Percentages quandary: payout to Amy and Katie, given inputs have changed

[MathBoggled]

I need to get a percent of a percent...kind of. This isn't simple averaging, though. We have 2 percentages for 2 people:
Amy has paid for 80% of the materials. Katie has paid for 20%
Amy has done 50% of the labor. Katie has done 50%

In this scenario, for a $10,000 payment amount, the labor is a wash so Amy would get 80%: $8000 and Katie would get 20%: $2000.

However, if the labor was instead Amy does 60% of the labor and Katie does 40% of the labor, Amy should walk away with a bit more because her labor contribution increased. If doing an average, the the take-home pay decreases, so that is not the answer. How do I obtain the end % to disperse to Amy and Katie?

 

[BigBeachBanana]

I need to get a percent of a percent...kind of. This isn't simple averaging, though. We have 2 percentages for 2 people:
Amy has paid for 80% of the materials. Katie has paid for 20%
Amy has done 50% of the labor. Katie has done 50%

In this scenario, for a $10,000 payment amount, the labor is a wash so Amy would get 80%: $8000 and Katie would get 20%: $2000.

However, if the labor was instead Amy does 60% of the labor and Katie does 40% of the labor, Amy should walk away with a bit more because her labor contribution increased. If doing an average, the the take-home pay decreases, so that is not the answer. How do I obtain the end % to disperse to Amy and Katie?

One naive way is as follows:

1) Calculate the material contributed per person:
Amy: [imath]10,000\times 80\% = 8,000[/imath]
Katie: [imath]10,000\times 20\% = 2,000[/imath]

2) Calculate the labor contributed per person:
Amy: [imath]10,000\times 50\% = 5,000[/imath]
Katie: [imath]10,000\times 50\% = 5,000[/imath]

3) Add up the contributions
Amy: [imath] 8,000 + 5,000 = 13,000[/imath]
Katie: [imath]2,000+5,000 = 7,000[/imath]

4) Calculate the percentage of total contribution:
Amy: [imath]\dfrac{13,000}{13,000+7,000} = 65\%[/imath]

Katie: [imath]\dfrac{7,000}{13,000+7,000} = 35\%[/imath]

5) Divide the revenue based on the % contribution:
Amy: [imath]10,000 \times 65\% = 6,500[/imath]
Kaite: [imath]10,000 \times 35\% = 3,500[/imath]

 

[The Highlander]

Why do we continue to supply answers to problems that are clearly ones that (small?) businesses have?

Anyone running a business should be able to do this kind of (simple) Arithmetic themselves or be prepared to employ someone in their firm who can do it for them!

I think we're far too free in giving out this kind of 'help' and indulging these people doesn't really help them in the end. (Give a man a fish... ?)

But that's just my opinion, I suppose.
(No disrespect to BBB intended; you're just too kind-hearted ?)

 

[Dr.Peterson]

Why do we continue to supply answers to problems that are clearly ones that (small?) businesses have?

Anyone running a business should be able to do this kind of (simple) Arithmetic themselves or be prepared to employ someone in their firm who can do it for them!

As I read it, this is not just simple arithmetic; the OP has shown that they can do the percentage part. It's a matter of deciding what sort of calculation is fair. I'm not sure there is any one correct answer.

I need to get a percent of a percent...kind of. This isn't simple averaging, though. We have 2 percentages for 2 people:
Amy has paid for 80% of the materials. Katie has paid for 20%
Amy has done 50% of the labor. Katie has done 50%

In this scenario, for a $10,000 payment amount, the labor is a wash so Amy would get 80%: $8000 and Katie would get 20%: $2000.

However, if the labor was instead Amy does 60% of the labor and Katie does 40% of the labor, Amy should walk away with a bit more because her labor contribution increased. If doing an average, the the take-home pay decreases, so that is not the answer. How do I obtain the end % to disperse to Amy and Katie?

My suggestion (not being a businessperson) is that the answer depends on the relative value of labor and materials. Do the materials count for most of the value, or is the labor very intensive but the materials cheap?

