<p>Is there an altruistic utility function that cannot represent a locally non-satiated preference?</p>

<p>As an example of an altruistic utility function:
$U^1(x^1,...,x^H)=u^1(x^1)+\sum^H_{j=2}U^j(x^j)$, where $x^j$ is a consumption bundle for agent j, and $U^j$ is increasing in $x^j$.</p>

CC BY-SA 3.0
2015-03-23T10:51:51.653Z
Local non-satiation is a property of preferences towards individual goods, not of utility functions. So, altruistic or not, we can specify a utility function that incorporates local-non satiation for good A, but local satiation for good B. So please clarify, and also I would suggest to provide a specific mathematical example of an "altruistic utility function" that does incorporate  local non-satiation towards the goods you are interested in.
Alecos Papadopoulos
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2015-03-23T11:17:30.547Z
Or did you mean non-satiated in the altruism "good"?
BKay
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2015-03-23T11:58:49.853Z
@AlecosPapadopoulos In page 42 of Mas-Collel, it seems that the preference orders consumption bundles, and not just individual goods. I've tried to follow your sugestions with my edit. But I'm not sure if I understood really what you meant.
An old man in the sea.
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2015-03-23T12:50:20.810Z
Violations of local non-satiation can have many variants. The question is, what are you trying to accomplish here? My only guess would be that you want to model an individual who "reasonably cares" for the welfare of others, but at the same time he "becomes satisfied/satiated" with respect to his altruism if others attain a certain level of utility but after that his altruistic utility does not increase as others enjoy even more. Is this what you are after? And if not, what is your target?
Alecos Papadopoulos
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2015-03-23T19:09:47.743Z
@AlecosPapadopoulos My original objective was to see if when one agent is altruistic, but the others are not, can we still be sure that the Walrasian equilibrium will be pareto efficient? I was thinking of finding an altruistic utility that cannot represent a LNS preference relation, and invalidate the applicability of the 1st welfare theorem...
An old man in the sea.
CC BY-SA 3.0
2015-04-05T12:19:45.157Z
Check Kranich, L (1988). Altruism and efficiency: A welfare analysis of the Walrasian mechanism with transfers. Journal of Public Economics, 36, 369–386. "A Walrasian equilibrium with altruistic transfers is generally not efficient in the sense that the equilibrium is generally not Pareto optimal."
Konstantinos
<microeconomics>
Altruism and locally non-satiated preferences
An old man in the sea.
# Altruism and locally non-satiated preferences

(Asked by: username_0 on 2015-03-23)

Is there an altruistic utility function that cannot represent a locally non-satiated preference?

As an example of an altruistic utility function:
$U^1(x^1,...,x^H)=u^1(x^1)+\sum^H\_{j=2}U^j(x^j)$, where $x^j$ is a consumption bundle for agent j, and $U^j$ is increasing in $x^j$.

**Tags:** microeconomics
> **Comments:**
> **username_1**: Local non-satiation is a property of preferences towards individual goods, not of utility functions. So, altruistic or not, we can specify a utility function that incorporates local-non satiation for good A, but local satiation for good B. So please clarify, and also I would suggest to provide a specific mathematical example of an "altruistic utility function" that does incorporate  local non-satiation towards the goods you are interested in.  
> **username_2**: Or did you mean non-satiated in the altruism "good"?  
> **username_0**: @AlecosPapadopoulos In page 42 of Mas-Collel, it seems that the preference orders consumption bundles, and not just individual goods. I've tried to follow your sugestions with my edit. But I'm not sure if I understood really what you meant.  
> **username_1**: Violations of local non-satiation can have many variants. The question is, what are you trying to accomplish here? My only guess would be that you want to model an individual who "reasonably cares" for the welfare of others, but at the same time he "becomes satisfied/satiated" with respect to his altruism if others attain a certain level of utility but after that his altruistic utility does not increase as others enjoy even more. Is this what you are after? And if not, what is your target?  
> **username_0**: @AlecosPapadopoulos My original objective was to see if when one agent is altruistic, but the others are not, can we still be sure that the Walrasian equilibrium will be pareto efficient? I was thinking of finding an altruistic utility that cannot represent a LNS preference relation, and invalidate the applicability of the 1st welfare theorem...  
> **username_3**: Check Kranich, L (1988). Altruism and efficiency: A welfare analysis of the Walrasian mechanism with transfers. Journal of Public Economics, 36, 369–386. "A Walrasian equilibrium with altruistic transfers is generally not efficient in the sense that the equilibrium is generally not Pareto optimal."  

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## 0 answers

