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