Chapter 17: Context, Framing, Salience, and Choice Architecture. The Encyclopedia of Economic Principals, interactive companion

Every example here is a constructed teaching example: it uses the hypothetical numbers of the chapter's worked examples, plus a few values added for comparison and labelled as such in each panel. Nothing here measures a real market, firm or household.

Demonstration 1 of 4

When more funds means fewer savers

Can a bigger fund menu push a worker out of a plan that pays her a match?

A larger menu can raise the best attainable portfolio benefit while raising the cost of finding it by more. The screening tool keeps every fund but cuts comparison time and regret, so the net value recovers without shrinking the menu.

$Equation, written in LaTeX: 1{,}000+600-200-50=\$1{,}350.$

$Equation, written in LaTeX: 1{,}100+600-600-150=\$950.$

$Equation, written in LaTeX: 1{,}100+600-200-75=\$1{,}425.$

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Maya's net enrollment value is portfolio benefit plus the $600 employer match, minus comparison hours valued at $100 per hour and minus anticipated regret. Keeping the money liquid is worth $1,250.

Predict first. With 30 funds and 6 hours of comparison, does Maya enroll?

Your prediction Yes, she enrolls No, she keeps the cash

Comparison hours

Figure: When more funds means fewer savers. A stacked bar for 6 funds: benefit $1,000 and match $600 above zero, time cost $200 and regret $50 below. The net $1,350 is marked against a dashed line at the $1,250 outside option. — Menu: 6 funds, Comparison hours: 2
Constructed example: the chapter's hypothetical employee Maya (6 funds with 2 hours, 30 funds with 6 hours, 30 funds with a screening tool and 2 hours); other menu and hour pairings and 4 hours are added for comparison.

Portfolio benefit: $1,000
Time cost: $200
Anticipated regret: $50
Net enrollment value: $1,350
Outside option: $1,250
Decision: Maya enrolls

With 6 funds and 2 hours of comparison, time costs 2 x 100 = 200 dollars and the net value is 1,000 + 600 - 200 - 50 = $1,350, which exceeds the $1,250 outside option. Maya enrolls.

Worked steps

Time cost = 2 x 100 = 200
Net = 1,000 + 600 - 200 - 50 = 1,350
Compare with the outside option 1,250: Maya enrolls

Use the idea

When adding options, count the hours and regret they impose on the chooser, not only the best option they make available.

Where the conclusion applies

Maya values her time at a constant $100 per hour, regret is a fixed dollar amount per menu, and the outside option does not change with the menu.

Check your understanding: With 30 funds and screening regret of $75, how many comparison hours make Maya exactly indifferent?

1,100 + 600 - 100h - 75 = 1,250 gives 100h = 375, so h = 3.75 hours.

Chapter 17 source: section "Choice overload".

Demonstration 2 of 4

Salience pulls weight toward the upside

When does a lottery worth less than $50 on average beat a sure $50?

The lottery itself never changes. Salience inflates the weight of the state that contrasts most with the alternative, here the upside, so a lottery slightly worse on average can look better.

$Equation, written in LaTeX: 0.10(180)+0.90(35)=\$49.50,$

$Equation, written in LaTeX: \frac{180-50}{180+50} =\frac{130}{230} \approx56.5\%,$

$Equation, written in LaTeX: 0.137(180)+0.863(35)\approx\$54.86,$

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Lottery L pays the upside with probability 0.10 and $35 with probability 0.90; the alternative is a sure $50. Contrast is |x - 50| / (x + 50). The less salient state's probability is multiplied by delta and the weights are normalized; pi_H is the weight on the high state.

Predict first. At delta = 1, which option is chosen?

Your prediction The lottery L The sure $50

Salience discount delta

Upside payoff ($)

Figure: Salience pulls weight toward the upside. Bars compare objective probabilities 0.10 and 0.90 with salience weights 0.137 and 0.863 at delta 0.70 and upside $180. The weighted value is $54.86. — Salience discount delta: 0.7, Upside payoff ($): $180
Constructed example: the chapter's hypothetical lottery ($180 with 0.10, $35 with 0.90, sure $50, delta 0.7 and 1); delta 0.5 and 0.85 and upsides of $150 and $220 are added for comparison.

Expected value: $49.50
Upside contrast: 56.5%
Downside contrast: 17.6%
Weight on high state: 0.137
Weighted value: $54.86
Choice: Lottery L

Expected value is 0.10(180) + 0.90(35) = $49.50. Contrasts are (180 - 50)/(180 + 50) = 56.5% and (50 - 35)/(50 + 35) = 17.6%. The upside is the more salient state, so the downside probability is discounted by delta: pi_H = 0.10 / (0.10 + 0.90 x 0.70) = 0.137. Weighted value = 0.136986(180) + 0.863014(35) = $54.86, so the chooser takes the lottery L.

Worked steps

EV = 0.10 x 180 + 0.90 x 35 = 49.50
Upside contrast = 130 / 230 = 0.5652; downside = 15 / 85 = 0.1765
pi_H = 0.10 / (0.10 + 0.90 x 0.70) = 0.137
Value = 0.136986 x 180 + 0.863014 x 35 = 54.86
Compare with the sure 50: the chooser takes the lottery L

Use the idea

When an option is pitched by its rare big payoff, recompute its value with the objective probabilities before comparing it with a sure alternative.

Where the conclusion applies

Linear utility, two states, the sure $50 as the comparison point and the rank-based discount delta. The ranking would flip only if the downside contrasted more than the upside.

