Chapter 29A - 719-720_CH29A_Econ.qxp 11:29 AM Page 719 >...

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>> 719 Chapter 29 Appendix: 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 in- crease in real GDP in the form of taxes, where t , the tax rate, is a fraction between 0 and 1. And let’s repeat the exercise we carried out in Chapter 27, where we consider 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 t )) × $50 billion, and so on. So the total effect on real GDP is +
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Chapter 29A - 719-720_CH29A_Econ.qxp 11:29 AM Page 719 >...

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