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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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