Question

Assume that, without taxes, the consumption schedule for an economy is as shown in the table below. Impose a progressive tax such that the tax rate is 0 percent when GDP is $100, 5 percent at $200, 10 percent at $300, 15 percent at $400, and so forth. Determine the new consumption schedule, noting the effect of this tax system on the MPC (tax inclusive) and the multiplier.


Instructions: In the table below, enter your answers (except the MPC) as whole numbers. For the MPC, round your answers to 2 decimal places.

	GDP, Billions Consumption Before Tax, Billions Tax, Billions Disposable Income, Billions Consumption After Tax, Billions Tax Rate, Percent MPC 100 120 0 null 200 200 300 280 400 360 500 440 600 520 700 600

Answer 1

Answer

Disposable Income = Total income - Total Tax

= GDP Billions - Tax Billions

Marginal propensity to consume (MPC) = change in consumption due to change in income (Y) or change in disposable income(Y_d)

Or MPC = ∆C/∆Y

For taxable or after-tax income, MPC = ∆C/∆Y_d

Tax rate is 0 percent for GDP = $100

Tax rate is 5 percent for GDP = $200

Tax rate is 10 percent for GDP = $300

Tax rate is 15 percent for GDP = $400, and so forth

Now completing the given table below

1	2	3	4	5	6	7
GDP Billions	Consumption Before Tax,Billions	Tax, Billions	Disposable Income, Billions	Consumption After Tax,Billions	Tax Rate,Percent	MPC
100	120	0	100	120	0	null
200	200	10	190	192	5	0.8
300	280	30	270	256	10	0.8
400	360	60	340	312	15	0.8
500	440	100	400	360	20	0.8
600	520	150	450	400	25	0.8
700	600	210	490	432	30	0.8

For 100 billions GDP, the consumption is 120 billion before tax., i.e. consumption is greater than GDP by 20 billions. This 20 billion is the borrowing of the economy. From the first two columns of the table, we see that the consumption before tax is rising by 80 billions for every 100 billions increase of GDP.

So MPC = ∆C/∆Y_d = 80/100 = 0.8

From the 7th column of the table, we see that this MPC is constant at 0.8 , so

Multiplier = 1/ (1-MPC)

or, Multiplier = 1/(1-0.8) = 1/0.2 = 5

The tax rate is progressive, and after 100 billions GDP, the tax rate rises by 5 percent for every 100 billions increase of GDP.The sixth column of the table shows the percent of tax for the income. The third column of the table shows total tax for each GDP in billions.The calculated disposable incomes are shown in the fourth column of the table.

Now for 100 billion GDP, consumption is 120 billion , and there is no tax for 100 billion GDP. For rest of the incomes(GDP), the consumption after tax has been calculated using the following method,

MPC=  ∆C/∆Y_d

Or, ∆C = MPC * ∆Y_d

Here MPC = 0.8

So, ∆C = 0.8 * ∆Y_d

When the disposable income rises to 190 billion ,

then ∆Y_d = 190 - 100 = 90 billion.

Therefore, ∆C = 0.8 * 90

Or,  ∆C = 72

For the previous disposable income, consumption was 120 billion. For 190 billion disposable income, it will be,,

120 + 72 = 192 billion.

In this way, the new consumption schedule has been calculated.

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