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Equation 17 · Part 6 · When Generation Becomes Free, Attention Becomes the Scarce Good

=

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

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

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

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.

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Sources cited in the surrounding passage

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