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KW_Macro_Ch_12_Appendix_Taxes_and_the_Multiplier

KW_Macro_Ch_12_Appendix_Taxes_and_the_Multiplier - appendix...

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>> Taxes and the Multiplier In the chapter, we described how taxes that depend positively on real GDP reduce the size of the multiplier and act as an automatic stabilizer for the economy. Let’s look a little more closely at the mathematics of how this works. Specifically, let’s assume that the government “captures” a fraction t of any increase in real GDP in the form of taxes, where t , the tax rate, is a number between 0 and 1. And let’s repeat the exercise we carried out in Chapter 10, where we consid- er the effects of a \$50 billion increase in investment spending. The \$50 billion increase in investment spending initially raises real GDP by \$50 billion (the first round). In the absence of taxes, disposable income would rise by \$50 billion. But because part of the rise in real GDP is collected in the form of taxes, dis- posable income only rises by (1 t ) × \$50 billion. The second-round increase in con- sumer spending, which is equal to the marginal propensity to consume (MPC) multiplied by the rise in disposable income, is MPC × (1 t ) × \$50 billion. This leads to a third-round increase in consumer spending of ( MPC × (1 t )) × ( MPC × (1

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KW_Macro_Ch_12_Appendix_Taxes_and_the_Multiplier - appendix...

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