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Unformatted text preview: Homework Assignment #1 6.2 In Missouri, federal income taxes are deducted from income before calculating state taxes. Write out and solve the system of equations which describes the state and federal taxes and charitable contributions of the firm in Example 1 if it were based in Missouri. Answer: Note that I’ve corrected the question. The formulas for aftertax profits and for federal tax are unchanged from Example 1. The difference is in the computation of state tax S . State tax is now calculated based on income of $100,000, minus charitable contributions C and federal tax F . Since the state income tax rate is 5%, the state tax is S = . 05(100 , 000 C F ). This yields the following system C + 0 . 1 S + 0 . 1 F = 10 , 000 . 05 C + S + 0 . 05 F = 5 , 000 . 4 C + 0 . 4 S + F = 40 , 000 . We form the augmented matrix 1 . 1 . 1 10000 . 05 1 . 05 5000 . 4 . 4 1 40000 (2) . 05(1)→ 1 . 1 . 1 10000 . 995 0 . 045 4500 . 4 . 4 1 40000 (3) . 4(1)→ 1 . 1 . 1 10000 0 0 . 995 0 . 045 4500 . 36 . 96 36000 (3) ( . 36 /. 995)(2)→ 1 . 1 . 1 10000 0 0 . 995 . 045 4500 . 94372 34372 We can find the answer by completing the row reduction or by substituting from the bottom up. Using the latter and rounding to the nearest dollar, the third equation yields F = 36 , 422. We substitute in the second equation to find S = 2875. Then the first equation tells us that C = 6070....
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 Fall '08
 STAFF
 Taxation in the United States, Income tax in the United States, unique solution

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