Assume That Without Any Taxes the Consumption Schedule for an Economy

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(a)What are the MPC,MPS,and the size of the multiplier?
(b)Assume a lump-sum tax of $10 billion is imposed at all levels of GDP.Determine consumption and the tax rate at each level of GDP by completing the following table.Is tax regressive,proportional,or progressive? Compare the multiplier under the lump-sum tax with the pre-tax multiplier.

(c)Assume instead that a proportional tax of 10% is imposed at all levels of GDP.Determine consumption at each level of GDP by completing the following table.Compare the multiplier under the proportional tax with the multiplier under the lump-sum tax.Explain why a proportional or progressive tax system contributes to greater economic stability as compared with the lump-sum tax.

(a)The MPC is .8.(160/200).The MPS is .2 (1 - .8).The multiplier is 5 (1/.2).
(b)The lump-sum tax reduces disposable income by $10 billion.Since the MPC is .8,consumption at each level of GDP falls by $8 billion.See the table below.

The lump-sum tax is a regressive tax because the average tax rate decreases as GDP increases.Since the after-tax MPC and MPS are unchanged,the multiplier under the lump-sum tax is the same as the pre-tax multiplier.
(c)Because the tax is 10% of GDP and the MPC is .8,consumption is reduced by the amount of the tax multiplied by .8.For example,when GDP is $800 billion,taxes are $80 billion and disposable income is reduced by $80 billion.This decrease in disposable income reduces consumption by $64 billion.See the table below.

Under the proportional tax,the after-tax MPC is .72 ($144/$200).As a result,the after-tax MPS is .28 (1 - .72)and the multiplier is 3.57 (1/.72).Therefore,the multiplier is smaller.
Compared to a regressive tax system,a proportional or progressive tax system takes a smaller portion of low income and a bigger portion of high incomes.Thus,a proportional or progressive tax system leaves more disposable income for spending during low-income periods and less disposable income for spending during expansionary phases.As a result,any change in aggregate expenditures produces a smaller change in GDP.In other words,the multiplier is smaller and there is greater built-in stability under a proportional or progressive tax system.

Assume That Without Any Taxes the Consumption Schedule for an Economy

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