Question 57352This question is from textbook Applied College Algebra
: The economist Arthur Laffer conjectured that if taxes were increased starting from very low levels, then the tax revenue received by the government would increase. But, as tax rates continued to increase, there would be a point at which the tax revenue would start to decrease. The underlying concept was that if taxes were increased too much, people would not work as hard because much of their additional income would be taken from them by the increase in taxes.
a. Assume that Laffer's curve is given by R(x) = -6.5(x^3 + 2x^2 - 3x) / x^2+x+1 where R is measured in trillion of dollars. Use a graphing calculator to determine the tax rate x, to the nearest tenth of a percent, that would produce the maximum tax revenue. (Hint: Use a domain of [0,1] and a range of [0,4].) b. Assume that Laffer's curve is given by R(x)= -1500(x^3+2x^2-3x)/x^2+x+400. Where R is measured in trillions of dollars. Use a graphing calculator to determine the tax rate x, to the nearest tenth of a percent, that would produce the maximum tax revenue.
This question is from textbook Applied College Algebra
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! a. Assume that Laffer's curve is given by R(x) = -6.5(x^3 + 2x^2 - 3x) / x^2+x+1 where R is measured in trillion of dollars. Use a graphing calculator to determine the tax rate x, to the nearest tenth of a percent, that would produce the maximum tax revenue. (Hint: Use a domain of [0,1] and a range of [0,4].)
-------------
Using a TI-83 I find x=0.39709951 or 0.397 or 39.7%
---------------------
b. Assume that Laffer's curve is given by R(x)= -1500(x^3+2x^2-3x)/x^2+x+400. Where R is measured in trillions of dollars. Use a graphing calculator to determine the tax rate x, to the nearest tenth of a percent, that would produce the maximum tax revenue.
0 solutions
x=0.53455305...=53.5%
Cheers,
Stan H.
|
|
|
