Problem

Interpret the subexpression \(80-p\) in \(R=p(80-p)\), where \(p\) is price in dollars and \(80-p\) is demand in items. State its modeled quantity, units, signed response to a \(\text{one}\text{-}\text{dollar}\) price increase, and role in revenue.

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What this problem is really about

The named subexpression should be interpreted on its own before using the full product. We’ll identify it as the quantity factor in revenue, attach its item units, compare its value before and after a one-dollar price increase, and use that signed change to describe the modeled demand response.

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Subexpression 80 − p; modeled quantity demanded; units dollars; demand decreases by 1 dollar for each 1-dollar increase in price; it is the demand factor.

Subexpression 80 − p; absolute elapsed time; units items; it is always nonnegative and has no signed dependence on price; it is the demand factor.

Subexpression 80 − p; whole revenue; units dollars; revenue decreases by 1 dollar for each 1-dollar increase in price; it is the full model output.

Subexpression 80 − p; modeled quantity demanded; units items; demand decreases by 1 modeled item for each 1-dollar increase in price; it is the demand factor in revenue.

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Interpret the subexpression \(80-p\) in \(R=p(80-p)\), where \(p\) is price in dollars and \(80-p\) is demand in items. State its modeled quantity, units, signed response to a \(\text{one}\text{-}\text{dollar}\) price increase, and role in revenue.

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