Equation 17 · When Generation Becomes Free, Attention Becomes the Scarce Good
What does this equation mean?
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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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Symbol p^*
is part of the quantity the equation computes from the expression on the right.
Symbol E
The expected value operator: the probability-weighted average of the quantity inside its brackets.
Symbol v
the buyer’s value of quality q and c(q) the seller’s reservation value.
Symbol q
q is one factor in the product that computes the quantity on the left.
Symbol c
c is one factor in the product that computes the quantity on the left.
=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →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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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 . 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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