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

What does this equation mean?

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

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Inputs and operationsEbig[ v(q) big| c(q) ≤ p^* big]
Result or conditionp^*
How to read the two sides of this formula. Follow the article passage for the meaning of each quantity.

This equation states a bound: one expression must stay on the indicated side of the other under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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p∗p^{*}

Symbol p^*

p∗p^* is part of the quantity the equation computes from the expression on the right.

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E\mathbb{E}

Symbol E

The expected value operator: the probability-weighted average of the quantity inside its brackets.

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vv

Symbol v

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

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qq

Symbol q

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

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cc

Symbol c

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

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=

=

The expressions on both sides represent the same quantity under the stated assumptions.

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superscript

superscript

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.

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How to interpret it

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What the article says around this equation

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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Sources cited in the surrounding passage

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