04-24-2018, 10:27 PM
(This post was last modified: 05-06-2018, 12:29 AM by Supersquare04.)
[div align=\\\"center\\\"]The Economics of the NSFL
A Look at Minimum Salary[/div]
Greetings! There has been yet another influx of talks recently about raising the minimum salary in the NSFL. Personally, I'm not a fan of it for a few reasons, the main being that it would make my job as a General Manager trying to field a competitive team that much harder. I do however, have another motive for my dislike of raising the minimum salary.
In real life, I hold a Bachelor of Science degree in Economics. I'm by no means an expert, but one of the main things economics students learn is that minimum prices, or salaries when we're talking about labor do nothing but cause what is called a dead-weight loss. This is a fancy-sounding word that basically means the economy isn't running efficiently because it's not operating at equilibrium. There are transactions that are no longer being made because the economy is forced out of equilibrium.
Methodology
I'll dive in first and talk a little bit about my methodology. Some of you may remember, late last week I posted a poll in the discussion thread Here. It was there that I asked "What's the minimum salary you'd be willing to sign a contract for?
Here's a screenshot of the results:
![[Image: MwZoC7W.jpg]](https://i.imgur.com/MwZoC7W.jpg)
Unfortunately, Google Forms lacks a bit in the display department. I couldn't find a way to get it to label everything better. I'll give you the highlights, 34.3% said they'd sign for the minimum $500,000 (12 of the 35 responses). 25.7% said they'd sign for $1,000,000 (9/35) and so on and so forth.
I initially did my calculations when there were only 32 responses, so the numbers might be a little different now, but I'm far too lazy to go through and do it all again. I used the responses to create a Labor Supply Curve. I operated under the assumption that if you'd be willing to take $500,000 that you'd also be willing to take $1,000,000 and so on and so forth. Simply, if you chose the $500,000 minimum, you contributed a vote for each of the tiers because it only makes sense you'd happily take more money to do the same job. I realize this isn't 100% true for everybody because they want to help their team by opening salary cap room. I didn't take this into account because I honestly don't know how I'd fit that into the labor supply model.
There are 184 starting positions available in the NSFL (including offensive line). To find my Labor Supply Curve, I set the total number of responses (32) equal to the total starting positions available (184) and then used the percent of votes for each tier to determine the amount of people that would be willing to take each tier of salary if there were 184 responses.
I then used Excel to calculate a line of best fit. The Labor Supply Curve equation that I calculated turned out to be: y = 32,312x - 3,000,000. Y equals the salary, and X is the number of players.
After determining the Labor Supply Curve, it only made sense to calculate the Labor Demand Curve. To calculate this I took the total salary cap available for the 8 NSFL teams, a whopping $600,000,000 and divided it by each salary tier to determine how many people the NSFL would employ at that average salary. To not end up with huge numbers, I set the highest end at 184, or the total number of starting positions available. We can debate all day about how I should have done stuff differently and all, and if I wanted to put even more time into this I could. I still think this method will give us a decent look at what we're dealing with.
With my data points, I again used Excel to determine a line of best fit, where my Labor Demand Curve calculated out to be: y = -50,519x + 10,000,000. Again, Y is the salary, X is the amount of labor.
That's all fine and dandy, but what does it matter?
Using the supply and demand curves, we can find the equilibrium price (salary) and quantity (players) the NSFL would achieve. The numbers aren't exactly accurate to the NSFL, but it can show us a good model.
Using the Labor Supply and Demand Curves
Here is a graph of the supply and demand curves.
![[Image: TRFQDd0.jpg]](https://i.imgur.com/TRFQDd0.jpg)
We can calculate the point of equilibrium by setting the two equations equal to each other and solving for X.
-50519x+10000000=32312x-3000000
13000000=82831x
156=x
This shows us the equilibrium quantity in the NSFL for labor. To solve for price (Salary) we simply need to plug X=156 into one of the equations.
32312(156)-3000000=2,040,672.
Graph:
![[Image: IqYVn5W.jpg]](https://i.imgur.com/IqYVn5W.jpg)
In equilibrium conditions, the NSFL would employ 156 players at a salary of $2,040,672. But Molarpistols! You said there are 184 positions available in the NSFL, why aren't they all filled?
While the teams would love to employ everybody that wants to play until all their positions are filled, it's simply not possible due to the supply of labor. If more people were willing to take less money, it's certainly plausible, even likely that the Labor Supply Curve would shift, giving us a new equilibrium. I don't feel like calculating it currently, but there's a good chance we'd eventually find one where all positions are filled.
