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Published equation contexts

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

Why this formula appears here

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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θ\theta

Symbol θ

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

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∂s ∂θ\partial s \, \partial \theta

Denominator: partial s partial θ

The complete quantity below the fraction bar; it must be nonzero for this division.

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How to interpret it

With a fixed numerator, increasing a nonzero denominator reduces the fraction.

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Published contexts (1)

A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.

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

Equation 23 · Institutions & Economy

When Generation Becomes Free, Attention Becomes the Scarce Good

This equation states a bound: one expression must stay on the indicated side of the other under the article’s assumptions.

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.

Meanings in this article

  • ss: the signal level.
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