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I would tend to agree with you on this point.
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__________________
i think sex is better than logic, but I can't prove it "The music business is a cruel and shallow money trench, a long plastic hallway where thieves and pimps run free and good men die like dogs every day. And there's also a bad side." -- Hunter S. Thompson |
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Where I'm from, taxes do not run economic performance, i.e., they are not that important. Where I'm from, cutting tax rates reduces tax revenue. I have no idea where you are coming from except that I have seen supplyside nonsense permeate flat tax proposals, national sales tax proposals and fair tax proposals. Why? B/c tax cuts for the rich pushes the tax burden down screwing the poor yet Supp.Side Econ justifies it to the masses. A Short Play Rich Guy: You mean cutting my taxes helps everyone by generating more tax revenue? Supply Sider: Yes sir! Rich Guy: By all means then, cut my taxes...I like to pitch in! |
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Let's begin with Rolle's Theorem: Suppose that y= f(x) is continuous at every point of the closed interval, [a,b] and differentiable at every point of its interior (a,b). If f(a)= f(b), then there is at least one number c in (a,b) at which f prime of c = 0. If we take the amount of government revenue as a function of tax rates, then that function can be defined as f(x). For the domain, we can have tax rates from 0% to 100%, so lets set a= 0% and b= 100%. We can see that f(a)= f(b) through the application of a limit to infinity at both 0% and 100%. When a government has a tax rate of 0%, the revenue will be $0, so f(a)= 0. When a government has a tax rate of 100%, it can also been seen that, while it may make an initial sum, the long term gain will be $0 after the first tax collection. Therefore, f(b)= $0 and f(a)= $0, so f(a)= f(b). The function would be continuous at every point because every tax rate would have an accompanying government revenue, and because the change would always be measurable due to the use of real world numbers, the function would be differentiable at every point as well. As you can see by looking at every possibility for tax rates, there is a closed domain of [0,100] because those domain numbers are all of the possibilities. Therefore, through application of this theorem to our function of government revenues, we can see that there is a number c, in (a,b) such that the derivative of c (f prime of c) is equal to 0. This point is a critical point, as the definition of a critical point is "An interior point of the domain of a function f where f prime is zero or undefined." Now I will use another theorem, the First Derivative Theorem for Local Extreme Values, which states that: if f has a local maximum or minimum value at an interior point c of its domain, and if f prime is defined at c, then f prime of c equals 0. Through this theorem, you can see that all minimum and maximum values for a function are found at critical points, where the derivative of the function is equal to 0. However, there is one possibility for Rolle's Theorem that would invalidate this theory, and that is if every f(x) value had a derivative of 0. In this case, every point would be both a minimum and a maximum, making a horizontal line because f(a) and f(b) (the end points) have the same y value on the graph. However, we know this not to be the case, as it is possible to have some government revenue from tax rates, so there would be an f(x) value other than 0. Now that the existence of a minimum or maximum on the domain of our function has been proven, we must next prove that this single c value that has been proven to exist is indeed a maximum and not a minimum value. This is easy to prove. For the c value to be a minimum, it would need to exist below the 0 value for f(a) and f(b). Since it is physically not possible to have a negative value for government revenue off of tax rates, this c value must be a maximum. Now we have proved that there is a value of x, c, on the domain (a,b), where the value f(c) is a maximum value for the function f(x). Now if we go back to the value of a= 0% and b= 100%, we can see that the value of c is between 0% and 100%. At any point p for the tax rate, at which c < p < b, government revenue will increase when tax rates are lowered, and the derivative at that point will be negative.
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The only thing I ask of you is to think rather than to believe.
Last edited by White Fox; 07-08-2008 at 12:14 PM. |
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Cause and effect of two things that happen at approximately the same time have not been demonstrated. |
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My proposition for taxes would be to work to find what this critical point is by gathering long term statistical values for tax returns at a constant rate with other factors accounted for, and then to use small shifts, once again for long periods of time, to figure out what direction to go in, and then to go that way and figure it out. This process would take a very long time, and today's politics would probably mess it up completely.
__________________
The only thing I ask of you is to think rather than to believe.
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A person makes $400,000 and reports $350,000 of it. He is taxed 40% an is left with 210,000, he's paid 140,000 in income tax. Then he spends all that is left and is taxed at 6% and pays 15,600 + 140,000 = 155,600. A person makes $400,000 and reports all of it. He is taxed 35% and pays $140,000 in taxes. Then spends the $260,000 taxed at 6%, he is taxed a total of $15,600 + $140,000 = 155,600. I know you all think rich people are noble people and that they would never cheat their taxes, but consider that 40% of 50k is 20k.
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