Demonstration 1 of 4
Public support and congregational participation
Can a public benefit end attendance without any change in belief?
Participation bundles worship with services such as emergency help. When a dependable outside source replaces the service, members whose margin rested on it leave, while members with high worship value stay. A doubted program replaces less and changes little.
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Worship and identity value is 14 for Lina and 23 for Omar. Emergency support from the congregation is worth 9, of which a public benefit replaces 7 if credible or 2 if doubted. Monthly participation costs 18 units of time and travel.
Predict first. After the credible program (7 units replaced), does Omar, with worship value 23, stop attending?
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Constructed example: the book's hypothetical values are worship 14 and 23, support 9, cost 18 and replacement 7 or 2; a replacement of 0 (no program) is added.
Calculated values
- Member
- Lina
- Remaining support
- 2
- Net return
- -2
- Decision
- Stop
Hypothetical teaching values, not estimates of real communities. For Lina, with worship and identity value 14 and a public benefit that replaces 7 of the 9 support units, the return is 14 + 2 - 18 = -2, so the return is negative and the member stops attending. Belief has not changed; only the support the congregation uniquely supplies has.
Worked steps
- Remaining support = 9 - 7 = 2
- Net return = 14 + 2 - 18 = -2
- -2 < 0: the return is negative and the member stops attending
Use the idea
Before reading falling attendance as falling belief, ask which services the organization supplied and whether a new outside source now supplies them.
Where the conclusion applies
Values are fixed utility units, additive, and the same each month; the program changes only the support component.
Check your understanding: For Lina with no public benefit, what is her return?
Chapter 92 source: section "Secularization hypothesis".
Demonstration 2 of 4
Religious capital and switching
Why does accumulated, tradition-specific capital keep members where they are?
Participation builds a stock that raises later returns. Because part of the stock is specific to one tradition, the same activity is worth less elsewhere, and a lapse lets the stock decay.
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K is religious capital, which depreciates 10 percent a period. The benefit of one unit of participation is 4 + K and its cost 6. Of 4.8 units, 1.8 transfer to a new tradition; a bridging program raises that to 3.8.
Predict first. Does the experienced member gain from switching when only 1.8 units transfer?
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Constructed example: the book's hypothetical values are K = 4.8, 3.8 and 1.8, decay 0.10, cost 6 and a three-period lapse; applying the lapse to 3.8 and 1.8 is added.
Calculated values
- Effective capital
- 4.80
- One-unit surplus
- 2.80
- Novice surplus
- -2.00
Hypothetical teaching values, not estimates of real communities. With effective capital 4.80, the one-unit surplus is (4 + 4.80) - 6 = 2.80, so participation pays this period. A novice gets 4 - 6 = -2. Capital of 4.8 in the original tradition, 3.8 after a bridging program and 1.8 when only transferable units count shows why switching is costly.
Worked steps
- Surplus = (4 + 4.80) - 6 = 2.80
- Novice surplus = 4 - 6 = -2.00
Use the idea
When comparing persistence across groups, separate accumulated capability from preference: programs that make capital transferable change switching without changing beliefs.
Where the conclusion applies
Linear benefit 4 + K, a fixed cost of 6 and geometric decay of 10 percent a period, all hypothetical teaching values.
Check your understanding: With K = 3.8 and a three-period lapse, what is the surplus?
Chapter 92 source: section "Religious human-capital accumulation".
Demonstration 3 of 4
Time cost and fellowship output
What happens to attendance and output when time becomes more valuable?
With Cobb-Douglas technology the household spends equal shares on goods and time. A higher time value cuts hours and output but leaves cash spending fixed; better time technology can restore output.
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Z is fellowship output, x purchased input at price 1 and t participation hours at time value w. The full budget is 100. Remote access doubles the productivity of time, so Z = 2 sqrt(x (2t)).
Predict first. When the wage rises from 4 to 8, do cash contributions change?
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Constructed example: the book's hypothetical values are a budget of 100, wages 4 and 8 and a time multiplier of 2; a wage of 6 is added.
Calculated values
- Purchased input x
- 50.00
- Hours t
- 12.50
- Fellowship output Z
- 50.00
- Cash contribution
- 50.00
Hypothetical teaching values, not estimates of real communities. At a time value of 4 per hour, the household spends half the budget on each input: x = 50.00, t = 12.50 hours, and output is Z = 2 sqrt(50.00 x 12.50) = 50.00. Cash contributions stay at 50.00, so an analyst who sees only cash would miss the change in output.
Worked steps
- Equal shares: x = 100 / 2 = 50.00; 4t = 50, so t = 50 / 4 = 12.50
- Z = 2 sqrt(50.00 x 12.50) = 2 sqrt(625.00) = 50.00
- Cash contribution = 50.00 in every state
Use the idea
Measure inputs, prices and output separately: attendance or donations alone can hide large changes in what a congregation produces.
Where the conclusion applies
A fixed full budget of 100, a goods price of 1 and the stated square-root technology.
Check your understanding: At wage 6 with no remote access, what are t and Z?
Chapter 92 source: section "Religious household-production model".
Demonstration 4 of 4
Mutual aid with correlated losses
How much insurance can a local pool give when members share the same risks?
An independent loss can be fully covered by small contributions from everyone. When losses are correlated, claims exceed the fund and each claimant gets only a share, so the local pool gives partial insurance.
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Ten households each have 40,000 units; a hit household loses 10,000. Each contributes s before the shock, and the fund is split among claimants up to the size of the loss.
Predict first. When five members share an employer and are hit together, how much does each claimant receive?
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Constructed example: the book's hypothetical values are 10 households, income 40,000, loss 10,000, contribution 1,000 and 1 or 5 claimants; 3 claimants and a 2,000 contribution are added.
Calculated values
- Fund
- 10,000
- Payout per claimant
- 10,000
- Consumption if hit
- 39,000
- Consumption if not hit
- 39,000
- Fund left over
- 0
Hypothetical teaching values, not estimates of real communities. With 1 household hit in the same state and contributions of 1,000, the fund of 10,000 pays each claimant 10,000, covering the full loss. A claimant consumes 40,000 - 10,000 - 1,000 + 10,000 = 39,000 and an unaffected household 39,000. Pooling moves resources across households; it never restores the lost 10,000 per claimant.
Worked steps
- Fund = 10 x 1,000 = 10,000
- Payout = min(10,000, 10,000 / 1) = 10,000
- Hit: 40,000 - 10,000 - 1,000 + 10,000 = 39,000
- Not hit: 40,000 - 1,000 = 39,000
Use the idea
To judge a mutual-aid arrangement, compare the fund with claims in the bad state, not with average claims.
Where the conclusion applies
Contributions are paid before anyone knows who is hit, and the fund is divided evenly among claimants up to their loss.
Check your understanding: With three claimants and contributions of 2,000, what does a claimant consume?
Chapter 92 source: section "Religious organizations as social insurance".