Suppose that a state's tax code states that tax liability is % on the first of taxable earnings and % on the remainder. Find the constants a and b in the tax function T(x) such that and exists.
A) and
B) and
C) and
D) and

Question

Suppose that a state's tax code states that tax liability is  % on the first  of taxable earnings and  % on the remainder. Find the constants a and b in the tax function T(x)  such that  and  exists.
A) and 
B) and 
C) and 
D) and

Quizplus · Accepted Answer

We need to find constants a and b such that the tax function T(x) satisfies the given conditions:

T(11) = 11% 
T'(11) = 11.25%

Let x be the taxable earnings. Then, the tax liability can be expressed as:

T(x) = {a for 0 ≤ x < 11 
b(x - 11) + a for x ≥ 11

To find a and b, we use the given conditions:

T(11) = a = 11%

T'(11) = b = 1.25% / 1 = 11.25%

Therefore, the constants a and b are 11% and 11.25%, respectively, which corresponds to choice B.

Suppose That a State's Tax Code States That Tax Liability