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Equation 23 · Part 6 · When Generation Becomes Free, Attention Becomes the Scarce Good

superscript

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

What this part means

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

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

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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Sources cited in the surrounding passage

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