Question

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=100+0.75×DI G= 50 I=80

Initially, this economy had a lump sum tax. Suppose net taxes were $40 billion, so that disposable income was equal to Y – 40, 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 5%. Because consumers retain the remaining 95% of their income, disposable income is now equal to 0.95Y. In this case, the economy's aggregate output demanded is ??

Under a proportional tax on income of 5%, 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 proportional tax of 5% OR proportional tax of 5%

Answer 1

C = 100+0.75Dt G=50 I=80

When Dt=Y-40

the Y = 100+0.75(Y-40)+50+80 So Y=800

Now with 10 billion increase in G

Y = 100+0.75(Y-40)+60+80 = 840

so spending multiplier = (840-800)/10=4

For progressive tax

C = 100+0.75Dt G=50 I=80

When Dt=0.95Y

the Y = 100+0.75(0.95Y)+50+80 So Y=800

Now with 10 billion increase in G

Y = 100+0.75(0.95Y)+60+80 = 834.8

so spending multiplier = (834.8-800)/10=3.48

So $10 billion increase in government purchase will have larger effect under lump sum tax