Chapter 91: Cultural Transmission, Persistence, and Economic Change. 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

Habits lag practice

How quickly does a habit catch up with a change in reinforced practice?

Habit closes only a fraction alpha of the gap to practice each period, so it lags any change and stalls if the reinforcement is withdrawn.

$Equation, written in LaTeX: h_{t+1}=(1-\alpha)h_t+\alpha x_t,$

Equation, written in LaTeX: h_2=0.75(0.05)+0.25(0.80)=0.2375,

Equation, written in LaTeX: h_2=0.75(0.05)+0.25(0.20)=0.0875.

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h_t is the share of employees for whom local resolution is habitual, x_t the share who practice it in period t, and alpha the speed at which habit updates toward practice.

Predict first. If evaluation reverts to the old rule (practice stays 0.20), where does h_2 land?

Your prediction 0.0875 0.2375 0.20

Habit updating speed

Reinforced practice after period 0

Figure: Habits lag practice. Habit share rising from 0 toward practice 0.80: 0.0500, 0.2375, 0.3781, 0.4836 in periods 1 to 4. — Habit updating speed: 0.25, Reinforced practice after period 0: 0.8
Constructed example: hypothetical teaching numbers, not historical data. The book's claims office has h_0 = 0, practice 0.20 then 0.80 or 0.20, and alpha = 0.25; alpha = 0.50 and practice 0.50 are added.

h_1: 0.0500
h_2: 0.2375
h_3: 0.3781
h_4: 0.4836
Gap to practice at t = 4: 0.3164

Hypothetical teaching numbers, not historical data. Practice is 0.20 in period 0 and 0.80 afterwards. With updating speed 0.25, h_2 = 0.75 x 0.0500 + 0.25 x 0.80 = 0.2375, and by period 4 the habit is 0.4836, still 0.3164 below current practice.

Worked steps

h_1 = 0.75(0) + 0.25(0.20) = 0.0500
h_2 = 0.75(0.0500) + 0.25(0.80) = 0.2375
h_3 = 0.75(0.2375) + 0.25(0.80) = 0.3781
h_4 = 0.75(0.3781) + 0.25(0.80) = 0.4836

Use the idea

When a reform changes rules or tools, expect behavior to adjust gradually and track whether incentives keep reinforcing the new practice.

Where the conclusion applies

A fixed updating speed and an instructional equation, not an estimate attributed to Veblen.

Check your understanding: With alpha = 0.50 and practice 0.80 after period 0, what is h_3?

h_1 = 0.10; h_2 = 0.5 x 0.10 + 0.40 = 0.45; h_3 = 0.5 x 0.45 + 0.40 = 0.625.

Chapter 91 source: section "Institutional habits and cumulative adaptation".

Demonstration 2 of 4

Moral terms and the investment choice

Can moral terms in preferences tip an owner from consumption toward investment?

Moral terms shift the comparison by a fixed number of points; they tip close calls but cannot justify a clearly inferior project.

Equation, written in LaTeX: 70+0.50(30)=85.

Equation, written in LaTeX: 40+0.50(78)=79.

Equation, written in LaTeX: 40+0.50(55)+5=72.5,

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Each workshop has 100 discretionary units. A machine costs 60 today and returns the chosen payoff next year; future units are discounted at 0.50. With moral terms, luxury above 40 costs 10 points and investing adds 5 stewardship points.

Predict first. With moral terms on, does the norm still favor investment when the payoff drops to 55?

Your prediction Yes No

Moral terms

Machine payoff next year

Consume plan score: 75.0
Invest plan score: 84.0
Choice: Invest

Hypothetical teaching numbers, not historical data. For Elias (moral terms on) with a machine payoff of 78, the consume plan scores 70 + 0.50(30) - 10 = 75.0 and the invest plan 40 + 0.50(78) + 5 = 84.0, so investing wins, 84.0 against 75.0.

Worked steps

Consume plan: 70 + 0.50(30) - 10 = 75.0
Invest plan: 40 + 0.50(78) + 5 = 84.0
Result: investing wins, 84.0 against 75.0

Use the idea

When attributing saving or investment to values, show the counterfactual with the moral terms removed and everything else fixed.

Where the conclusion applies

Identical productivity, credit and discounting for both owners; the example estimates no historical community.

Check your understanding: With moral terms off and payoff 90, which plan is chosen?

Invest = 40 + 0.5 x 90 = 85, equal to the consume plan's 85: indifferent.

Chapter 91 source: section "Protestant ethic mechanism".

Demonstration 3 of 4

Family versus institutional transmission

Which raises the next generation's share of a trait more: stronger family effort or outside exposure?

Family transmission works only through the minority's own children, so its effect is scaled by x_t. Exposure reaches every child without the trait, so it can move the share much faster.

