<p>Either I totally misunderstand the question, or this is just adding up numbers, there are no economic or mathematical principles involved. (In which case this is not the right SE for it.)</p>

<p>Denoting the "balances" by <span class="math-container">$b_1,b_2,...$</span> and the "supplies" by <span class="math-container">$s_1,s_2,...$</span> total profits are
<span class="math-container">$$
\Pi_{total} = \sum_i (b_i-s_i)
$$</span>
You want everyone to end up with a proportional share of this, so that in the end they have
<span class="math-container">$$
\frac{s_i}{\sum_i s_i} \Pi_{total}.
$$</span>
To compensate for their investment, each person should get
<span class="math-container">$$
x_i = s_i + \frac{s_i}{\sum_i s_i} \Pi_{total}.
$$</span>
One can verify that
<span class="math-container">$$
\begin{align*}
\sum_i x_i &amp; = \sum_i s_i + \sum_i\frac{s_i}{\sum_i s_i} \Pi_{total} \\
&amp; = \sum_i s_i + \Pi_{total} = \sum_i b_i
\end{align*}
$$</span>
so we made no mistakes, you can indeed give people their values <span class="math-container">$x_i$</span>.</p>

CC BY-SA 4.0
2020-04-12T08:00:04.660Z
2020-04-12T08:00:04.660Z
Giskard
<p>I am looking for a formula to calculate even distribution of loss or profit between involved parties. Let's speak with some examples as I feel it will be easier.</p>

<h2>Example 1</h2>

<h3>Person 1</h3>

<p>Balance: 2,000,000
Supplies (investment): 70,000</p>

<h3>Person 2</h3>

<p>Balance: -260,000
Supplies (investment): 260,000</p>

<h3>Person 3</h3>

<p>Balance: -17,000
Supplies (investment): 84,000</p>

<h3>Description</h3>

<p>As we can see one person made profit in this example. To distribute everything evenly he should pay every person loss (so 259,000 to Person 2 and 17,000 to Person 3) and divide what's left by 3 and distribute that as well.</p>

<h2>Example 2</h2>

<h3>Person 1</h3>

<p>Balance: 2,000,000
Supplies (investment): 80,000</p>

<h3>Person 2</h3>

<p>Balance: 1,000,000
Supplies (investment): 150,000</p>

<h3>Person 3</h3>

<p>Balance: -900,000
Supplies (investement): 900,000</p>

<h3>Person 4</h3>

<p>Balance: -150,000
Supplies (investment): 100,000</p>

<h3>Description</h3>

<p>As we can see two people here made profit so it gets trickier. We still want to distribute everything evenly. Easiest way I see is to sum all the negative balances (1,050,000 here), subtract that from profit (3,000,000 - 1,050,000 = 2,950,000) so everyone 737,500 / 4 so Person 2 has to give back a little from his balance (profit) and so does Person 1. Easiest would be to cumulate all profit in one account (e.g. Person 1) and make Person 1 split everything but it seems more work. </p>

<h2>Example 3</h2>

<h3>Person 1</h3>

<p>Balance: -10,000
Supplies (investment): 50,000</p>

<h3>Person 2</h3>

<p>Balance: -20,000
Supplies (investment): 20,000</p>

<h3>Person 3</h3>

<p>Balance: -500
Supplies (investment): 500</p>

<h3>Description</h3>

<p>As we can see no-one made any profit but Person 1 earned 40,000 as he used 50,000 for supplies and  has only -10,000 in losses. So this 40,000 should be evenly distributed but according to their usage of supplies. </p>

<p>Is that correct way of thinking? Is there a formula for splitting profit and loss?</p>

CC BY-SA 4.0
2020-04-11T23:34:01.763Z
What are these numbers? Supplies of what? Why are profits expected to be shared?
Brian Romanchuk
CC BY-SA 4.0
2020-04-12T00:53:45.727Z
@BrianRomanchuk it's something for a game, scavenger-hunt-like. You have to work as a team and get the best result for everyone so no-one loses more than the other so to say. I thought that maybe something like that already exists in economics.
nass
CC BY-SA 4.0
2020-04-12T01:26:34.183Z
In tl;dr the goal is to distribute wealth as close to perfection as it can be achieved while taking into account the number of supplies each person used to get that result.So if the whole team has profit - everyone gets the same cut out of it so everyone gets richer equally and if the team has loss in general everyone gets a portion of earnings and portion of loss so to say.
nass
CC BY-SA 4.0
2020-04-12T03:02:40.210Z
This isn’t really an economics question. If you want to weight by “supplies”, you calculate the weight of the person as (person’s supplies) / (all supplies). Add up all profits to get a total, then use that weight to see their share.
Brian Romanchuk
CC BY-SA 4.0
2020-04-12T07:51:36.063Z
I'm voting to close this question as off-topic because it is about a numerical formula, not the discipline of economics.
Giskard
CC BY-SA 4.0
2020-04-12T09:14:19.883Z
Voted as off-topic myself. Sorry for that and thank you for your time.
nass
<cost-functions>
Formula for splitting profit and loss for every person
nass
# Formula for splitting profit and loss for every person

