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Equation 2 · The Granary as an Institution

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StS_t

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the stock held. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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StS_t

Symbol S_t

the stock held.

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subscript

subscript

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

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How to interpret it

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What the article says around this equation

where StS_t is the stock held, HtH_t the harvest added, CtC_t own consumption, TtT_t the quantity appropriated by others, and δ\delta the proportional loss rate to pests, damp and spoilage. The equation is illustrative rather than estimated, and its value is that it separates two subtractions usually conflated. Grain that rots is gone; grain that is taken still exists and has changed owner. A society can be losing a large share of its stock while nobody is being taxed at all, and a low loss rate is what makes a high appropriation rate worth organising. Loss sets the horizon over which any claim on stored food is meaningful: when δ\delta is high, a granary cannot underwrite an obligation more than a…
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where StS_t is the stock held, HtH_t the harvest added, CtC_t own consumption, TtT_t the quantity appropriated by others, and δ\delta the proportional loss rate to pests, damp and spoilage. The equation is illustrative rather than estimated, and its value is that it separates two subtractions usually conflated. Grain that rots is gone; grain that is taken still exists and has changed owner. A society can be losing a large share of its stock while nobody is being taxed at all, and a low loss rate is what makes a high appropriation rate worth organising. Loss sets the horizon over which any claim on stored food is meaningful: when δ\delta is high, a granary cannot underwrite an obligation more than a season away, and neither insurance nor extraction can be planned around it.

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