I would start by deciding how much of the payment should be taken as payment for materials, and how much for labor, and then do the percent calculations separately for each part.

 

[The Highlander]

Since we do seem to be tackling this (against my "better" judgement ?), I have to agree with @Dr.Peterson's 'method'.

Surely the cost of the materials must be known or calculable so the "payment" needs to be split into Labour (L) & Material (M) costs and then apportioned appropriately between the workers.

So the "formulae" become:-

Amy's Pay = 0.6L + 0.8M dollars
and
Katie's Pay = 0.4L + 0.2M dollars​

So if, for example, the Material cost amounted to $4,000, then M = 4,000 & L = 6,000 (ie: 10,000 - 4,000)

Thus, Amy gets: $6,800 (0.6×6,000 + 0.8×4,000) and Katie gets: $3,200 (0.4×6,000 + 0.2×4,000)
and $6,800 + $3,200 = $10,000, of course.

Which, I have to say, (I think) is pretty simple Arithmetic. ?

 

[MathBoggled]

One naive way is as follows:

1) Calculate the material contributed per person:
Amy: [imath]10,000\times 80\% = 8,000[/imath]
Katie: [imath]10,000\times 20\% = 2,000[/imath]

2) Calculate the labor contributed per person:
Amy: [imath]10,000\times 50\% = 5,000[/imath]
Katie: [imath]10,000\times 50\% = 5,000[/imath]

3) Add up the contributions
Amy: [imath] 8,000 + 5,000 = 13,000[/imath]
Katie: [imath]2,000+5,000 = 7,000[/imath]

4) Calculate the percentage of total contribution:
Amy: [imath]\dfrac{13,000}{13,000+7,000} = 65\%[/imath]

Katie: [imath]\dfrac{7,000}{13,000+7,000} = 35\%[/imath]

5) Divide the revenue based on the % contribution:
Amy: [imath]10,000 \times 65\% = 6,500[/imath]
Kaite: [imath]10,000 \times 35\% = 3,500[/imath]

Thank you for this! However, herein lies my issue: Amy's contribution has gone DOWN with your calculation. If she contributed a greater percentage of the labor, then her value should go up, see?

I am looking for an answer where the overall percent contributed (or total amount paid) would be higher than the original 80% for Amy and lower than the original 20% for Katie.

 

[MathBoggled]

One naive way is as follows:

1) Calculate the material contributed per person:
Amy: [imath]10,000\times 80\% = 8,000[/imath]
Katie: [imath]10,000\times 20\% = 2,000[/imath]

2) Calculate the labor contributed per person:
Amy: [imath]10,000\times 50\% = 5,000[/imath]
Katie: [imath]10,000\times 50\% = 5,000[/imath]

3) Add up the contributions
Amy: [imath] 8,000 + 5,000 = 13,000[/imath]
Katie: [imath]2,000+5,000 = 7,000[/imath]

4) Calculate the percentage of total contribution:
Amy: [imath]\dfrac{13,000}{13,000+7,000} = 65\%[/imath]

Katie: [imath]\dfrac{7,000}{13,000+7,000} = 35\%[/imath]

5) Divide the revenue based on the % contribution:
Amy: [imath]10,000 \times 65\% = 6,500[/imath]
Kaite: [imath]10,000 \times 35\% = 3,500[/imath]

In a real-life quandary, the cost of the materials can actually ended up costing MORE than the job pays. However, the total contribution percent then needs to be applied to another amount.

 

[MathBoggled]

Why do we continue to supply answers to problems that are clearly ones that (small?) businesses have?

Anyone running a business should be able to do this kind of (simple) Arithmetic themselves or be prepared to employ someone in their firm who can do it for them!

I think we're far too free in giving out this kind of 'help' and indulging these people doesn't really help them in the end. (Give a man a fish... ?)

But that's just my opinion, I suppose.
(No disrespect to BBB intended; you're just too kind-hearted ?)

Funny you say that. It isnt even anything to do with a business, but best explained in that way. It is ok if you dont know the answer, but you dont have to pose questions you dont know as being too simple.

