Marginal rate of time preference: Meaning, Criticisms & Real-World Uses

What Is Marginal Rate of Time Preference?

The marginal rate of time preference (MRTP) is a core concept in microeconomics and behavioral finance that quantifies an individual's willingness to substitute present consumption for future consumption while maintaining the same level of overall satisfaction or utility. In simpler terms, it measures how much additional future benefit a person requires to forgo a small unit of benefit today. It reflects the subjective trade-off individuals make when deciding between immediate gratification and delayed rewards. This rate is influenced by various factors, including an individual's financial situation, future expectations, and psychological biases. Understanding the marginal rate of time preference is crucial for analyzing saving, investment, and intertemporal choice decisions.

History and Origin

The concept of time preference, and by extension the marginal rate of time preference, has deep roots in economic thought. Early economists recognized that individuals generally prefer goods and services sooner rather than later, a phenomenon often attributed to human "impatience." A significant contribution to the formalization of this idea came from American economist Irving Fisher. In his seminal 1930 work, The Theory of Interest, Fisher detailed how interest rates are determined by the interaction of people's time preference for present income over future income and the investment opportunities available⁶. He viewed the rate of time preference as a subjective and exogenous factor influencing an individual's utility function, representing their trade-off between current and future consumption. This neoclassical perspective laid the groundwork for how economists interpret the relationship between individual preferences and market phenomena like interest rates.

Key Takeaways

The marginal rate of time preference measures an individual's subjective willingness to trade present consumption for future consumption.
It reflects how much more future utility is needed to compensate for less current utility, keeping overall satisfaction constant.
A higher marginal rate of time preference implies a stronger preference for immediate gratification.
This concept is fundamental to understanding decisions related to saving, investment, and capital allocation.
The marginal rate of time preference is a key determinant in economic models of consumption and capital theory.

Formula and Calculation

The marginal rate of time preference (MRTP) is formally represented as the rate at which an individual is willing to substitute consumption between two periods, say period 0 (present) and period 1 (future), while remaining on the same indifference curve (maintaining the same level of utility).

It can be expressed using marginal utilities:

MRTP = \frac{MU_{C_0}}{MU_{C_1}} - 1

Where:

(MU_{C_0}) = Marginal utility of consumption in period 0 (present)
(MU_{C_1}) = Marginal utility of consumption in period 1 (future)

This formula indicates that if the marginal utility of present consumption is higher than that of future consumption, the individual has a positive marginal rate of time preference, meaning they value present consumption more than future consumption. In equilibrium, for a consumer maximizing utility, the marginal rate of time preference equals the market interest rates (or the rate of return on investment opportunities), adjusted for expectations about inflation and risk. This equality guides individuals in optimizing their consumption smoothing over time.

Interpreting the Marginal Rate of Time Preference

Interpreting the marginal rate of time preference involves understanding an individual's inclination towards immediate versus delayed gratification. A high marginal rate of time preference indicates a strong preference for current consumption over future consumption. Such an individual might require a substantial additional future return to defer current enjoyment. This can lead to lower saving rates and a greater propensity for immediate spending. Conversely, a low marginal rate of time preference suggests that an individual places a relatively similar value on present and future consumption. These individuals are typically more patient and willing to postpone current consumption for smaller future benefits, often leading to higher savings and long-term investment.

This rate also reflects the "impatience" factor in economic models. For instance, an individual facing financial hardship might exhibit a higher marginal rate of time preference, prioritizing urgent needs over potential future gains. On the other hand, someone with stable income and strong future prospects might have a lower rate. The practical implication is that this rate helps explain observed disparities in financial behaviors, from debt accumulation to retirement planning.

Hypothetical Example

Consider Jane, who recently received a bonus of $1,000. She faces a choice:

Spend the $1,000 immediately on a new gadget.
Invest the $1,000 for one year, which would yield a return, resulting in $1,050 next year.

To determine her marginal rate of time preference, we can ask how much future money she would need to be indifferent between spending today and saving for later.

Scenario 1: If Jane chooses to spend the $1,000 today, it implies that the immediate satisfaction of the new gadget outweighs the prospect of $1,050 next year. Her marginal rate of time preference is at least 5% (i.e., she needs more than a 5% return to wait).
Scenario 2: If she decides to invest the $1,000 for one year to receive $1,050, it suggests that the additional $50 is sufficient compensation for deferring her gratification. Her marginal rate of time preference is equal to or less than 5%.

If we keep reducing the future reward, say to $1,020 next year (a 2% return), and Jane still chooses to invest, it indicates her marginal rate of time preference is below 2%. By systematically varying the future amount, her exact marginal rate of time preference can be estimated, revealing her personal trade-off between the present value and future value of money. This exercise highlights her opportunity cost of immediate consumption.

