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Equation 17 · Part 3 · When Generation Becomes Free, Attention Becomes the Scarce Good

Symbol v

p∗  =  E[ v(q)  ∣  c(q)≤p∗ ],p^{*} \;=\; \mathbb{E}\big[\, v(q) \;\big|\; c(q) \le p^{*} \,\big],
vv

What this part means

the buyer’s value of quality q and c(q) the seller’s reservation value.

Its job in the formula

v is one factor in the product that computes the quantity on the left.

Where the article explains it

where v(q) is the buyer’s value of quality q and c(q) the seller’s reservation value.

The passage around this formula

Akerlof supplied the canonical model of a market in that condition. Where sellers know quality and buyers do not, buyers can rationally offer only the expected value of what is on offer; sellers whose goods are worth more than that price withdraw; the expected quality of what remains falls; the price falls again. The equilibrium is a fixed point of the form p∗  =  E[ v(q)  ∣  c(q)≤p∗ ]p^{*} \;=\; \mathbb{E}\big[\, v(q) \;\big|\; c(q) \le p^{*} \,\big]. where v(q) is the buyer’s value of quality q and c(q) the seller’s reservation value. Only sellers whose reservation value lies below the prevailing price participate, and the price is the expectation over exactly that self-selected pool [ 2 ] .

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Learn the underlying idea

A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the surrounding passage

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