 

[MathBoggled]

Since we do seem to be tackling this (against my "better" judgement ?), I have to agree with @Dr.Peterson's 'method'.

Surely the cost of the materials must be known or calculable so the "payment" needs to be split into Labour (L) & Material (M) costs and then apportioned appropriately between the workers.

So the "formulae" become:-

Amy's Pay = 0.6L + 0.8M dollars
and
Katie's Pay = 0.4L + 0.2M dollars​

So if, for example, the Material cost amounted to $4,000, then M = 4,000 & L = 6,000 (ie: 10,000 - 4,000)

Thus, Amy gets: $6,800 (0.6×6,000 + 0.8×4,000) and Katie gets: $3,200 (0.4×6,000 + 0.2×4,000)
and $6,800 + $3,200 = $10,000, of course.

Which, I have to say, (I think) is pretty simple Arithmetic. ?

Herein lies my issue: Amy's contribution has gone DOWN with your calculation. If she contributed a greater percentage of the labor, then her value should go up.

I am looking for an answer where the overall percent contributed (or total amount paid) would be higher than the original 80% for Amy and lower than the original 20% for Katie. As stated in the original post, equal contributions of labor would be a wash so that Amy still gets 80% and Katie still gets 20%. If Amy has a larger labor contribution, her percent should increase, not decrease.

Not simple arithmetic once you read!!

 

[Dr.Peterson]

It isnt even anything to do with a business, but best explained in that way.

It's possible that we'd understand better if you either told us what it is really about, or at least gave a different analogy so we can tell what not to assume as real. The point is that there is information you haven't given us, without which we can't really help. The problem is not solvable given only what you've said.

Amy's contribution has gone DOWN with your calculation. If she contributed a greater percentage of the labor, then her value should go up.

I am looking for an answer where the overall percent contributed (or total amount paid) would be higher than the original 80% for Amy and lower than the original 20% for Katie. As stated in the original post, equal contributions of labor would be a wash so that Amy still gets 80% and Katie still gets 20%. If Amy has a larger labor contribution, her percent should increase, not decrease.

You're saying that Amy's amount should increase when her share of the work increased from 50% to 60%, right?

But neither BBB nor Highlander has shown both calculations. Both, on the other hand, imply that your assumption that 50:50 labor should not affect the pay is incorrect (that is, if their proposals are appropriate).

Let's take Highlander's formula. Here is his work with the 60:40 ratio, as he calculated it:

Amy's Pay = 0.6L + 0.8M dollars
Katie's Pay = 0.4L + 0.2M dollars​

So if, for example, the Material cost amounted to $4,000, then M = 4,000 & L = 6,000 (ie: 10,000 - 4,000)

Thus, Amy gets: $6,800 (0.6×6,000 + 0.8×4,000) and Katie gets: $3,200 (0.4×6,000 + 0.2×4,000)
and $6,800 + $3,200 = $10,000, of course.

Here is what this becomes for the 50:50 case:

Amy's Pay = 0.5L + 0.8M dollars
Katie's Pay = 0.5L + 0.2M dollars​

So if, for example, the Material cost amounted to $4,000, then M = 4,000 & L = 6,000 (ie: 10,000 - 4,000)

Thus, Amy gets: $6,200 (0.5×6,000 + 0.8×4,000) and Katie gets: $3,800 (0.5×6,000 + 0.2×4,000)

So when Amy's work increases from 50% to 60%, her pay increases from $6200 to $6800. That fits your expectation.

 

[MathBoggled]

Ok, this is actually a situation where there are a bunch of projects. I can financially add all of the costs of those projects up. From that, I can get a financial contribution of Katie (80%) vs Amy (20%). Now, I do the same with labor contribution. I find that Katie contributed 60% labor and Amy 40% on the same bucket of projects. If the labor were equal contributions, then we would just go by the financial contribution. But, since the labor was not equal, we need to increase Katie's share of the pot.
This is a question of "equal distribution" for a divorce. 41 states on the US use equal distribution. The labor amount is not necessarily discounted by a judge for any reason. I dont think this context changes the original question.
Since the financial contribution calculation would be $8000 for Katie AND her labor contribution was more, then I would assume that the $8000 would increase. If Katie and Amy had contributed the same labor, only the financial contribution applies.

