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Why or when does the area under the demand curve equals the total utility for consumers (perfect competition)?

From the demand side, one knows that when combining the utility function and the budget curve/line, it follows that in the optimum for the consumer: $$ \frac{p_1}{p_2} = \frac{MU_1}{MU_2} $$

That is, the price ratio equals the ratio of the marginal utilities.

But this does NOT mean that p1 equals U'1, right? So why then, one says that the demand curve is the marginal utility function, and the area under its curve is the total utility for consumers?

source: Cuyvers et al. 2014, internationale economie, page 234

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  • $\begingroup$ "one says that the demand curve is the marginal utility function" Who says this? I don't think any economists say this in a general context. It may hold for quasi-linear utility functions if $p_2 = 1$. $\endgroup$ – denesp Jan 8 '18 at 22:37
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    $\begingroup$ Possible duplicate of relation between the demand function and the marginal utility function $\endgroup$ – denesp Jan 8 '18 at 22:39
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    $\begingroup$ It is said in Cuyvers et. al, 2014, Internationale economie, for Figure 11.1, page 234 which discusses the effects of tarifs by a small country: partial-equilibrium analysis... $\endgroup$ – babipsylon Jan 8 '18 at 23:49
  • $\begingroup$ Here they claim they are the same, but they don't completely go through the derivation process quora.com/… $\endgroup$ – babipsylon Jan 9 '18 at 22:38

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