Question

The algebra of tax multipliers 

Consider a small country that is closed to trade, so its net exports are equal to zero. 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= 30 + 0.5 x DI

 G= 40

 I = 70

 Initially, this economy had a lump sum tax. Suppose net taxes were $30 billion, so that disposable income was equal to Y - 30, 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 12%. Because consumers retain the remaining 88% of their income, disposable income is now equal to 0.88Y. In this case, the economy's aggregate output demanded is _______ 

  Under a proportional tax on income of 12%, the spending multiplier is approximately _______ . Therefore, if the government decided to increase spending by $10 billion without raising tax rates, this would increase the economy's aggregate output demanded by approximately _______ 

 A $10 billion increase in government purchases will have a larger effect on output under a _______ 

Answer 1

We consider a closed Economy.

So, the aggregate output demanded is,

Y = C + I + G