Discounted utility model

The discounted utility model (short DU model or German discounted utility theory , or perhaps utility discounting model ) is a dominant concept of intertemporal choices in microeconomics . The model goes back to the Nobel Prize winner Paul A. Samuelson (1936) and is currently the starting point for criticism and improvements in behavioral economics . The DU model explains decisions made by people in which time plays a role in the prevailing theory.

The model

Individuals want to maximize their utility , this is represented by the utility function . It represents the consumption of the respective period, more precisely the -th period, thus it depends on . Because future consumption does not bring about the same benefit as current consumption, but less, this benefit is discounted . This allows the benefit from future consumption to be made comparable to that of today's consumption. The discount factor is represented by . is the personal interest rate. A high interest rate results from a high preference for the present. This gives the formula ${\displaystyle u=u(c_{0},c_{1},\ldots ,c_{t})}$ ${\displaystyle c_{t}}$ ${\displaystyle t}$ ${\displaystyle u}$ ${\displaystyle c}$ ${\displaystyle \beta ={\frac {1}{1+i}}}$ ${\displaystyle i}$

${\displaystyle u(c_{0},c_{1},\ldots ,c_{t})=\sum _{t=0}^{T}\beta ^{t}u(c_{t})}$,

to model the present utility out of the total utility of an individual's future consumption. In many experiments, a steady interest rate is assumed. This can be justified by the fact that every claim to consumption would bring benefits in every unit of time.

Assumptions

Some assumptions need to be made in advance.

• Utility functions are assumed. Due to decreasing marginal utility , not all of the potential consumption is consumed in the first period.
• Independence in utility is assumed. The total benefit is the sum of the discounted benefits for each individual period. However, no assumptions are made about the distribution of this benefit. It may not be in an individual's best interest if future benefits vary widely. The benefit from the previous period can have an impact on the benefit of the next period. The same total utility of one state could thus be exactly equivalent to another state and the individual is not indifferent. This is a contradiction in terms.
• Consumption independence is assumed. The benefit from consumption in the previous period does not affect the benefit from consumption in the next period. As an example, it would not change the benefit if the individual consumed the same thing every day.
• Constant discount factors for all goods.
• Time consistency is assumed.
• Positive time preference is assumed. The time horizon is mostly a devaluation factor, so a preference for the present is assumed. Individuals therefore prefer today's payouts or experiences over later ones.

See also

Time preference

literature

Hanno Beck : Behavioral Economics: An Introduction . Springer Gabler, Wiesbaden 2014. ISBN 978-3-658-03366-8 . Pp. 197-213.

Individual evidence

1. ↑ Brockmann, Hilke. The Life Organization of Older People: A Trend Analysis. Springer-Verlag, 2013. p. 125.
2. ^ Wilkinson, Nick, and Matthias Klaes. An introduction to behavioral economics. Palgrave Macmillan, 2012. pp. 261ff.