<p>If I understand correctly, this is because in standard consumer theory, consumers don't hold money. They just spend all of their budget in consumption good. This fact is already captured by <span class="math-container">$d$</span> following your notation.</p>
<p>In other words, money is &quot;indirectly&quot; valued by the indirect utility function <span class="math-container">$v(p,m)$</span>. Therefore, as long as the shape of your utility function is determined, how you value the &quot;incidence&quot; (using your language) is determined. Technically speaking, the total payment <span class="math-container">$d_i^*\cdot p \equiv m_i$</span>. In your objective function, you have <span class="math-container">$$U_i(d_i^*) \equiv v_i(p, d_i^*\cdot p)$$</span>
which already reflect how the consumer values the &quot;incidence.&quot;</p>
<p>If consumer's value has been accounted for, then <span class="math-container">$d_i^*\cdot p$</span> is simply a transfer from the consumers to the firms, which are, again, owned by the consumers. You are gonna ignore any transfers in the welfare function, to avoid double-counting.</p>

CC BY-SA 4.0
2024-07-18T03:43:02.360Z
2024-07-18T03:43:02.360Z
DiZ
<p>I am very confused on why incidence is not included in social welfare maximization of one good. Typically, I see the optimization over price done something like this:</p>
<p><span class="math-container">$C$</span> ~ production cost function<br />
<span class="math-container">$U_i$</span> ~ consumer <span class="math-container">$i$</span>'s utility from consumption of good <span class="math-container">$d_i$</span> <br />
<span class="math-container">$d_i$</span> ~ consumption of user <span class="math-container">$i$</span>   <br />
<span class="math-container">$p$</span>  ~ price</p>
<p><br />
<span class="math-container">$\max -C(\sum_i d^*_i) + \sum U_i(d^*_i)$</span></p>
<p>s.t.
<span class="math-container">$d^*_i = \arg\max{ U_i(d_i) - p\cdot d_i }$</span></p>
<p>There might be other components but this is the basic framework. What I don't understand is why it does not include incidence as below</p>
<p><span class="math-container">$\max -C(\sum_i d^*_i) + \sum U_i(d^*_i) - d^*_i\cdot p$</span></p>
<p>s.t.
<span class="math-container">$d^*_i = \arg\max{ U_i(d_i) - p\cdot d_i }$</span></p>
<p>Additionally, if consumers value incidence differently wouldn't this affect the role of incidence in the social welfare maximizers problem? Based on other reading it seems as though there is some equilibrium assumed with all other goods but I don't fully understand this.</p>
<p>I appreciate any help. Happy to clarify if my question is unclear.</p>

CC BY-SA 4.0
2024-07-18T00:49:34.630Z
Please use LaTeX input. I can't read these equations, e.g. what is "-C(Demand)"?
VARulle
CC BY-SA 4.0
2024-07-18T01:42:45.130Z
@VARulle Apologies, I have not posted before and didn't realize I could latex
EngineerinEcon
CC BY-SA 4.0
2024-08-17T08:55:24.997Z
What is incidence?
Jesper Hybel
<utility><optimization><welfare-economics><social-welfare>
Why is incidence not included in social welfare maximization?
EngineerinEcon
# Why is incidence not included in social welfare maximization?

(Asked by: username_0 on 2024-07-17)

I am very confused on why incidence is not included in social welfare maximization of one good. Typically, I see the optimization over price done something like this:

$C$ ~ production cost function  
$U\_i$ ~ consumer $i$'s utility from consumption of good $d\_i$   
$d\_i$ ~ consumption of user $i$   
$p$ ~ price

$\max -C(\sum\_i d^\*\_i) + \sum U\_i(d^\*\_i)$

s.t.
$d^\*\_i = \arg\max{ U\_i(d\_i) - p\cdot d\_i }$

There might be other components but this is the basic framework. What I don't understand is why it does not include incidence as below

$\max -C(\sum\_i d^\*\_i) + \sum U\_i(d^\*\_i) - d^\*\_i\cdot p$

s.t.
$d^\*\_i = \arg\max{ U\_i(d\_i) - p\cdot d\_i }$

Additionally, if consumers value incidence differently wouldn't this affect the role of incidence in the social welfare maximizers problem? Based on other reading it seems as though there is some equilibrium assumed with all other goods but I don't fully understand this.

I appreciate any help. Happy to clarify if my question is unclear.

**Tags:** utility, optimization, welfare-economics, social-welfare

> **Comments:**
> **username_1**: Please use LaTeX input. I can't read these equations, e.g. what is "-C(Demand)"?  
> **username_0**: @username_1 Apologies, I have not posted before and didn't realize I could latex  
> **username_2**: What is incidence?  

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## 1 answers

### Answer by username_3 on 2024-07-18. Score: 0

If I understand correctly, this is because in standard consumer theory, consumers don't hold money. They just spend all of their budget in consumption good. This fact is already captured by $d$ following your notation.

In other words, money is "indirectly" valued by the indirect utility function $v(p,m)$. Therefore, as long as the shape of your utility function is determined, how you value the "incidence" (using your language) is determined. Technically speaking, the total payment $d\_i^\*\cdot p \equiv m\_i$. In your objective function, you have $$U\_i(d\_i^\*) \equiv v\_i(p, d\_i^\*\cdot p)$$
which already reflect how the consumer values the "incidence."

If consumer's value has been accounted for, then $d\_i^\*\cdot p$ is simply a transfer from the consumers to the firms, which are, again, owned by the consumers. You are gonna ignore any transfers in the welfare function, to avoid double-counting.


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