Intertemporal Preference

Classical economics assumes that consumers are perfect in decision-making and in maintaining those decisions. However, consumers often struggle with predicting their future behavior and expectations due to a discrepancy between their intentions and actions. This challenge is exemplified by individuals failing to follow through with their intentions, such as a student planning but failing to study adequately, or someone intending to change their behavior to avoid being late for work but still failing.

There are three main reasons why consumers value present consumption more than future consumption: impatience, uncertainty, and memory utility. Impatience suggests that consumers inherently prefer immediate rewards over delayed ones. Uncertainty about the future makes immediate consumption more appealing because the future is unpredictable, and there's a risk that the anticipated utility might not be realized. Lastly, memory utility implies that experiences enjoyed today can provide not only immediate satisfaction but also long-term utility in the form of cherished memories, making present consumption seem more valuable.

The Exponential Discounted Utility (EDU) model addresses the limitations of the DU model, particularly its generality and time inconsistency, by offering a framework for time-consistent choices. The EDU model ensures that consumer preferences remain consistent over time, thereby providing a more reliable basis for predicting consumer behavior and making intertemporal choices that do not change due to shifting preferences or external influences.

The "Utility Independence" assumption states that the total utility of an individual depends only on the discounted consumption utility for different periods and that there is no other factor that changes consumer utility other than time.

Constant Discounting means that the discount rate is the same for each period, which ensures that a consumer's present choices are consistent with future preferences, thereby maintaining time consistency in decision-making.

The concavity of the utility function u(.) means that as consumption increases, the additional satisfaction gained from consuming an extra unit diminishes. With a positive discount rate ρ, future utility is valued less than present utility. The interplay of these two forces affects a consumer's consumption choices by encouraging postponement of consumption due to diminishing marginal utility, while the positive discount rate motivates more immediate consumption, balancing the consumer's allocation of consumption between today and tomorrow.

These include common difference effect, gain-loss asymmetry, absolute magnitude effect and delay-speedup asymmetry.

The Strategy of Precommitment proposed by Strotz is a method to counteract time inconsistency issues in the EDU model. It involves making decisions about the future that are either irreversible or setting up penalties for behaviors that deviate from the planned decision. An example would be committing to a savings plan with a rising annual rate and facing penalties for withdrawing from this plan. This strategy aims to maintain consistency in future-oriented decisions and prevent changes in preferences over time.

Hyperbolic discounting uses a continuous rate that decreases over time, whereas quasi-hyperbolic discounting incorporates a two-parameter model with an immediate discount factor (β) and a constant discount rate (δ) over time. The quasi-hyperbolic model accounts for present bias by adding the factor β, which adjusts the value of immediate rewards relative to future rewards, leading to time-inconsistent preferences.

Quasi-hyperbolic discounting is a model of intertemporal choice that combines elements of exponential and hyperbolic discounting. It assumes that people are more sensitive to short-term delays than long-term delays.

A sophisticated individual with present bias is aware of their tendency to prioritize immediate rewards and takes into account how this bias will affect their future choices, unlike a naive individual who does not recognize or plan for the influence of this bias.

Procrastination is the act of delaying or postponing a task or set of tasks. It can be caused by a number of factors, including anxiety, perfectionism, and time management problems.

Naive present bias refers to the situation where an individual is unaware that they have a preference for immediate rewards over future rewards and does not anticipate how this bias will affect their decisions over time.

A time-consistent individual evaluates the options and sticks to the plan that maximizes utility from the first period, recognizing the highest utility in the last period and resisting present-bias. In contrast, a naive individual, despite having present-bias, does not account for this bias when making future decisions, leading to a shift in preference to immediate utility as each new period becomes the present.

Commitment: Individuals may make long-term plans to control their consumption, like buying a house or investing in retirement, preventing impulsive short-term spending.

Unawareness: People might underestimate the future enjoyment they would get from certain products, leading to different choices later.

Habits: Past consumption patterns establish habits that influence future decisions, impacting how much consumers adapt to changes in income or prices.

In the context of habit formation, a change in income or prices can lead to larger changes in consumption than expected because past habits strongly influence current consumption patterns. When income or prices change, these habits may be disrupted, necessitating a period of adjustment as the individual's consumption slowly adapts to the new economic situation.

The most crucial feature of habit formation models is that consumption adjusts very slowly to new situations after any shock or change, like an income increase or price shift. This means consumers gradually adapt their spending habits, leading to slower reactions compared to models without habit formation.

The Reference Time Model differs from the habit formation model by not incorporating all past habits entirely but rather using a specific reference time and output level as the basis for decision-making. It focuses on how current decisions are influenced by deviations from a reference point, which could be established by past habits, the status quo, or social norms.

Loss aversion, a concept from Prospect Theory, indicates that individuals feel the impact of losses more intensely than gains of the same size. This behavior means that when faced with postponing consumption, individuals may perceive the delayed consumption as a loss, making it psychologically harder to commit to the delay due to the greater weight they attach to losses.

Reference-dependent utility: Values are evaluated relative to a reference point, influenced by factors like past habits, expectations, or norms.

Loss aversion: Individuals prioritize avoiding losses over acquiring gains of the same size.

Diminishing elasticity: The impact of changes in value diminishes as the level of gain or loss increases.

The Lowenstein-Prelec model always starts the reference time from zero, while the RT Model utilizes the current moment as the reference point, reflecting real-life decision-making contexts.