Behavioral Economics — Biases & Decision Making
Behavioral economics integrates psychology into economic models to explain why people systematically deviate from the predictions of standard rational-agent theory. Kahneman and Tversky's Prospect Theory shows that people evaluate outcomes relative to a reference point, feel losses more acutely than equivalent gains, and overweight small probabilities. Hyperbolic discounting explains why people procrastinate and make time-inconsistent plans. Heuristics — mental shortcuts — produce predictable biases such as anchoring, availability, and representativeness. Thaler and Sunstein's nudge theory applies these insights to design choice architectures that improve decisions without restricting freedom.
Prospect Theory & Loss Aversion
People evaluate gains and losses relative to a reference point $r$, not absolute wealth:
$$v(x) = \begin{cases} x^\alpha & x \geq 0 \\ -\lambda(-x)^\beta & x < 0 \end{cases}$$
Typically $\alpha \approx \beta \approx 0.88$ and $\lambda \approx 2.25$ (loss aversion coefficient). Losses loom about twice as large as equivalent gains.
People do not use objective probabilities $p$; instead they use a weighting function $w(p)$ that overweights small probabilities and underweights large ones:
$$w(p) = \frac{p^\gamma}{(p^\gamma + (1-p)^\gamma)^{1/\gamma}}, \quad \gamma \approx 0.65$$
Exponential (rational) discounting: $D(t) = e^{-rt}$ or $D(t) = \delta^t$.
Hyperbolic discounting: $D(t) = \frac{1}{1+kt}$.
Hyperbolic discounters prefer \$100 now over \$110 next week, but prefer \$110 in 53 weeks over \$100 in 52 weeks — a time-inconsistency.
Expected utility: $EU = \sum_i p_i u(w_i)$ — preferences depend on final wealth levels.
Prospect theory: $V = \sum_i w(p_i)v(x_i)$ — preferences depend on gains/losses relative to reference point, with distorted probabilities.
- Anchoring: Initial information disproportionately influences judgments.
- Availability heuristic: Frequency judged by ease of recall (plane crashes overestimated).
- Representativeness: Judging probability by similarity to prototypes (base-rate neglect).
- Status quo bias: Default options are powerful; people stick with the current situation.
- Sunk cost fallacy: Past unrecoverable costs influence future decisions irrationally.
- Mental accounting: Money is not fungible — people categorize and treat it differently by source/use.
Would you accept a bet: win $\$150$ with probability 0.5, lose $\$100$ with probability 0.5? Standard EU theory says yes if you are risk-neutral. What does prospect theory predict?
- $V = 0.5 \cdot v(150) + 0.5 \cdot v(-100) \approx 0.5 \cdot 150^{0.88} - 0.5 \cdot 2.25 \cdot 100^{0.88}$.
- Since $\lambda = 2.25 > 1$, the loss term dominates for most people — they decline the bet even though it has positive expected value.
In the UK, switching pension enrollment to opt-out (default enrolled) raised participation from 65\% to 90\%. Why is this a nudge, not coercion?
- The choice is preserved — workers can still opt out.
- But by exploiting status quo bias and inertia, the default option dramatically changes behavior without reducing freedom.
- This is the essence of libertarian paternalism.
Practice Problems
Show Answer Key
1. $v(50)=50^{0.88}\approx 33.1$. $v(-50)=-2\cdot 50^{0.88}\approx -66.2$. Loss feels twice as bad as the equivalent gain feels good.
2. $EV = 0.5(200)+0.5(-80)=\$60$ (positive). Many people still decline due to loss aversion.
3. Lottery: overweight tiny win probability (big thrill for small cost). Insurance: overweight tiny loss probability (big relief to avoid large loss). Both are consistent with Prospect Theory's probability weighting.
4. Hyperbolic: $D(1)=1/2=0.5$; $D(10)=1/11\approx 0.09$. Exponential: $D(1)=e^{-0.5}\approx 0.61$; $D(10)=e^{-5}\approx 0.0067$. Hyperbolic discounts less steeply at long horizons but more steeply near present.
5. Attend the concert despite feeling sick — the \$200 (irrecoverable) irrationally influences the forward-looking decision.
6. People demand more to give up an object they own than they would pay to acquire it. This asymmetry stems from loss aversion — giving up the object feels like a loss.
7. The \$50 anchor makes \$30 seem cheap by comparison, likely increasing orders of \$30 items.
8. Present bias: extra weighting on immediate rewards. Time inconsistency: plans made for the future are reversed when the future arrives ("I'll diet starting Monday" repeated every Monday).
9. Frame the default as paying the tax but give an easy opt-in to sustainable options (e.g., a green energy default with opt-out). Preserves choice while guiding toward socially optimal behavior.
10. Gains are in the concave region (want to lock in) and losses are in the convex region (risk-seeking to break even). Investors sell winners to realize gains and hold losers hoping to recover, even when fundamental value suggests the opposite.