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Equation 23 · Part 2 · When Generation Becomes Free, Attention Becomes the Scarce Good

Symbol s

∂2c(s,θ)∂s ∂θ  <  0,\frac{\partial^{2} c(s,\theta)}{\partial s \, \partial \theta} \;<\; 0,
ss

What this part means

the signal level.

Its job in the formula

s is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Where the article explains it

In the standard notation, with signal level s and type θ\theta increasing in ability, the single-crossing condition is ∂2c(s,θ)∂s ∂θ  <  0\frac{\partial^{2} c(s,\theta)}{\partial s \, \partial \theta} \;<\; 0.

The passage around this formula

Spence’s contribution was to explain how information can cross the asymmetry without direct verification. An agent takes a costly action — in his original case, education — and the action separates types only under a specific condition: the marginal cost of the signal must be lower for the type the signal is supposed to identify. In the standard notation, with signal level s and type θ\theta increasing in ability, the single-crossing condition is ∂2c(s,θ)∂s ∂θ  <  0\frac{\partial^{2} c(s,\theta)}{\partial s \, \partial \theta} \;<\; 0. and it is this inequality, not the content of the signal, that does the work [ 3 ] . Spence’s model famously does not require the signalling activity to be productive at all. It requires only that it be differentially costly.

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

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