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>> 319 Chapter 12 Appendix: Taxes and the Multiplier In the chapter, we described how taxes reduce the size of the multiplier and act as an automatic stabilizer for the economy. Let’s look a little more closely at the mathemat- ics of how this works. Specifically, let’s assume that the government “captures” a fraction t of any in- crease in 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 consider the effects of a $50 billion increase in investment spending. The $50 billion increase in investment spending initially raises GDP by $50 billion (the first round). In the absence of taxes, disposable income would rise by $50 bil- lion. But because part of the rise in GDP is collected in the form of taxes, disposable income only rises by (1 - t ) × $50 billion. The second-round increase in consumer 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 GDP is
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