Are We at Equilibrium?
No! Various minimum wages have caused the average salary in the NSFL to rise above the equilibrium salary. I took all of the current NSFL contract data, each players salary per season for however many seasons they were signed and averaged it all out.
The average salary per season in the NSFL is $2,947,432.76. If we solve for X at that price, we find out 144.XX players would be employed by the NSFL (I forgot to write down the decimals, since you can't really have a fraction of a player and I didn't use the decimals in later maths). Coincidentally, this is the number of starting positions available if all 8 teams have a full offensive lines filled with OL Bots. I did say coincidentally, and I do think it is complete coincidence but I thought it was kind of fitting.
Here is a graph showing the average salary:
![[Image: GaRSLJs.jpg]](https://i.imgur.com/GaRSLJs.jpg)
Salary conditions as they are, 12 players that would be employed under equilibrium conditions are no longer employed. We can calculate the deadweight loss (the cost born by society (NSFL) due to market inefficiency.)
![[Image: ckcue3b.jpg]](https://i.imgur.com/ckcue3b.jpg)
The deadweight loss is $5,440,564.56, which means that the NSFL economy is missing out on that five million that would be spent if we were at equilibrium. Minimum salaries in the NSFL have caused the average salary to rise above the equilibrium level that the Labor Supply and Labor Demand curve have dictated.
And for the umpteenth time, there is again talk about raising the minimum wage further. If I was less lazy, I could go through each of the ideas being thrown around about raising the minimum wage, but alas, I am lazy. Instead, I decided to go through and use an example.
I upped every single contract value by $500,000 per season, which would raise the average NSFL salary to $3,447,432.76.
By doing this, we end up increasing the dead-weight loss in the NSFL Economy to a total of $18,991,270.26.
![[Image: Rc5vn16.jpg]](https://i.imgur.com/Rc5vn16.jpg)
That's an awful lot of economic activity not taking place due to a simple $500,000 increase in salary, that doesn't seem all that far-fetched when looking at a few of the ideas floating around to increase minimum salaries.
Summary
I've gone through and showed you a model for the supply and demand of labor (players) in the NSFL, based on data I retrieved and/or constructed. Using this, I calculated the optimal level of salary and quantity of players based off of these supply and demand equations.
I then showed where the current salary lies, based off of all the available NSFL contract data. This allowed me to calculate the expected number of players at that salary. The average salary in the NSFL is higher than the equilibrium salary calculated by the supply and demand functions. Since we're not operating at equilibrium, there is bound to be what economists call a "Dead-weight loss", which simply means the amount of economic activity being lost by not producing at equilibrium.
Conclusions
What conclusions can we draw from this model?
We can practically guarantee that raising the minimum salary would raise the average salary across the NSFL. By how much, and to what degree of damage is hard to say. Raising the amount of dollars paid to each player won't really have an effect on the Labor Supply Curve, as there was already a fair proportion of the player base willing to take minimum wage.
Instead, rising salaries would eventually cause NSFL teams to be unable to afford to employ more players. The DSFL might fill out, and enough people could go inactive that it doesn't really matter in the end. However, if recruitment picks up and we're able to see a sustainable amount of players, the NSFL simply won't be able to employ everybody willing to make a player and remain active.
Luckily, the NSFL is fake dollars, so we can effectively print out more and raise the salary cap for each team. Alternatively, or possibly even simultaneously we could increase the number of teams in the NSFL. Each of these activities would shift the Labor Demand Curve to the right like the following poorly drawn MS Paint example.
![[Image: jW1D52Y.jpg]](https://i.imgur.com/jW1D52Y.jpg)
I didn't do any calculations for this new Labor Demand Curve, but a simple glance will show that the equilibrium salary would rise, as would the equilibrium quantity of labor (players). The specifics of the shift of the curve would need to be known to understand the exact effect. Depending on the shift, salary could go up by a much higher amount than the quantity, they could go up in proportion to each other, or they could even shift to a point where a higher amount of players is demanded in a greater proportion than the salary paid.
All we'll manage to do by raising contract minimums is make everybody happy for a few seasons until the NSFL dies, or find ourselves in the same quandary we're in now and have to do it all over again. The only thing coming out of raising minimum wage is an increase in the overall price level. This is called inflation.
