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This might just be a misunderstanding. The textbook contains various passages like e.g. "An alternative approach holds real income (or utility) constant while examining reactions to changes in $p_x$" (p. 151). When this terminology is introduced, however, "real" stands in quotation marks. This is in the context of explaining the ...


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Real income and utility are not the same thing but utility can be expressed as a function of income because income is what allows you to consume goods and services. For example, let us assume there are only two goods $x_1$ an $x_2$ and consumer is given budget $p_1 x_1 + p_2 x_2 = m$, where $p_i$ are prices for good 1 and 2 respectively and $m$ is an income. ...


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