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

is based on several asumptions:
 -  consumer's income is constant
 -  maximization of the utility
 -  anything above the line is out of explanation
 -  investments are generators of savings
 -  any property is indivisible and unchangeable
According to this model there are three types of consumption: past, present and future.
Consumer when making decision between present and future consumption takes into account her previous consumption. 

This decision making is based on indiference map with negative slope because if she consumes something today it

means that she can't consume it in future and vice versa. In general households prefer present consuption to the future 

one.The most important reason why the consumer should prefer future consumption is a revenue which invested savings can bring.

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

Denote

        r as a rate of interest,
        Y(t+1)as an income in time t+1  or a future income 
        Y(t)  as an income in time t    or a present income.

Then maximum present concumption is:
        
       Y(t) + (1-r)Y(t+1)
    The maximum future consumption is    
       
       (1+r)*Y(t) + Y(t+1)
 

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