0:00
All right, guys.
00:01
So this is more of an economics question.
00:04
So i had to do some research.
00:06
So i didn't study economics.
00:07
But that's okay.
00:08
I know how to do this problem, so i can help you.
00:11
So this function, f of x is the distribution list of income right here.
00:16
It describes it.
00:18
So it's how much different percent of populations, how much income they get of the total country's income.
00:28
So the lorentz curve, it's kind of a neat read.
00:32
It just goes basically from zero to one, or some do it from zero to 100%, because obviously 100 % of the people have 100 % of the income.
00:44
0 % of the people have 0 % of the income because there ain't nobody making money.
00:49
100 % of the people is everybody.
00:51
I did it from 0 to 1, so i used the decimals.
00:55
All right.
00:55
So this point up here at one, it has to go to 1 -1.
01:01
Along the x -axis, so to speak, that's the percent of the population of the country or the group, the population of whatever group you're talking about.
01:14
Going up the vertical axis, the y -axis is the percent of the income of the country or of the group of the population.
01:25
You know, if you think of it for a family, you know, 50 percent, you know, there's two kids that don't make any money.
01:32
Well, they're the bottom earners.
01:35
Those two kids, 50 percent of the population and actually make zero of the family's income because the kids don't make anything.
01:43
And then you got the parents, you know, and so you start ranking people based on their income.
01:48
And one parent makes more than the other, assume, you know, they might be closed to the same, but one makes a little more.
01:54
Mom, dad, who knows, it could be either.
01:58
So when you get to about 75%, well, now all of a sudden it jumps up to, you know, maybe it's close to 50 % of the income is, you know, is made by 75 % of the people.
02:10
And then 100 % of the family makes 100 % of the money when you add the other spouse in, so to speak.
02:17
Okay.
02:18
Anyways, it's kind of needs, shows the distribution of wealth.
02:22
So you notice, as you know, for like 20 % of the population, they don't make that big of a percent of the income.
02:29
But then as you get to 80 % of the population, it gets really, really big.
02:33
That blue dotted line is if it was perfectly balanced, if 20 % of the people made 20 % of the income and 30 % of the people made 30 % of the income.
02:42
So everyone basically is making the same.
02:44
Yeah, all right.
02:45
All right.
02:46
That's what it means.
02:46
It's kind of cool.
02:47
So i did it on desmos.
02:49
There it is.
02:49
The red graph is the lorentz curve.
02:52
The blue line is like kind of the equilibrium line or the it's perfectly balanced if you had to do this by hand so that's why i got the blank graph there so what you would have to do is you would have to start plugging in you make like this little table and you basically just start putting numbers in for x so you like i'll just use the point two point four you could do point one point two point three points but doesn't matter point two point four point six point eight and one and remember one has to equal one a hundred percent the population makes a hundred percent of the income has to zero percent of the population make zero so you start here at zero zero we're gonna end here at one comma one and then connect those dots with the blue dotted line and that's your equilibrium line don't know if you need that or not and so when you start plugging like point two and you plug it into your calculator square times it by the fraction 15 over 16 write that number down take the 1 over 16 times it by 0 .2 take those two numbers add them up um it looks like looking at the graph it's about 0 .0 5 you know and you just kind of put a dot there i did it on desmos it looks like it's about right here and then at point four it's at 1 .1 .1 .1 so it's just below the point two at point six.
04:33
It looks like it's just below the point four.
04:37
So jump pretty quick there.
04:41
About there.
04:42
And then point eight we're at let's see about here about right there.
04:52
I'm just kind of looking at my graph and then i you know point nine is one of the ones we had to find and and so at 0 .9, which is about halfway between 0 .8 and the 1, we're about right here.
05:06
And it's a curve.
05:07
And so notice the small percent of the popularity don't make much, and then it curves up, up, up, but, but, but, okay.
05:14
So that's how you would graph the graph it by hand.
05:17
You just have to plug these numbers in and you get some numbers here.
05:21
Do it in your calculator.
05:24
All right.
05:25
Now, here is what it means.
05:26
And so it says compute f of 0 .04, or 0 .4.
05:32
So f of 0 .4, and i have it on the graph there, is 0 .1767.
05:40
So what this means is 40%, the bottom 40%, say it correctly, lowest 40 % of earners makes 17 .6, 7 % of the total income.
06:17
That's what that number means.
06:24
Okay? so only, you know, think about, you know, if you have 100 people working, 40 of them, the lowest 40 of those 100 people is only bringing in 17 .67, not even 18 % of the total income of the group, right? 40 of the people out of the hundred are only bringing in like less than 18 % of the income.
06:51
Okay.
06:53
Now when you get to f of point nine and that number is 0 .8194, 0 .8194.
07:04
So what that means is the bottom 90 % of the earners, you know, so if you ranked every all hundred people from who makes the least to who makes the most? the bottom 90, think of 90 out of 100 people...