<p>Yes this is done via social welfare function. Generally the steps in almost any public policy scenario analysis that requires comparison of benefits among different people (such as optimal taxation and redistribution analysis) is :</p>
<ol>
<li>Assume utilities are cardinal - this is not innocuous assumption since most economists would say utility is ordinal, but without cardinal utility interpersonal utility comparisons, optimal taxation and redistribution etc are virtually futile exercises. However, you would still want to parametrize this cardinal utility in a way that it fits empirical observable facts (e.g. degree of preference between leisure and consumption etc).</li>
<li>Pick some social welfare function, or whole list of social welfare function (to compare results among them). The three most popular welfare functions are:
<ul>
<li>Rawlsian Min-Max social welfare function. Give welfare weight of 1 to the utility of the poorest members of society and 0 to everyone else.</li>
<li>Utilitarian welfare function - distributes weights to individuals based on their incomes given that marginal utility of last dollar is higher for poor than for  a rich. This is very similar to what the person in a link you shared does although in research proper more complex models are used.</li>
<li>Chartable Conservative/Libertarian - This is basically a Rawlsian welfare function where other people than the poorest get some non-zero welfare weight as well.</li>
</ul>
</li>
</ol>
<p>You can see examples of this put in a practice in seminal works such as Saez (2001) or Diamond (1998). For example, below you can see optimal marginal tax schedule from Saez (2001) that is calculated under both Rawlsian and Utilitarian social welfare function. The excercise tells you the difference between value of \$1 for every single person not just poor vs other poor or poor vs rich but every single person vs everyone else.</p>
<p><a href="https://i.sstatic.net/6ExY7.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/6ExY7.png" alt="enter image description here" /></a></p>

CC BY-SA 4.0
2021-10-23T16:49:48.320Z
The answer is a good starting point and it does represent the standard textbook discussion pretty well. But I'm looking to get at (or find references to a full and modern discussion of) to some of the deeper questions like 

- how do we justify either of these three SWF's (e.g., 'veil of ignorance choice')?

- how do we justify a 'representative agent' utility-of-income function to use in this? 

- how to choose *which* functional form to use for the utility-of-income function. 

Will try to come back to this later. Thanks for answering!
daaronr
CC BY-SA 4.0
2021-10-23T16:53:00.220Z
@daaronr 1. "how do we justify either of these three SWF's (e.g., 'veil of ignorance choice')?"  < -  **This is not an economics question but moral philosophy question**. From Econ perspective justification is simply that social planner is Rawlsian - end of story.  Please ask that on Philosophy stack exchange. "how do we justify a 'representative agent' utility-of-income function to use in this?" <- Again such question would be off topic on economics.se for the same reason as the previous one.  3. "how to choose which functional form to use for the utility-of-income function"
1muflon1
CC BY-SA 4.0
2021-10-23T16:53:51.600Z
<- this is on topic here and I actually addressed that in my answer - you simply pick the one that based on the available evidence is the most appropriate one, for example, if people do not empirically have separable utility function, maybe choose some utility function that is also non-separable etc, try to find utility function that offers the best trade-off between being realistic and being usable (as too complex utility functions might be unworkable), there is no simple recipe that exists here, other than pick reasonable function and then put in it est parameters for economy of interest
1muflon1
CC BY-SA 4.0
2021-10-24T17:09:52.420Z
> From Econ perspective justification is simply that social planner is Rawlsian - end of story.

I disagree, although I realise that this question straddles economics and philosophy. But this is part of several fields in economics, such as Public Choice. 

We can envision an optimization-based justification of a particular social welfare function, and this indeed uses tools that are central to Economics.
daaronr
CC BY-SA 4.0
2021-10-24T17:12:49.283Z
> how do we justify a 'representative agent' utility-of-income function to use in this?" <- Again such question would be off topic on economics.se for the same reason as the previous one.


The discussion of when it is reasonable to assume a representative agent and aggregation is a core topic in microeconomics.
daaronr
CC BY-SA 4.0
2021-10-24T17:15:33.120Z
> - you simply pick the one that based on the available evidence is the most appropriate one, for example,...find utility function that offers the best trade-off between being realistic and being usable (as too complex utility functions 

I understand this but I was looking for some pointers to literature where this is discussed in a both theoretically-sound and practical way
daaronr
CC BY-SA 4.0
2021-10-23T16:12:10.343Z
2021-10-23T16:12:10.343Z
1muflon1
<p>What is the best analysis/literature/text, that gives a theoretical justification for approaches that can be used in practice, for</p>
<p>How we <em>should</em> weight income/consumption at different income levels (especially for the very poor and the poor) in a 'social welfare function'?</p>
<p>Especially regarding Toby Ord's framework in <a href="https://bit.ly/ordvalue" rel="nofollow noreferrer">https://bit.ly/ordvalue</a> &amp; the</p>
<ul>
<li>isoelastic utility function (restriction)</li>
<li>justifying 'max expected utility'... (via a 'veil of ignorance?)</li>
</ul>

<public-economics><welfare-economics><development-economics><social-welfare><philosophy-of-economics>
How *should* weigh income/consumption at different income levels (esp. to the very poor vs poor) ... perhaps in a 'social welfare function'?
daaronr
# How *should* weigh income/consumption at different income levels (esp. to the very poor vs poor) ... perhaps in a 'social welfare function'?