$Equation, written in LaTeX: P(A\mid A)=\tau_A+(1-\tau_A)x_t$

$Equation, written in LaTeX: P(A\mid B)=(1-\tau_B)x_t.$

$Equation, written in LaTeX: x_{t+1}=x_tP(A\mid A)+(1-x_t)P(A\mid B).$

$Equation, written in LaTeX: x_{t+1}=0.30(0.65)+0.70(0.24)=0.363.$

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x_t = 0.30 is the share of parents with trait A. tau_A and tau_B are the chances each type passes on its own trait directly; otherwise children copy a random adult. Institutional exposure reaches that share of children without the trait after family socialization.

Predict first. Which raises the share more: tau_A rising to 0.80, or 40 percent institutional exposure?

Your prediction tau_A to 0.80 40 percent exposure

Type A direct transmission

Type B direct transmission

Institutional exposure

Figure: Family versus institutional transmission. Three bars: 0.30 among parents, 0.3630 after family transmission and 0.3630 after institutional exposure. — Type A direct transmission: 0.5, Type B direct transmission: 0.2, Institutional exposure: 0
Constructed example: hypothetical teaching numbers, not historical data. The book's population has x = 0.30, tau_A = 0.50 and 0.80, tau_B = 0.20 and exposure 0.40; tau_B = 0.50 is added.

P(A | A): 0.650
P(A | B): 0.240
x_t+1 after family: 0.3630
Share after institutional exposure: 0.3630

Hypothetical teaching numbers, not historical data. Starting from 30 percent, family transmission gives x_t+1 = 0.30 x 0.650 + 0.70 x 0.240 = 0.3630. Institutional exposure of 0.00 then brings the share to 0.3630.

Worked steps

P(A|A) = 0.50 + 0.50(0.30) = 0.650
P(A|B) = 0.80(0.30) = 0.240
x_t+1 = 0.30(0.650) + 0.70(0.240) = 0.3630
With exposure: 0.3630 + 0.00(1 - 0.3630) = 0.3630

Use the idea

When explaining a change in values, name the channel: parents, peers or institutions give very different speeds.

Where the conclusion applies

One generation, random oblique copying and independent exposure, as in the chapter's stylized example.

Check your understanding: With tau_A = 0.50, tau_B = 0.50 and no exposure, what is x_t+1?

P(A|A) = 0.65; P(A|B) = 0.5 x 0.30 = 0.15; x = 0.30 x 0.65 + 0.70 x 0.15 = 0.30.

Chapter 91 source: section "Cultural transmission".

Demonstration 4 of 4

When does tradition survive?

How much environmental instability can a tradition of copying parents survive?

Copying saves the learning cost but fails when the environment has changed. The more stable the environment, the larger the share that can rely on tradition.

$Equation, written in LaTeX: x^*=\frac{\kappa-\Delta\beta}{\kappa(1-\Delta)}, \Delta\leq\frac{\kappa}{\beta}.$

$Equation, written in LaTeX: \frac{\kappa}{\beta}=\frac{18}{60}=0.30.$

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beta = 60 is the payoff from the correct action, kappa the cost of learning the current optimal action, and Delta the chance the environment is redrawn between generations. x* is the equilibrium share of traditionalists who copy rather than learn.

Predict first. At Delta = 0.35, does any traditionalist share survive?

Your prediction Yes No

Environmental instability

Cost of learning

Figure: When does tradition survive? Traditionalist share falling with instability and hitting zero at 0.30; at Delta = 0.10 the share is 0.741. — Environmental instability: 0.1, Cost of learning: 18
Constructed example: hypothetical teaching numbers, not historical data. The book's values are beta = 60, kappa = 18 and Delta of 0.10, 0.25 and 0.35; kappa = 24 is added.

x*: 0.741
Threshold kappa / beta: 0.30
Numerator kappa - Delta beta: 12.0

Hypothetical teaching numbers, not historical data. With learning cost 18 and instability 0.10, x* = (18 - 0.10 x 60) / (18 x 0.90) = 12.0 / 16.2, so a traditionalist share of 0.741 survives. Tradition disappears once instability passes 18 / 60 = 0.30.

Worked steps

Numerator: 18 - 0.10(60) = 12.0
Denominator: 18(0.90) = 16.2
x* = 12.0 / 16.2 = 0.741
Threshold: 18 / 60 = 0.30

Use the idea

Expect inherited practices to persist where conditions are stable across generations and to fade quickly where they are not.

Where the conclusion applies

The chapter's stylized source model with a fixed payoff and learning cost.

Check your understanding: With kappa = 24 and Delta = 0.25, what is x*?

(24 - 15) / (24 x 0.75) = 9 / 18 = 0.50.

Chapter 91 source: section "Cultural persistence".

Habits lag practice

Choose an example

Calculated values

Worked steps

Use the idea

Where the conclusion applies

Moral terms and the investment choice

Choose an example

Calculated values

Worked steps

Use the idea

Where the conclusion applies

Family versus institutional transmission

Choose an example

Calculated values

Worked steps

Use the idea

Where the conclusion applies

When does tradition survive?

Choose an example

Calculated values

Worked steps

Use the idea

Where the conclusion applies