic of modern economics.
Stocks and other assets
While individuals save during the early years of their professional careers, they accumulate wealth. Wealth may be held in the form of money, but this appears relevant only in times of crisis and war (see Box 2.2). Normally, savings are placed into interest-bearing bank accounts, government bonds, corporate stocks or real estate. Individuals expect to draw on these assets and the gener-ated returns later on in their lives, when salaries and wage payments dry up. If the value of acquired assets changes, this mandates an adjustment of consump-tion plans.
Suppose again that you are lucky as an heiress or heir. This time, though, you inherit€1,000,000 worth of corporate stocks. While you are still partying and to your utter dismay, the stock market plunges by 22.6% on a single day, just as Wall Street did on 19 October 1987. So your inherited million is down to
€774,000, and the initial lifetime consumption plan you drew up after you had learned the good news is no longer viable. After you recover from the shocking news, you implement a more modest consumption plan, along with all other households whose wealth took a beating from the stock market crash.
This example adds to last section’s discussion of intertemporal aspects of consumption spending. Households’ consumption decisions take into account not only the lifetime patterns of labour income, but also changes that result
Empirical note. Empirical studies indicate that the marginal propensity to consume out of permanent income increases is close to 1, say 0.9. Out of transitory income increases, individuals consume much less, between 0.2 and 0.4. This is much more, however, than our theoretical arguments would suggest.
2.4 An intertemporal view of consumption and investment 55