Question

The following table shows the U.S. rates of personal tax as of the year 2016, and these tax rates presented in this table are marginal tax rates. (This is Table 3.7 on Page 74 of your textbook.)

Single Taxpayers	Married Taxpayers Filing Joint Returns	Tax Rate (%)
0-$9,275	0-$18,550	10.0
$9,276-$37,650	$18,551-$75,300	15.0
$37,651-$91,150	$75,301-$151,900	25.0
$91,151-$190,150	$151,901-$231,450	28.0
$190,151-$413,350	$231,451-$413,350	33.0
$413,351-$415,050	$413,351-$466,950	35.0
$415,051 and above	$466,951 and above	39.6

Based on this table, answering the following questions:

(Please show your intermediate processes, instead of just a final number for your answers. Only round your final answers to two decimal places.)

(a1) Suppose there is a person called Alpha who has an annual income of $300,000 and Alpha’s spouse has an annual income of $20,000. What dollar amount of tax do Alpha and Alpha’s spouse each need to pay respectively, if they choose to file their taxes separately? What dollar amount of tax do they need to pay if they choose to file their taxes jointly?

(a2) What are the average tax rates for Alpha and Alpha’s spouse respectively, if they choose to file separately? What is the average tax rate if they choose to file jointly?

(b1) Suppose there is another person called Beta who has an annual income of $160,000 and Beta’s spouse also has an annual income of $160,000. What dollar amount of tax do Beta and Beta’s spouse each need to pay respectively, if they choose to file their taxes separately? What dollar amount of tax do they need to pay if they choose to file their taxes jointly?

(b2) What are the average tax rates for Beta and Beta’s spouse respectively, if they choose to file separately? What is the average tax rate if they choose to file jointly?

(c) Based on what you obtained from (a1) to (b2), what are the conclusions you could infer regarding the ways of filing taxes? (What are the advantages and disadvantages of these two ways?)

Answer 1

a1) Alpha's Income = $300,000

Alpha has to pay marginal tax under each slab as shown in the table below

ON 1stslab : $ 9275,  Tax = 9275 x 10% = 927.50 . Balance Income to be taxed = 300000 - 9275 = 290725

On 2nd slab : $37650 - 9275 = 28735 ,Tax = 28735 X 15% = 4256.25. Balance Income to be taxed = 290725 - 28735 = 262,350

On 3rd slab : $91150 - 37650= 53500 ,Tax = 53500 X 25% = 13375. Balance Income to be taxed = 262350 - 53500 = 208850

On 4th slab : $190150 - 91150= 99000 ,Tax = 99000 X 28% = 27720. Balance Income to be taxed = 208850 - 99000 = 109850

On 5th slab : $413,350 - 190150= 223200 ,Tax = 109850 X 33% = 36250. Balance Income to be taxed = 109850 - 109850 = 0

Similarly others can be checked from the tables given below :

Slab	Tax Rate T	Amount to be taxed under the slab A	Marginal Tax Paid under the slab (A x T%)	Balance Income to be taxed (Income - Income already Taxed)
0-$9,275	10.00	9275	927.50	290,725
$9,276-$37,650	15.00	28,375	4,256.25	262,350
$37,651-$91,150	25.00	53,500	13,375.00	208,850
$91,151-$190,150	28.00	99,000	27,720.00	109,850
$190,151-$413,350	33.00	109,850	36,250.50	-
$413,351-$415,050	35.00	-	-	-
$415,051 and above	39.60	-	-	-
Total	27.51%		82529.25

For Alpha's wife

Slab	Tax Rate T	Amount to be taxed under the slab A	Marginal Tax Paid under the slab (A x T%)	Balance Income to be taxed (Income - Income already Taxed)
0-$9,275	10.00	9275	927.50	10,725
$9,276-$37,650	15.00	10,725	1,608.75	-
Total Tax	12.68%		2536.25

If they File their taxes jointly, combined income would be 3,20,000

The taxes would be paid as below

Slab	Tax Rate T	Amount to be taxed under the slab A	Marginal Tax Paid under the slab (A x T%)	Balance Income to be taxed (Income - Income already Taxed)
0-$18,550	10.00	18550	1,855.00	301,450
$18,551-$75,300	15.00	56,750	8,512.50	244,700
$75,301-$151,900	25.00	76,600	19,150.00	168,100
$151,901-$231,450	28.00	79,550	22,274.00	88,550
$231,451-$413,350	33.00	88,550	29,221.50	-
Total Tax Paid	25.32%		81,013.00

The taxes paid by

Alpha = $82529 , Alpha's wife = 2536.35 , Jointly = $81013

a2) Average Tax rate for Alpha = Tax Paid/ Total Income = 82529/300000 = 27.51%

Average Tax rate for Alpha's wife = 2536.35 / 20000 = 12.68%

Their Joint Average Tax rate = 81013 / 320000 = 25.32%

b1) Beta & Beta's wife both have $160,000 annual income. Both will pay equal amount of tax, if they file taxes separately as shown below:

Slab	Tax Rate T	Amount to be taxed under the slab A	Marginal Tax Paid under the slab (A x T%)	Balance Income to be taxed (Income - Income already Taxed)
0-$9,275	10.00	9275	927.50	150,725
$9,276-$37,650	15.00	28,375	4,256.25	122,350
$37,651-$91,150	25.00	53,500	13,375.00	68,850
$91,151-$190,150	28.00	68,850	19,278.00	-
Total Tax Paid	23.65%		37,836.75

If they Pay Jointly, The tax paid would be as shown below

Slab	Tax Rate T	Amount to be taxed under the slab A	Marginal Tax Paid under the slab (A x T%)	Balance Income to be taxed (Income - Income already Taxed)
0-$18,550	10.00	18550	1,855.00	301,450
$18,551-$75,300	15.00	56,750	8,512.50	244,700
$75,301-$151,900	25.00	76,600	19,150.00	168,100
$151,901-$231,450	28.00	79,550	22,274.00	88,550
$231,451-$413,350	33.00	88,550	29,221.50	-
Total Tax Paid	25.32%		81,013.00

The taxes paid by

Beta = $37836.75 , Beta's wife = $37836.75 , Jointly = $81013

b2)

Average Tax rate for Beta = Tax Paid/ Total Income = 37836.75/160000 = 23.65%

Average Tax rate for Beta's wife = 37836.75/160000 = 23.65%

Their Joint Average Tax rate = 81013 / 320000 = 25.32%

c) If one of the spouse is in lower tax slabs, it would be better to file separately.

If the combined income takes you to higher tax slab, better to file jointly.