(Asked by: username_0 on 2020-04-11)

I am looking for a formula to calculate even distribution of loss or profit between involved parties. Let's speak with some examples as I feel it will be easier.

## Example 1

### Person 1

Balance: 2,000,000
Supplies (investment): 70,000

### Person 2

Balance: -260,000
Supplies (investment): 260,000

### Person 3

Balance: -17,000
Supplies (investment): 84,000

### Description

As we can see one person made profit in this example. To distribute everything evenly he should pay every person loss (so 259,000 to Person 2 and 17,000 to Person 3) and divide what's left by 3 and distribute that as well.

## Example 2

### Person 1

Balance: 2,000,000
Supplies (investment): 80,000

### Person 2

Balance: 1,000,000
Supplies (investment): 150,000

### Person 3

Balance: -900,000
Supplies (investement): 900,000

### Person 4

Balance: -150,000
Supplies (investment): 100,000

### Description

As we can see two people here made profit so it gets trickier. We still want to distribute everything evenly. Easiest way I see is to sum all the negative balances (1,050,000 here), subtract that from profit (3,000,000 - 1,050,000 = 2,950,000) so everyone 737,500 / 4 so Person 2 has to give back a little from his balance (profit) and so does Person 1. Easiest would be to cumulate all profit in one account (e.g. Person 1) and make Person 1 split everything but it seems more work.

## Example 3

### Person 1

Balance: -10,000
Supplies (investment): 50,000

### Person 2

Balance: -20,000
Supplies (investment): 20,000

### Person 3

Balance: -500
Supplies (investment): 500

### Description

As we can see no-one made any profit but Person 1 earned 40,000 as he used 50,000 for supplies and has only -10,000 in losses. So this 40,000 should be evenly distributed but according to their usage of supplies.

Is that correct way of thinking? Is there a formula for splitting profit and loss?

**Tags:** cost-functions

> **Comments:**
> **username_1**: What are these numbers? Supplies of what? Why are profits expected to be shared?  
> **username_0**: @username_1 it's something for a game, scavenger-hunt-like. You have to work as a team and get the best result for everyone so no-one loses more than the other so to say. I thought that maybe something like that already exists in economics.  
> **username_0**: In tl;dr the goal is to distribute wealth as close to perfection as it can be achieved while taking into account the number of supplies each person used to get that result.So if the whole team has profit - everyone gets the same cut out of it so everyone gets richer equally and if the team has loss in general everyone gets a portion of earnings and portion of loss so to say.  
> **username_1**: This isn’t really an economics question. If you want to weight by “supplies”, you calculate the weight of the person as (person’s supplies) / (all supplies). Add up all profits to get a total, then use that weight to see their share.  
> **username_2**: I'm voting to close this question as off-topic because it is about a numerical formula, not the discipline of economics.  
> **username_0**: Voted as off-topic myself. Sorry for that and thank you for your time.  

---

## 1 answers

### Answer by username_2 on 2020-04-12. Score: 1 | Accepted answer

Either I totally misunderstand the question, or this is just adding up numbers, there are no economic or mathematical principles involved. (In which case this is not the right SE for it.)

Denoting the "balances" by $b\_1,b\_2,...$ and the "supplies" by $s\_1,s\_2,...$ total profits are
$$
\Pi\_{total} = \sum\_i (b\_i-s\_i)
$$
You want everyone to end up with a proportional share of this, so that in the end they have
$$
\frac{s\_i}{\sum\_i s\_i} \Pi\_{total}.
$$
To compensate for their investment, each person should get
$$
x\_i = s\_i + \frac{s\_i}{\sum\_i s\_i} \Pi\_{total}.
$$
One can verify that
$$
\begin{align\*}
\sum\_i x\_i & = \sum\_i s\_i + \sum\_i\frac{s\_i}{\sum\_i s\_i} \Pi\_{total} \\
& = \sum\_i s\_i + \Pi\_{total} = \sum\_i b\_i
\end{align\*}
$$
so we made no mistakes, you can indeed give people their values $x\_i$.


---

