# Changes: Intertemporal choice

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Intertemporal choice is the study of the relative value people assign to two or more payoffs at different points in time. This relationship is usually simplified to today and some future date. Intertemporal choice was introduced by John Rae in 1834 in the "Sociological Theory of Capital". Later, [[Eugen von Böhm-Bawerk in 1889 and Irving Fisher in 1930 elaborated on the model.

George Loewenstein of Carnegie Mellon University has been at the foreground of modern work in intertemporal choice.

Description:

## Fisher model Edit

### Assumptions of the modelEdit

1. consumer's income is constant
2. maximization of the utility
3. anything above the line is out of explanation
4. investments are generators of savings
5. any property is indivisible and unchangeable

According to this model there are three types of consumption: past, present and future.

When making decision between present and future consumption, the consumer takes his previous consumption into account.

This decision making is based on indifference map with negative slope because if he consumes something today it means that he can't consume it in the future and vice versa. In general households prefer present consumption to the future one. The most important reason why the consumer should prefer future consumption is the revenue the invested savings can bring.

The revenue is in form of interest rate. Nominal interest rate - inflation = real interest rate

Denote

• r: interest rate
• Y(t+1): income in time t+1 or a future income
• Y(t): income in time t or a present income

Then maximum present consumption is: Y(t) + (1-r)Y(t+1)

The maximum future consumption is: (1+r)*Y(t) + Y(t+1)

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