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I recently learned about the relationship between utilization maximization and cost minimization.

Are there studies on whether this duality holds in real life?

Any information on this topic for a beginner to consumer choice theory would be appreciated. Any tips on key things to consider when starting to learn about the topic would also be helpful.

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There is nothing that can "hold in practice".

Utility maximisation and expenditure minimization are theoretical framework that are used to model behavior by factors that are thought to motivate choices.

This is useful if they approximately or on average correlate with how those factor influence choices. For example, wage will surely be a major factor in the labor supply of an individual.

But utility cannot be measured and arguably does not exist. Both approaches rely on either a utility function or a level of utility, so neither can be practically verified.

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  • $\begingroup$ I would partly disagree with this. The whole concept of duality implies that we can create testable hypotheses about decision making. Via the Slutsky decomposition we can test substitution effects (changes in the Hicksian demand) through its components as Marshallian demands which are directly observable in experiment settings, at the least. This approach does not rely on a utility function per se, but enables us to test whether decisions (and preferences) are conducted according to something resembling a utility function. $\endgroup$
    – Brennan
    Commented Oct 27, 2020 at 6:22
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    $\begingroup$ I agree with you, but whether duality holds is not possible to actually verify, since utility functions don't really exist and are just approximations of behavior. Duality itself is just a mathematical link between two different optimzation problem. It can then be used, as you say, to get us from an unobservable, theoretical framework to an observable and empircal one. But we have to buy into the framework being valid before we actually use it and can't really test the framework itself (though we might argue or possibly test whether it is a useful or not useful one). $\endgroup$
    – Three Diag
    Commented Oct 27, 2020 at 14:40
  • $\begingroup$ Very good points! $\endgroup$
    – Brennan
    Commented Oct 28, 2020 at 3:27

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