14. The algebra of tax multipliers Aa Aa Consider a small country that is closed

Question

14. The algebra of tax multipliers Aa Aa Consider a small country that is closed to trade, so its net exports are equal to zero. Suppose the following equations describe the economy of this country in billions of dollars, where C is consumption, DI is disposable income, I is investment, and G is government purchases: C 300.8DI G-50 I- 60 Initially, this economy had a lump sum tax. Suppose net taxes were $50 billion, so that disposable income was equal to Y- 50, where Y is real GDP. In this case, this economy's aggregate output demanded was Suppose the government decides to increase spending by $10 billion without raising taxes. Because the spending multiplier is , this will increase the economy's aggregate output demanded by Now suppose that the government switches to a proportional tax on income of 10%. Because consumers retain the remaining 90% of their income, disposable income is now equal to 0.90Y. In this case, the economy's aggregate output demanded is Under a proportional tax on income of 10%, the spending multiplier is approximately government decided to increase spending by $10 billion without raising tax rates, this would increase the economy's aggregate output demanded by approximatelyy . Therefore, if the A $10 billion increase in government purchases will have a larger effect on output under a lump sum tax of $50 billion proportional tax of 10%

Explanation / Answer

(1) In equilibrium: Y = C + I + G

Y = 30 + 0.8DI + 50 + 60 = 140 + 0.8DI

When DI = Y - 50,

Y = 140 + 0.8 x (Y - 50) = 140 + 0.8Y - 40

0.2Y = 100

Y = 500 ($ Billion)

(2)

Spending multiplier= 1 / (1 - MPC) = 1 / (1 - 0.8) = 1 / 0.2 = 5

So, as government spending rises by $10 billion, aggregate output will rise by $10 billion x 5 = $50 billion

(3) DI = 0.9Y

Y = 140 + 0.8 x 0.9Y = 140 + 0.72Y

0.28Y = 140

Y = 500

(4)

Spending multiplier = 1 / (1 - 0.72) = 1 / 0.28 = 3.57

As spending rises $10 billion, aggregate output rises by $10 billion x 3.57 = $35.7 billion

(5) Effect of rise in spending has larger effect on output under lump-sum tax of $50 billion.

Note: First 5 sub-questions are answered.

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