Practical Applications

The marginal rate of time preference has wide-ranging practical applications across economics and finance:

Financial Planning: Financial advisors consider an individual's marginal rate of time preference when recommending savings strategies, retirement plans, and investment products. A client with a high MRTP might need more aggressive incentives or behavioral nudges to encourage long-term savings.
Capital Budgeting: Businesses use concepts related to time preference, such as the discount rate, to evaluate investment projects. Projects are assessed based on their net present value, which inherently discounts future cash flows based on an assumed rate of time preference or cost of capital.
Monetary Policy: Central banks implicitly consider the aggregate time preference of an economy when setting interest rates. Higher interest rates can encourage saving and discourage immediate consumption, influencing overall economic activity.
Public Policy: Policymakers use time preference in evaluating long-term public investments, such as infrastructure projects, environmental regulations, or social security programs. The choice of the social discount rate for these projects often reflects society's collective time preference. Research has explored various methods for measuring these preferences, offering insights into their predictive power for real-world economic behaviors involving intertemporal trade-offs⁵.
Development Economics: Studies show that time preferences can vary significantly across socioeconomic groups. For instance, research suggests that households with lower permanent incomes may exhibit higher rates of time preference, influencing their saving behavior and potentially contributing to cycles of poverty⁴.

Limitations and Criticisms

While the concept of marginal rate of time preference is foundational, it faces several limitations and criticisms, particularly from the field of behavioral economics:

Dynamic Inconsistency: A significant critique is that individuals do not always exhibit consistent time preferences over time. This phenomenon, known as dynamic inconsistency or hyperbolic discounting, suggests that people tend to be more impatient over shorter horizons than longer ones. For example, someone might prefer $100 today over $110 tomorrow but choose $110 in 31 days over $100 in 30 days, even though both represent a one-day delay. This violates the assumption of a constant rate of time preference³.
Context Dependence: Time preferences can be highly sensitive to the context of the decision, including the magnitude of the rewards, the type of good (e.g., money vs. health outcomes), and emotional states. This challenges the idea of a single, stable marginal rate of time preference for an individual².
Framing Effects and Cognitive Biases: Decisions involving time are often influenced by psychological biases, such as loss aversion or present bias, which are not fully captured by the traditional rational choice model of time preference. The way choices are framed can significantly alter an individual's expressed preference for immediate versus future rewards.
Measurement Challenges: Empirically measuring an individual's precise marginal rate of time preference can be difficult. Experimental methods often yield widely varying results, suggesting that a single, universal discount rate might not adequately represent complex human decision-making¹.

Marginal Rate of Time Preference vs. Time Preference

The terms "marginal rate of time preference" and "time preference" are closely related but refer to distinct aspects of intertemporal choice.

Time preference is a broader concept that refers to an individual's general inclination to value present satisfaction or utility more than future satisfaction or utility. It's the underlying psychological or economic phenomenon that people prefer to consume now rather than later, all else being equal. It acknowledges that a dollar today is generally worth more than a dollar in the future.

The marginal rate of time preference, on the other hand, is a specific, quantitative measure of this broader preference at the margin. It articulates how much more future consumption or utility is required to compensate an individual for giving up a small amount of present consumption, while keeping their overall satisfaction constant. While time preference explains why people generally prefer the present, the marginal rate of time preference quantifies the precise trade-off they are willing to make at a given point in time. It is the slope of an indifference curve at a specific point on an intertemporal consumption possibilities frontier.

FAQs

What does a high marginal rate of time preference indicate?

A high marginal rate of time preference means an individual places a significantly higher value on immediate satisfaction or consumption compared to future satisfaction. They require a large amount of future benefit to compensate for delaying current enjoyment, often indicating a degree of impatience.

How does the marginal rate of time preference influence saving decisions?

Individuals with a high marginal rate of time preference tend to save less because they prioritize current consumption. Conversely, those with a low marginal rate of time preference are more likely to postpone consumption and engage in higher rates of saving for future goals.

Is the marginal rate of time preference constant for an individual?

Traditional economic models often assume a constant marginal rate of time preference, but behavioral economics research suggests this is not always the case. Factors like the time horizon (e.g., preference for immediate versus slightly delayed rewards), the type of good, and emotional states can lead to dynamic inconsistencies, where the rate changes over time or across different scenarios.

How is the marginal rate of time preference different from the discount rate?

The marginal rate of time preference is a subjective measure of an individual's personal trade-off between present and future utility. The discount rate, while related, is often an objective rate used in financial calculations (like net present value) to translate future cash flows into present values. In equilibrium, an individual's marginal rate of time preference may align with market interest rates, which often serve as a basis for discount rates.

Why is the concept of marginal rate of time preference important in economics?

It is fundamental for understanding how individuals make intertemporal choice decisions regarding consumption, saving, and investment. It helps explain observed economic behaviors, the formation of interest rates, and is crucial for designing effective public policies related to long-term economic planning and resource allocation.