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From Introduction to Economic Analysis by McAfee and Lewis. They write that:

the marginal value curve is the inverse of the demand function, where the demand function gives the quantity purchased at a given price. Formally, if $x(p)$ is the quantity a consumer buys at price $p$, then $v(x(p))=p$.

I'm having some trouble justifying this. $x(p)$ is a function of price yet $v(x)$ describes marginal utility (I'm guessing "marginal value" is synonymous with this), so I'm not sure how $x$ is the inverse function of $v$.

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  • $\begingroup$ Note it’s $v(x)$, not $v(p)$. So the marginal value of the $x$-th unit is $v$, and the unit price for buying $x$ units is $p$. $\endgroup$
    – Herr K.
    Commented Aug 20 at 22:41

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