| 11. | This feature explains why the exponential utility function is considered unrealistic.
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| 12. | Conversely, every utility function can be used to construct a unique preference relation.
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| 13. | Later standalone programs typically were provided for utility functions such as disk formatting.
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| 14. | A simple proof assuming differentiable utility functions and production functions is the following.
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| 15. | That is, there is no real-valued representation of a utility function.
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| 16. | Second, because the utility function is concave, households prefer a smooth consumption path.
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| 17. | The expenditure function is the inverse of the indirect utility function:
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| 18. | In contrast, a cardinal utility function is only unique up to positive affine transformation.
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| 19. | Given the connection to utility functions, it can be used in utility maximization problems.
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| 20. | An agent possesses risk aversion if and only if the utility function is concave.
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