Discounting the Future

Time preference dictates intertemporal choice, which represents the trade-off between consumption today and consumption tomorrow. The Walter Mischel Marshmallow experiment tested patience by offering children a choice between one marshmallow immediately or two marshmallows after ten minutes. Initial patience exhibited by children was found to be a valid predictor of future life outcomes, including SAT scores, career success, and health. Common intertemporal decisions involve savings, investing in human capital (studying vs. entertainment), and health (exercising vs. relaxing). Individuals generally prefer to smooth their consumption over time rather than consuming everything at once and having nothing later.

Time Preference and Discount Factors

Future utility must be appropriately discounted because future value is inherently less than present value from today's perspective. The discount factor, denoted by $\delta$, represents the rate at which the future is discounted. The value of $\delta$ is bound between 0 and 1.

Exponential Discounting

Exponential discounting represents the standard neoclassical approach to intertemporal choice developed by Paul Samuelson. The present value of a future stream of discounted utility is calculated as $U_0 = u_0 + \Sigma \delta^i u_i$.

An individual who uses exponential discounting is classified as an "econ". The defining characteristic of an econ's intertemporal choice is dynamic time consistency. Dynamic time consistency occurs when preferences between two options do not change simply due to the passage of time. The present self and the future selves agree on optimal plans, meaning a decision made at time $t=0$ will still be executed at time $t=1$.

Anomalies and Present-Biased Discounting

Optimal plans for human beings often change simply because of the passage of time, resulting in dynamically time-inconsistent preferences. While early selves plan for beneficial long-term outcomes, later selves seek instant gratification.

To mathematically model this human behavior, behavioral economists use present-biased discounting, also known as hyperbolic or beta-delta discounting. Impatience is higher in the short run than in the long run.

The present-biased utility function evaluates future utility as $U_0 = u_0 + \beta(\delta u_1 + \delta^2 u_2 + \delta^3 u_3 ...)$. The parameter $\beta$ generates the present-biased behavior, as it heavily discounts the immediate future while maintaining patience for long-run trade-offs. In empirical studies, humans often behave as if $\beta$ is small while $\delta$ is close to 1.

Empirical Evidence of Present Bias

Researchers conducted an experiment asking thirsty subjects to choose between juice now and double the juice in 5 minutes. 60 percent chose juice now. However, when asked to choose between juice in 20 minutes and double the juice in 25 minutes, only 30 percent chose the earlier option. The implied 5-minute discount rate was roughly 50 percent, whereas the long-run discount rate approached 0, demonstrating extreme short-run impatience. Richard Thaler found similar results in monetary experiments, where the implied discount factor for a 1-month delay was 345 percent per year, compared to 19 percent for a 10-year delay.

Preference Reversals

Present bias leads directly to preference reversals, particularly when evaluating goods with misaligned benefits and costs. When choosing today for next week, individuals generally choose healthy options (apples) or highbrow movies (The Seventh Seal). When choosing today for today, individuals switch to unhealthy options (fries) or lowbrow movies (Fast and Furious).

Naifs and Sophisticates

Behavioral economics categorizes present-biased individuals based on their awareness of their own self-control problems.

Commitment Contracts

Sophisticates utilize commitment strategies to manage temptation. These strategies involve removing cues or intentionally limiting one's own future choices to force compliance with long-term goals. The classic example is Ulysses having his crew tie him to the ship's mast and plug their ears with wax to survive the Sirens' song.

Modern Commitment Devices and Contracts

Patience and the Wealth of Nations

A 2018 macroeconomic study measuring patience across 76 countries found that patience is a significant determinant of national development. The data shows that national patience levels positively correlate with log GDP per capita, economic growth, net adjusted savings, and the average number of years of schooling.

Strategic Thinking Among Econs (Game Theory)

Strategic environments are modeled using three foundational components: players (those who affect payoffs), strategies (actions available to each player), and payoffs (wellbeing or money resulting from actions). Models categorize games into simultaneous move games (all players move at once in ignorance of others) and sequential move games (players move in sequence with knowledge of prior moves).

Standard economic game theory relies on two critical assumptions: rationality (players maximize welfare and hold correct beliefs) and common knowledge (each player knows everyone is rational, knows that others know, to infinity).

Equilibrium Concepts

Strategic Thinking Among Humans (Level K Thinking)

John Maynard Keynes introduced the beauty contest game to explain equity price volatility, noting that participants do not pick what they think is best, but rather what average opinion expects average opinion to be.

In a numerical beauty contest, participants guess a number from 0 to 100, aiming to hit two-thirds of the average guess. The Nash equilibrium is 0, reached through the iterative elimination of dominated strategies. However, actual human participants apply different levels of reasoning:

Empirical data from Financial Times readers and laboratory experiments show massive clusters around 33 and 22, whereas only trained theorists frequently play 0.

Centipede Game Application

In the sequential Centipede Game, the SPNE dictates that the first player stops at the very first node. However, empirical tests reveal that stopping points depend on the opponent. Grand master chess players playing against other chess players stop at the first node 69 percent of the time. When playing against college students, they adjust their strategy to continue further, proving that human strategic thinking requires assessing the rationality of the opponent.

Cognitive Hierarchy Model

The Cognitive Hierarchy Model generalizes Level K thinking by positing that Type K players assume other players are distributed across lower types (Type 0 through Type K-1) according to a probability distribution, specifically a Poisson distribution parameterized by Tau ($\tau$). As $\tau$ increases, a higher proportion of the population exhibits sophisticated strategic thinking.

In an application evaluating the US ISP Market in 1997, researchers estimated $\tau$ across managerial teams. Firms operating in educated, urban areas with high competition exhibited higher $\tau$ values. High $\tau$ positively correlated with higher firm profits and higher likelihood of long-term survival, indicating that strategic sophistication yields measurable business advantages.

The Idea of Fairness

Human perception of fairness is frequently in direct conflict with standard neoclassical economic models. While standard economics dictates that prices respond to excess demand, consumers view price gouging during shortages as predatory and unfair.

In Frans de Waal's monkey fairness experiment, Capuchin monkeys gladly exchanged stones for cucumbers until they observed another monkey receiving grapes for the same task, demonstrating an innate, comparative view of fairness. Similarly, human effort drops if an employee discovers a peer was offered a higher salary for the same role.

Pricing Framing and Consumer Retaliation

Endowment effects dictate that deviations from the status quo (established by cultural expectations or regular prices) are considered highly unfair.

Nominal Wage Rigidity and Caselets

Nominal wages exhibit downward rigidity; wages rise during booms but fail to drop proportionately during recessions. Because wage cuts violate fairness perceptions and drastically reduce worker productivity, managers prefer to retrench (lay off) some workers while maintaining the status quo nominal wage for the remaining staff. Workers evaluate fairness based on nominal wages, not real wages, meaning a 5 percent raise during 12 percent inflation is viewed as fair, while a 7 percent pay cut during 0 percent inflation is viewed as unfair.

Corporate Fairness Caselets

Ultra-Quick Revision (Exam Essentials)

Key Concepts & Distinctions

Must-Know Terms