# Consumption Function, Consumption Smoothing, and the Life-Cycle

You can review the consumption function, consumption smoothing, and the life-cycle model in the toolkit. Let us see how this model works. According to the life-cycle model of consumption, the individual first calculates her lifetime resources as working years × disposable income + retirement years × Social Security payment. (We continue to suppose that the real interest rate is zero, so it is legitimate simply to add her income in different years of her life.) She then decides how much she wants to consume in every period. Consumption smoothing starts from the observation that people do not wish their consumption to vary a lot from month to month or from year to year. Instead, households use saving and borrowing to smooth out fluctuations in their income. They save when their income is high and dissave when their income is low. Perfect consumption smoothing means that the household consumes exactly the same amount in each period of time (month or year). Going back to the consumption function, perfect consumption smoothing means that the marginal propensity to consume is (approximately) zero. [1] If a household wants to have perfectly smooth consumption, we can easily determine this level of consumption by dividing lifetime resources by the number of years of life. Returning to our equations, this means that

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working years + retirement years .

This is the equation we used earlier to find Carlo’s consumption level. We took his lifetime income of \$1,800,000, noted that lifetime income equals lifetime consumption, and divided by Carlo’s 60 remaining years of life, so that consumption each year was \$30,000. That is really all there is to the life-cycle model of consumption. Provided that income during working years is larger than income in retirement years, individuals save during working years and dissave during retirement. This is a stylized version of the life-cycle model, but the underlying idea is much more general. For example, we could extend this story and make it more realistic in the following ways:  Households might have different income in different years. Most people’s incomes are not

constant, as in our story, but increase over their lifetimes.  Households might not want to keep their consumption exactly smooth. For example, if the

household expects to have children, then it would probably anticipate higher consumption—paying for their food, clothing, and education—and it would expect to have lower consumption after the children have left home.

 The household might start with some assets and might also plan to leave a bequest.  The real interest rate might not be zero.  The household might contain more than one wage earner.

Working through the mathematics of these cases is more complicated—sometimes a lot more complicated—than the calculations we just did, and so is a topic for advanced courses in macroeconomics. In the end, though, the same key conclusions continue to hold even in the more sophisticated version of the life-cycle model:  A household will examine its entire expected lifetime income when deciding how much to

consume and save.  Changes in expected future income will affect current consumption and saving.

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