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While studying the Marshallian Theory of Consumer Behaviour, I came across the assumption that the marginal utility of money is assumed to be constant. Can someone please explain why is this so?

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Marshallian Theory is notoriously about computing consumer surplus (and then welfare changes).

But it would be nonsensical to perform such calculations if at the level of one individual, the unit of valuation of surplus, i.e. the marginal utility of money (or the utility of one extra euro), were changing before and after changes in, say, prices. Also, what sense would it make to compute surplus (pleonastically) over many individuals if each of them had a different marginal utility of money?

In these two "within-individual" and "between-individual" cases, not having a constant marginal utility of money would be like summing objects with different units... Hence this assumption.

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    $\begingroup$ Beautiful answer. However, I do not agree with the fact that the constancy of MU of money enables interpersonal comparison. This is because the MU of money may not differ with the level of income but may still be different for different individuals. For interpersonal comparison we must assume that not only does MU of money remains constant but is the same across individuals. That is, all individuals have the same preferences when it comes to money. $\endgroup$ Commented May 29 at 4:47
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    $\begingroup$ @PallakGoyal you are right. I had "time-constant" and "constant within the space of individuals" in mind. $\endgroup$
    – keepAlive
    Commented May 29 at 7:21
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Unlike the ordinal analysis or the revealed preference approach, where there is no need for a measuring rod, the cardinal utility analysis requires a measuring rod. Money acts as this measuring rod.

For any meaningful measure the measuring rod itself should remain constant. For example, if you were comparing the length of two lines, and between the two measures your scale changes, say 1 cm becomes 11mm, the comparison will be incorrect.

Note that two individuals having different preferences can have different marginal utilities of money even if the marginal utility for each individual does not change with their income level. Therefore for interpersonal comparison of consumer surplus or utilities we don't just have to assume that marginal utility of money is constant but also that it is the same across individuals.

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