I welcome any and all comments and criticisms. Someday I might be able to write this more coherently and in a more "explain it like I'm five" type of words. I'm satisfied with my nerdy ramblings and my poorly drawn MS Paint graphics for now.
Thanks for stopping by and wasting some time being and Econ nerd with me!
A Look at Minimum Salary[/div]
Greetings! There has been yet another influx of talks recently about raising the minimum salary in the NSFL. Personally, I'm not a fan of it for a few reasons, the main being that it would make my job as a General Manager trying to field a competitive team that much harder. I do however, have another motive for my dislike of raising the minimum salary.
In real life, I hold a Bachelor of Science degree in Economics. I'm by no means an expert, but one of the main things economics students learn is that minimum prices, or salaries when we're talking about labor do nothing but cause what is called a dead-weight loss. This is a fancy-sounding word that basically means the economy isn't running efficiently because it's not operating at equilibrium. There are transactions that are no longer being made because the economy is forced out of equilibrium.
Methodology
I'll dive in first and talk a little bit about my methodology. Some of you may remember, late last week I posted a poll in the discussion thread Here. It was there that I asked "What's the minimum salary you'd be willing to sign a contract for?
Here's a screenshot of the results:
Unfortunately, Google Forms lacks a bit in the display department. I couldn't find a way to get it to label everything better. I'll give you the highlights, 34.3% said they'd sign for the minimum $500,000 (12 of the 35 responses). 25.7% said they'd sign for $1,000,000 (9/35) and so on and so forth.
I initially did my calculations when there were only 32 responses, so the numbers might be a little different now, but I'm far too lazy to go through and do it all again. I used the responses to create a Labor Supply Curve. I operated under the assumption that if you'd be willing to take $500,000 that you'd also be willing to take $1,000,000 and so on and so forth. Simply, if you chose the $500,000 minimum, you contributed a vote for each of the tiers because it only makes sense you'd happily take more money to do the same job. I realize this isn't 100% true for everybody because they want to help their team by opening salary cap room. I didn't take this into account because I honestly don't know how I'd fit that into the labor supply model.
There are 184 starting positions available in the NSFL (including offensive line). To find my Labor Supply Curve, I set the total number of responses (32) equal to the total starting positions available (184) and then used the percent of votes for each tier to determine the amount of people that would be willing to take each tier of salary if there were 184 responses.
I then used Excel to calculate a line of best fit. The Labor Supply Curve equation that I calculated turned out to be: y = 32,312x - 3,000,000. Y equals the salary, and X is the number of players.
After determining the Labor Supply Curve, it only made sense to calculate the Labor Demand Curve. To calculate this I took the total salary cap available for the 8 NSFL teams, a whopping $600,000,000 and divided it by each salary tier to determine how many people the NSFL would employ at that average salary. To not end up with huge numbers, I set the highest end at 184, or the total number of starting positions available. We can debate all day about how I should have done stuff differently and all, and if I wanted to put even more time into this I could. I still think this method will give us a decent look at what we're dealing with.
With my data points, I again used Excel to determine a line of best fit, where my Labor Demand Curve calculated out to be: y = -50,519x + 10,000,000. Again, Y is the salary, X is the amount of labor.
That's all fine and dandy, but what does it matter?
Using the supply and demand curves, we can find the equilibrium price (salary) and quantity (players) the NSFL would achieve. The numbers aren't exactly accurate to the NSFL, but it can show us a good model.
Using the Labor Supply and Demand Curves
Here is a graph of the supply and demand curves.
We can calculate the point of equilibrium by setting the two equations equal to each other and solving for X.
-50519x+10000000=32312x-3000000
13000000=82831x
156=x
This shows us the equilibrium quantity in the NSFL for labor. To solve for price (Salary) we simply need to plug X=156 into one of the equations.
32312(156)-3000000=2,040,672.
Graph:
In equilibrium conditions, the NSFL would employ 156 players at a salary of $2,040,672. But Molarpistols! You said there are 184 positions available in the NSFL, why aren't they all filled?
While the teams would love to employ everybody that wants to play until all their positions are filled, it's simply not possible due to the supply of labor. If more people were willing to take less money, it's certainly plausible, even likely that the Labor Supply Curve would shift, giving us a new equilibrium. I don't feel like calculating it currently, but there's a good chance we'd eventually find one where all positions are filled.
Are We at Equilibrium?
No! Various minimum wages have caused the average salary in the NSFL to rise above the equilibrium salary. I took all of the current NSFL contract data, each players salary per season for however many seasons they were signed and averaged it all out.