 

[BigBeachBanana]

Thank you for this! However, herein lies my issue: Amy's contribution has gone DOWN with your calculation. If she contributed a greater percentage of the labor, then her value should go up, see?

I am looking for an answer where the overall percent contributed (or total amount paid) would be higher than the original 80% for Amy and lower than the original 20% for Katie.

I misunderstood the original question. Do these numbers fit your purpose? It's a simple linear interpolation.

 

[MathBoggled]

Yes, perfect!! I will look into interpolation. I know this is something that has probably been done a million times, but is definitely far from on the tip of my tongue. Thank you so much for this!

 

[BigBeachBanana]

Yes, perfect!! I will look into interpolation. I know this is something that has probably been done a million times, but is definitely far from on the tip of my tongue. Thank you so much for this!

Note from the table, when Amy's Labor is 100% she gets the entire $10,000 even though Katie's Material Share was 20%. This doesn't make much practical sense. A limit is needed when Amy's Labor is 100% to Katie's 0%.

 

[Steven G]

Imagine two people, A and B, open up a closing store together. They are equal partners. This means that A and B share equally in the profits. Everything is fine here.
Now A and B need to talk about how much they are going to be paid per hour since A and B will not always work the same number of hours. In my opinion, they should each get the same hourly wage.

We can change this a bit by saying that A put up 80% of the cost to open the store and B put for the remaining 20%. So A should get 80% of the profit and A and B should get the same hourly wage for the hours they worked in the store.

In either scenario, A or B could earn more money than the other.

 

[Dr.Peterson]

Ok, this is actually a situation where there are a bunch of projects. I can financially add all of the costs of those projects up. From that, I can get a financial contribution of Katie (80%) vs Amy (20%). Now, I do the same with labor contribution. I find that Katie contributed 60% labor and Amy 40% on the same bucket of projects. If the labor were equal contributions, then we would just go by the financial contribution. But, since the labor was not equal, we need to increase Katie's share of the pot.
This is a question of "equal distribution" for a divorce. 41 states on the US use equal distribution. The labor amount is not necessarily discounted by a judge for any reason. I dont think this context changes the original question.
Since the financial contribution calculation would be $8000 for Katie AND her labor contribution was more, then I would assume that the $8000 would increase. If Katie and Amy had contributed the same labor, only the financial contribution applies.

I don't see that this answers any of the issues; I don't understand the scenario at all. Are we talking about distributing shared property, or a business, or what? What does the reference to the judge "discounting" mean? (That you should ignore the labor?) Are there no laws that tell you what numbers to use?

In what way does my suggestion not fit the real situation? I showed you how the numbers do increase for more labor; but you need some information about the financial effect of the labor.

 

[MathBoggled]

No, no specific laws. It is actually the "judge's discretion" but something like interpoaltion can be used as a way to calculate and make your case. Financial contribution matters but say one spouse built the house instead of getting a job? Now, what if one spouse paid for 80% of the finances AND built 60% of the house? The way equitable distribution works is EVERYTHING gets put in one pot: equity in houses, increase in 401K, value of a car, whatever. If it could be divided only on the financial contribution, that would be easy. But the labor (homemaker, building a house, etc) comes into play, too. Calculate the financial % (easy, because based on numbers), now come up with a % contributed of labor (couples will fight over this, but ultimately come up with a %), once you have those 2 numbers combine them. Seems interpolation is the best? The other equations seem to discount the 80% if the labor contribution is 60%. Why should that person get less for contributing more labor?

BBB, in your last example it would probably make sense for the spouse who only contributed 20% financial to get nothing. The overall contribution, with labor, isnt much.

May help to know that these contribution fights really only pertain to short marriages. In long marriages the assets are too comingled. And, in a short marriage, that 20% financial contribution probably doesnt amount to much. Although, if it is....it is always the judges discretion to award more.