Temporal discounting (also called delay or time discounting) refers to the tendency of individuals to value present rewards more than future rewards. As a reward moves further away in time, its perceived value decreases. For example, a person may strongly prefer a reward available today but place very little value on the same reward months later.
It is important to distinguish between time discounting and time preference. According to Shane Frederick and others, time discounting includes all reasons why future outcomes are valued less (such as uncertainty or changing preferences), while time preference specifically refers to the preference for immediate utility over delayed utility.
This concept is widely used in fields such as microeconomics, intertemporal choice theory, and neuroeconomics. Earlier economic models assumed a constant discount rate (exponential), but later research showed that real human behavior often follows non-constant patterns (hyperbolic). Temporal discounting is also important in real-world decisions like voting and climate change, where people often prioritize short-term benefits over long-term outcomes.
Exponential Discounted Utility Model
The exponential model is the traditional and most basic model of time discounting. It assumes that individuals discount future utility at a constant rate over time. This leads to a smooth and consistent decline in the value of future rewards.
Ut(ct, …, cT) = ∑k=0T−t (1 / (1 + ρ))k u(ct+k)
Here, utility is calculated as the sum of present and future consumption utilities, discounted by a constant rate ( \rho ). The discount factor ensures that future benefits are always valued less than present ones.
This model is simple and mathematically convenient, making it widely used in traditional economics. However, it assumes consistent preferences over time, which often does not match real human behavior. Empirical observations show that people’s discount rates are not constant, leading to inconsistencies and the need for alternative models.
Hyperbolic Discounting Model
The hyperbolic model was developed to better explain actual human behavior. Unlike the exponential model, it assumes that the discount rate decreases over time. This means people are much more impatient in the short run than in the long run.
v / V = 1 / (1 + kD)
In this equation, (v) is the discounted value, (V) is the actual value, (k) is the discount rate, and (D) is the delay.
This model explains preference reversal, a common behavioral phenomenon. For example, people may prefer ₹10 today over ₹11 tomorrow, but may prefer ₹11 in 101 days over ₹10 in 100 days. Even though the difference is the same, decisions change depending on how close the reward is to the present.
Hyperbolic discounting captures real-life decision-making more accurately, especially in cases involving addiction, savings behavior, and impulsive choices.
Quasi-Hyperbolic Discounting Model (Beta-Delta Model)
The quasi-hyperbolic model refines the hyperbolic approach by introducing a strong present bias. It highlights that individuals give disproportionately high importance to immediate rewards compared to all future rewards.
Ut(ut, ut+1, …, uT) = δt ut + β ∑s=t+1T δs−t us
In this model:
- β captures the present bias (extra preference for immediate rewards)
- δ represents the standard discount factor over time
This explains why people strongly prefer ₹10 today over ₹11 tomorrow but show less preference difference when both rewards are in the future.
The quasi-hyperbolic model is widely used in behavioral economics because it realistically captures procrastination, lack of self-control, and short-term decision biases.
Conclusion
The development of discounting models shows a shift from simple theoretical assumptions to more realistic behavioral insights.
- Exponential model → consistent but unrealistic
- Hyperbolic model → explains changing impatience
- Quasi-hyperbolic model → captures strong present bias
Together, these models help economists understand how individuals make decisions over time, especially in areas like savings, health, and public policy.