### Abstract

We offer a new, succinct proof of the fact that the money metric utility is concave for any preference relation representable by a concave function if and only if the indirect utility is affine in wealth. Our proof exploits the existence of a least concave representation established in Debreu (1976), and brings into salience the observation that the money-metric utility to be itself a least-concave representation of the preferences if it is concave. This observation is apparently new.

Original language | English (US) |
---|---|

Pages (from-to) | 10-12 |

Number of pages | 3 |

Journal | Economics Letters |

Volume | 154 |

DOIs | |

State | Published - May 1 2017 |

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### Keywords

- Expenditure function
- Least-concave representation
- Money metric

### ASJC Scopus subject areas

- Finance
- Economics and Econometrics

### Cite this

*Economics Letters*,

*154*, 10-12. https://doi.org/10.1016/j.econlet.2017.02.007

**The nonconcavity of money-metric utility : A new formulation and proof.** / Ali Khan, M.; Schlee, Edward.

Research output: Contribution to journal › Article

*Economics Letters*, vol. 154, pp. 10-12. https://doi.org/10.1016/j.econlet.2017.02.007

}

TY - JOUR

T1 - The nonconcavity of money-metric utility

T2 - A new formulation and proof

AU - Ali Khan, M.

AU - Schlee, Edward

PY - 2017/5/1

Y1 - 2017/5/1

N2 - We offer a new, succinct proof of the fact that the money metric utility is concave for any preference relation representable by a concave function if and only if the indirect utility is affine in wealth. Our proof exploits the existence of a least concave representation established in Debreu (1976), and brings into salience the observation that the money-metric utility to be itself a least-concave representation of the preferences if it is concave. This observation is apparently new.

AB - We offer a new, succinct proof of the fact that the money metric utility is concave for any preference relation representable by a concave function if and only if the indirect utility is affine in wealth. Our proof exploits the existence of a least concave representation established in Debreu (1976), and brings into salience the observation that the money-metric utility to be itself a least-concave representation of the preferences if it is concave. This observation is apparently new.

KW - Expenditure function

KW - Least-concave representation

KW - Money metric

UR - http://www.scopus.com/inward/record.url?scp=85013004939&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85013004939&partnerID=8YFLogxK

U2 - 10.1016/j.econlet.2017.02.007

DO - 10.1016/j.econlet.2017.02.007

M3 - Article

AN - SCOPUS:85013004939

VL - 154

SP - 10

EP - 12

JO - Economics Letters

JF - Economics Letters

SN - 0165-1765

ER -