Intertemporal Choice - Fisher's Model of Intertemporal Consumption

Fisher's Model of Intertemporal Consumption

Irving Fisher developed the theory of Intertemporal Choice in his book Theory of interest (1930). Contrary to Keynes, who related consumption to current income, Fisher’s model showed how rational forward looking consumers chooses consumption for the present and future to maximize their lifetime satisfaction. According to Fisher, an individual's impatience depends on four characteristics of his income stream: the size, the time shape, the composition and risk. Besides this foresight, self-control, habit, expectation of life, and bequest motive (or concern for lives of others) are the five personal factors that determine a person's impatience which in turn determines his time preference. In order to understand the choice exercised by a consumer across different periods of time we take consumption in one period as a composite commodity. Suppose there is one consumer, commodities, and two periods. Preferences are given by where . Income in period is . Savings in period 1 is, spending in period is, and is the interest rate.

(1)

(2)

We arrive at the following equation from equation 1 and 2

(3)

The left hand side shows the present value expenditure and right hand side depicts the present value income respectively. Multiplying the equation by gives us the future value.

Now the consumer has to choose a and such that

Maximize

subject to

A consumer maybe a net saver or a net borrower. If he's initially at a level of consumption where he's neither of the above(i.e. a net borrower or net saver), an increase in income may make him a net saver or a net borrower depending on his preferences. An increase in current income or future income will increase current and future consumption(consumption smoothing motives).

Now, let us consider a scenario where the interest rates are increased. If the consumer is a net saver, he will save more in the current period due to the substitution effect and consume more in the current period due to the income effect. The net effect thus, becomes ambiguous. If the consumer is a net borrower, however, he will tend to consume less in the current period due to the substitution effect and income effect thereby reducing his overall current consumption.