(Asked by: username_0 on 2021-10-23)

What is the best analysis/literature/text, that gives a theoretical justification for approaches that can be used in practice, for

How we *should* weight income/consumption at different income levels (especially for the very poor and the poor) in a 'social welfare function'?

Especially regarding Toby Ord's framework in <https://bit.ly/ordvalue> & the

* isoelastic utility function (restriction)
* justifying 'max expected utility'... (via a 'veil of ignorance?)

**Tags:** public-economics, welfare-economics, development-economics, social-welfare, philosophy-of-economics

---

## 1 answers

### Answer by username_1 on 2021-10-23. Score: 1

Yes this is done via social welfare function. Generally the steps in almost any public policy scenario analysis that requires comparison of benefits among different people (such as optimal taxation and redistribution analysis) is :

1. Assume utilities are cardinal - this is not innocuous assumption since most economists would say utility is ordinal, but without cardinal utility interpersonal utility comparisons, optimal taxation and redistribution etc are virtually futile exercises. However, you would still want to parametrize this cardinal utility in a way that it fits empirical observable facts (e.g. degree of preference between leisure and consumption etc).
2. Pick some social welfare function, or whole list of social welfare function (to compare results among them). The three most popular welfare functions are:
   * Rawlsian Min-Max social welfare function. Give welfare weight of 1 to the utility of the poorest members of society and 0 to everyone else.
   * Utilitarian welfare function - distributes weights to individuals based on their incomes given that marginal utility of last dollar is higher for poor than for a rich. This is very similar to what the person in a link you shared does although in research proper more complex models are used.
   * Chartable Conservative/Libertarian - This is basically a Rawlsian welfare function where other people than the poorest get some non-zero welfare weight as well.

You can see examples of this put in a practice in seminal works such as Saez (2001) or Diamond (1998). For example, below you can see optimal marginal tax schedule from Saez (2001) that is calculated under both Rawlsian and Utilitarian social welfare function. The excercise tells you the difference between value of \$1 for every single person not just poor vs other poor or poor vs rich but every single person vs everyone else.

[![enter image description here](https://i.sstatic.net/6ExY7.png)](https://i.sstatic.net/6ExY7.png)

> **Comments:**
> **username_0**: The answer is a good starting point and it does represent the standard textbook discussion pretty well. But I'm looking to get at (or find references to a full and modern discussion of) to some of the deeper questions like   - how do we justify either of these three SWF's (e.g., 'veil of ignorance choice')?  - how do we justify a 'representative agent' utility-of-income function to use in this?   - how to choose *which* functional form to use for the utility-of-income function.   Will try to come back to this later. Thanks for answering!  
> **username_1**: @daaronr 1. "how do we justify either of these three SWF's (e.g., 'veil of ignorance choice')?"  < -  **This is not an economics question but moral philosophy question**. From Econ perspective justification is simply that social planner is Rawlsian - end of story.  Please ask that on Philosophy stack exchange. "how do we justify a 'representative agent' utility-of-income function to use in this?" <- Again such question would be off topic on economics.se for the same reason as the previous one.  3. "how to choose which functional form to use for the utility-of-income function"  
> **username_1**: <- this is on topic here and I actually addressed that in my answer - you simply pick the one that based on the available evidence is the most appropriate one, for example, if people do not empirically have separable utility function, maybe choose some utility function that is also non-separable etc, try to find utility function that offers the best trade-off between being realistic and being usable (as too complex utility functions might be unworkable), there is no simple recipe that exists here, other than pick reasonable function and then put in it est parameters for economy of interest  
> **username_0**: > From Econ perspective justification is simply that social planner is Rawlsian - end of story.  I disagree, although I realise that this question straddles economics and philosophy. But this is part of several fields in economics, such as Public Choice.   We can envision an optimization-based justification of a particular social welfare function, and this indeed uses tools that are central to Economics.  
> **username_0**: > how do we justify a 'representative agent' utility-of-income function to use in this?" <- Again such question would be off topic on economics.se for the same reason as the previous one.   The discussion of when it is reasonable to assume a representative agent and aggregation is a core topic in microeconomics.  
> **username_0**: > - you simply pick the one that based on the available evidence is the most appropriate one, for example,...find utility function that offers the best trade-off between being realistic and being usable (as too complex utility functions   I understand this but I was looking for some pointers to literature where this is discussed in a both theoretically-sound and practical way  

---

