Assume that, without taxes, the consumption schedule for an economy is as shown below:
GDP, Consumption,
Billions Billions
$100 ..........$120
200 .......... 200
300 .......... 280
400 .......... 360
500 .......... 440
600 .......... 520
700 .......... 600
a. Graph this consumption schedule and determine the size of the MPC.
b. Assume that a lump-sum (regressive) tax of $10 billion is imposed at all levels of GDP. Calculate the tax rate at each level of GDP. Graph the resulting consumption schedule and compare the MPC and the multiplier with those of the pretax consumption schedule.
c. Now suppose a proportional tax with a 10 percent tax rate is imposed instead of the regressive tax. Calculate and graph the new consumption schedule and note the MPC and the multiplier.
d. Finally, 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 and graph the new consumption schedule, noting the effect of this tax system on the MPC and the multiplier.
e. Explain why proportional and progressive taxes contribute to greater economic stability, while a regressive tax does not. Demonstrate, using a graph similar to Figure.
Built-instability

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Surplus Deficit GDP GDPGDP3 Real domestic output, GDP