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20 TAXES &amp; THE MULTIPLIER

# 20 TAXES &amp; THE MULTIPLIER - 1 SECTION 20 HOW INCOME...

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1 SECTION 20: HOW INCOME TAXES AFFECT THE MULTIPLIER

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2 HOW DO INCOME TAXES INFLUENCE THE MAGNITUDE OF THE MULTIPLIER? Suppose the mpc = .75 Suppose we consider an economy without taxes. Suppose autonomous spending increases by \$100. The successive increases in output will be Round 1: \$100 Round 2: \$100 x .75 = \$75 Round 3: \$100 x .75 x .75 = \$75 x .75 = \$56.25 Round 4: \$100 x (.75) 3 = \$42.19 Round 5: \$100 x (.75) 4 = \$31.64 And so forth
3 Now consider the same economy with an income tax of, say, 20%. Suppose autonomous spending increases by \$100. The successive increases in output will be as follows: Round 1: \$100 Because there is a 20% tax, in round 2, the worker who earned \$100 only has \$80 of disposable income. Given an mpc of .75, the worker spends 75% of the \$80. This yields new spending, and new output of \$60. Round 2: \$100 x (1 - .20) x .75 = \$100 x .60 = \$60 Round 3: \$100 x (1 - .20) x .75 x (1 - .20) x .75 = \$100 x (.60) 2 = \$36 Round 4: \$100 x (.60) 3 = \$21.60 Round 5: \$100 x (.60) 4 = \$12.96

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4 COMPARISON OF THE MULTIPLIER EFFECT WITH AND WITHOUT TAXES mpc = .75 mpc = .75; tax rate = .20 Round 1: \$100.00 \$100.00 Round 2: \$ 75.00 \$ 60.00 Round 3: \$ 56.25 \$ 36.00 Round 4: \$ 42.19 \$ 21.60 Round 5: \$ 31.64 \$ 12.96 And so forth Sum \$100 x [1/(1 - .75)] \$100 x [1/(1 – {.75 x (1 - .20)}] \$100/ (1 - .75) \$100 / (1 - .60) \$100/ .25 \$100 / .40 \$400 \$250
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20 TAXES &amp; THE MULTIPLIER - 1 SECTION 20 HOW INCOME...

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