Check your understanding: With delta = 0.7, what is the smallest upside payoff (low still $35) that makes the weighted value exceed $50?

0.13699 H + 0.86301 x 35 = 50 gives 0.13699 H = 50 - 30.205 = 19.795, so H is about 144.5.

Chapter 17 source: section "Salience theory".

Demonstration 3 of 4

The 70,000 mile cliff

How much of a price gap between two used cars is the odometer's first digit?

Smooth depreciation makes value fall a little per mile. A buyer who reads only the leading digit adds a cliff at the round number, so a car just past it looks much cheaper than one just below.

$Equation, written in LaTeX: \$15{,}000-200(\$0.10)=\$14{,}980.$

$Equation, written in LaTeX: \$14{,}980-\$500=\$14{,}480$

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Car A has 69,900 miles and is worth $15,000. Ordinary wear lowers value by $0.10 per mile. The left-digit penalty is a drop in perceived value once the odometer reads 70 thousand.

Predict first. If B had 69,950 miles, how large is the perceived gap from A?

Your prediction $5 $505 $520

Car B mileage

Left-digit penalty ($)

Figure: The 70,000 mile cliff. Car value against mileage: a dashed line falling $0.10 per mile and a solid perceived-value line that drops by $500 at 70,000 miles. Car A at 69,900 miles is worth $15,000; car B at 70,100 miles is perceived at $14,480. — Car B mileage: 70,100, Left-digit penalty ($): $500
Constructed example: the chapter's hypothetical cars (69,900 and 70,100 miles, $15,000, $0.10 per mile, $500 penalty); mileages 69,950 and 70,500 and penalties of $0, $250 and $750 are added for comparison.

Benchmark value of B: $14,980
Perceived value of B: $14,480
Perceived gap from A: $520
Smooth depreciation: $20
Excess discontinuity: $500

B has 200 more miles than A, so smooth wear lowers its value by 200 x 0.10 = 20 dollars, to $14,980. B's odometer reads 70 thousand, so the $500 category penalty applies: 14,980 - 500 = $14,480. The perceived gap from A is $520.

Worked steps

Extra miles = 70,100 - 69,900 = 200
Benchmark = 15,000 - 200 x 0.10 = 14,980
Perceived = 14,980 - 500 = 14,480
Gap = 15,000 - 14,480 = 520

Use the idea

Before reading a price jump at a round number as bias, check whether something real, such as a warranty, also changes there.

Where the conclusion applies

Identical cars apart from mileage, linear wear of $0.10 per mile and a fixed penalty that applies at or above 70,000 miles.

Check your understanding: With B at 70,500 miles and a $500 penalty, what is the perceived price gap from A?

Smooth drop 600 x 0.10 = $60, plus the $500 penalty, gives $560.

Chapter 17 source: section "Left-digit bias".

Demonstration 4 of 4

Defaults, switching costs, and active choice

How much of an enrollment rate comes from the default rather than from what workers want?

A default changes who must pay the cost of acting. Workers whose gain is smaller than the switching cost stay wherever the default puts them, and inattentive workers never act at all. Active choice removes the default and the nonresponse.

$Equation, written in LaTeX: \Delta_i=V_i(E)-V_i(N)=\$30.$

Equation, written in LaTeX: 60+9=69,

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Of 100 workers, 60 gain $30 from enrolling (Delta_i), 25 lose $10, and 15 do not act before the deadline. Leaving the default costs the switching cost. Prompted, the 15 split 9 favorable and 6 unfavorable.

Predict first. Under automatic enrollment, if the switching cost falls to $5, what is enrollment?

Your prediction 100% 75% 60%

Default

Switching cost ($)

Regime: Opt-in (not enrolled by default)
Switching cost: $20
Favorable enrolled: 60 of 60
Unfavorable enrolled: 0 of 25
Inattentive enrolled: 0 of 15
Enrollment rate: 60%

With non-enrollment as the default, the favorable workers switch only if $30 exceeds the $20 cost, which it does. The 25 unfavorable and 15 inattentive workers stay out. Enrollment is 60 + 0 + 0 = 60, or 60%.

Worked steps

Favorable: gain 30 > cost 20, so 60 enroll
Unfavorable 25 stay out (enrolling loses 10)
Inattentive 15 keep the default: out
Enrollment = 60 + 0 + 0 = 60, so 60%

Use the idea

When comparing enrollment under two defaults, separate the workers who chose from those who simply did not act or found switching too costly.

Where the conclusion applies

Fixed intrinsic gains, one switching cost for everyone, no endorsement effect from the default, and a prompted split of 9 and 6 for the inattentive workers.

Check your understanding: Under opt-in, what switching cost makes the 60 favorable workers stop enrolling?

They switch only when 30 exceeds the cost, so any cost of 30 or more drops opt-in enrollment to 0%; at the $40 setting it is 0%.

Chapter 17 source: section "Default effect".

When more funds means fewer savers

Choose an example

Calculated values

Worked steps

Use the idea

Where the conclusion applies

Salience pulls weight toward the upside

Choose an example

Calculated values

Worked steps

Use the idea

Where the conclusion applies

The 70,000 mile cliff

Choose an example

Calculated values

Worked steps

Use the idea

Where the conclusion applies

Defaults, switching costs, and active choice

Choose an example

Calculated values

Worked steps

Use the idea

Where the conclusion applies