Wealth, Class, and Collapse

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1. In a village of 100 people, 10 people hold 90% of the total grain supply. If the total grain supply is 1,000 kg, how many kilograms of grain does each of the 10 wealthy individuals own on average?
2. A society's total wealth is defined by W = 500x², where x represents the resource accessibility index (0 to 1). If accessibility drops from 0.8 to 0.4 due to a crisis, what is the change in total wealth?
3. If a group controls a share of resources S = 1 / (1 + e^-k), where k is the concentration factor. If k increases from 2 to 4, which values represent the growth in resource control share?
4. A city's resource supply is modeled by R = 1000 * (1/2)^t, where t is time in decades. At what time t does the resource supply drop below 125 units?
5. In a social hierarchy with 100 people, the top 1% hold 40% of the total resources. If the total resource pool is 1,000 units, how many units does each person in the top 1% hold on average?
6. A social hierarchy follows a power law where the wealth of a class is defined by W = k/n². If k = 100 and the class rank n = 2, what is the wealth of this class?
7. In a three-tiered Social Hierarchy, the ratio of wealth between tiers is 9:3:1. If the total wealth is 520, what is the wealth of the middle tier?
8. A Social Hierarchy structure collapses if the bottom tier holds less than 5% of total wealth. If total wealth is 2000 and the bottom tier holds 90 units, is the system stable?
9. In a village, the top 10% own 80% of the land. If the total land is 1000 acres, how many acres does the bottom 90% own?
10. If wealth in a system grows by 5% annually, what is the multiplier after 2 years for the initial wealth W?
11. Two classes have wealth ratios of 4:1 and 6:1. If the total wealth is $7000, what is the difference in wealth for a unit if the first group has 4 units?
12. If the Gini coefficient (G) for wealth is 0.5, and the inequality index is defined as G/(1-G), what is the index?
13. In a simple stratification model, the top 10% of a population controls 80% of resources. If the total resource pool is 1,000 units, how many units are held by the remaining 90% of the population?
14. If a society's wealth gap follows the equation W = 2x², where x is the class rank (1 being the highest), what is the wealth value for class rank 4?
15. In a tiered stratification system, the bottom tier loses 1/4 of its resources each year. If they start with 160 units, how many units remain after 2 years?
16. A resource distribution model is defined by the sum S = Σ from n=1 to 3 of (2n). What is the total resource sum for these three tiers?
17. In a simple model of Systemic Fragility, a society's stability S is defined by S = 100 - (I × R), where I is the inequality index and R is the resource scarcity. If I = 4 and R = 15, what is the stability level?
18. A civilization's total energy output E declines over time T according to E = 500 - 2T². Calculate the energy output at T = 10 years.
19. If a system requires a minimum stability of 50 to avoid collapse, and stability is given by S = 200 / (1 + F), where F is the systemic friction (inequality factor), find the maximum allowable F.
20. A social network's connectivity index C follows the rule C = 100 × (0.5)^n, where n is the number of disconnected groups. What is the connectivity after 3 groups disconnect?
21. A society's total resource pool is 1000 units. If the elite class controls 90% of the resources and the remaining 10% is divided equally among 50 lower-class individuals, how many units does each lower-class individual receive?
22. A system's fragility is modeled by the equation F = 2x² - 4x + 10, where x represents the Gini coefficient of wealth inequality (0 to 1). At what level of inequality (x) is the system's fragility at its minimum?
23. If a society loses 15% of its agricultural output every year due to environmental degradation, what is the remaining output percentage after 2 years?
24. A social hierarchy consists of 3 tiers. If the population in the top tier is 100, middle is 400, and bottom is 500, what is the probability that a randomly selected person is NOT in the top tier?

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