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Equation 1 · Part 7 · The Granary as an Institution

=

St+1=(1−δ) St+Ht−Ct−Tt,S_{t+1} = (1-\delta)\,S_t + H_t - C_t - T_t,
=

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

The dynamics are simple enough to write down, and writing them down exposes an assumption that verbal accounts tend to hide. Let the stock carried into the next period be St+1=(1−δ) St+Ht−Ct−TtS_{t+1} = (1-\delta)\,S_t + H_t - C_t - T_t. 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…

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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

Open the illustrated equality: what the equals sign claims guide →

Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.