The average salary per season in the NSFL is $2,947,432.76. If we solve for X at that price, we find out 144.XX players would be employed by the NSFL (I forgot to write down the decimals, since you can't really have a fraction of a player and I didn't use the decimals in later maths). Coincidentally, this is the number of starting positions available if all 8 teams have a full offensive lines filled with OL Bots. I did say coincidentally, and I do think it is complete coincidence but I thought it was kind of fitting.
Here is a graph showing the average salary:
Salary conditions as they are, 12 players that would be employed under equilibrium conditions are no longer employed. We can calculate the deadweight loss (the cost born by society (NSFL) due to market inefficiency.)
The deadweight loss is $5,440,564.56, which means that the NSFL economy is missing out on that five million that would be spent if we were at equilibrium. Minimum salaries in the NSFL have caused the average salary to rise above the equilibrium level that the Labor Supply and Labor Demand curve have dictated.
And for the umpteenth time, there is again talk about raising the minimum wage further. If I was less lazy, I could go through each of the ideas being thrown around about raising the minimum wage, but alas, I am lazy. Instead, I decided to go through and use an example.
I upped every single contract value by $500,000 per season, which would raise the average NSFL salary to $3,447,432.76.
By doing this, we end up increasing the dead-weight loss in the NSFL Economy to a total of $18,991,270.26.
That's an awful lot of economic activity not taking place due to a simple $500,000 increase in salary, that doesn't seem all that far-fetched when looking at a few of the ideas floating around to increase minimum salaries.
Summary
I've gone through and showed you a model for the supply and demand of labor (players) in the NSFL, based on data I retrieved and/or constructed. Using this, I calculated the optimal level of salary and quantity of players based off of these supply and demand equations.
I then showed where the current salary lies, based off of all the available NSFL contract data. This allowed me to calculate the expected number of players at that salary. The average salary in the NSFL is higher than the equilibrium salary calculated by the supply and demand functions. Since we're not operating at equilibrium, there is bound to be what economists call a "Dead-weight loss", which simply means the amount of economic activity being lost by not producing at equilibrium.
Conclusions
What conclusions can we draw from this model?
We can practically guarantee that raising the minimum salary would raise the average salary across the NSFL. By how much, and to what degree of damage is hard to say. Raising the amount of dollars paid to each player won't really have an effect on the Labor Supply Curve, as there was already a fair proportion of the player base willing to take minimum wage.
Instead, rising salaries would eventually cause NSFL teams to be unable to afford to employ more players. The DSFL might fill out, and enough people could go inactive that it doesn't really matter in the end. However, if recruitment picks up and we're able to see a sustainable amount of players, the NSFL simply won't be able to employ everybody willing to make a player and remain active.
Luckily, the NSFL is fake dollars, so we can effectively print out more and raise the salary cap for each team. Alternatively, or possibly even simultaneously we could increase the number of teams in the NSFL. Each of these activities would shift the Labor Demand Curve to the right like the following poorly drawn MS Paint example.
I didn't do any calculations for this new Labor Demand Curve, but a simple glance will show that the equilibrium salary would rise, as would the equilibrium quantity of labor (players). The specifics of the shift of the curve would need to be known to understand the exact effect. Depending on the shift, salary could go up by a much higher amount than the quantity, they could go up in proportion to each other, or they could even shift to a point where a higher amount of players is demanded in a greater proportion than the salary paid.
All we'll manage to do by raising contract minimums is make everybody happy for a few seasons until the NSFL dies, or find ourselves in the same quandary we're in now and have to do it all over again. The only thing coming out of raising minimum wage is an increase in the overall price level. This is called inflation.
I welcome any and all comments and criticisms. Someday I might be able to write this more coherently and in a more "explain it like I'm five" type of words. I'm satisfied with my nerdy ramblings and my poorly drawn MS Paint graphics for now.
Thanks for stopping by and wasting some time being and Econ nerd with me!
Code:
Ready for Grading: 1819 words this is saying, and several hours of calculations/graph making[div align=center]
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Jurisprudence Jones, OL ![[Image: cYhSwFY.png]](https://i.imgur.com/cYhSwFY.png)
![[Image: h5Ta7H1.png]](https://i.imgur.com/h5Ta7H1.png)
![[Image: XSfVUgo.png]](https://i.imgur.com/XSfVUgo.png)
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