Consider a small country that is closed (to trade, so its net exports are equal
ID: 1228110 • Letter: C
Question
Consider a small country that is closed (to trade, so its net exports are equal to zero. The following equations deserve the economy of this country in billions of dollars, where C is consumption, DI is disposable income, I is investment, and G a government purchases: Assume that this economy initially has a fixed tax and that net taxes (taxes minus transfer payments) are $40 billion. Disposable income is then (Y - 40). where Y is real GDP. Aggregate output demanded is Suppose the government decides to increase spending by $10 billion without raising taxes. Because the expenditure multiplier is, this will the economy's aggregate output demanded by Now suppose that the government switches to an income tax, which is a type of variable tax, of 5%. Because consigners retain only 95% of each additional dollar of income, disposable income is now 095x Y. In this case, the economy's aggregate output demanded is Given ari income tax of 5%, the expenditure multiplier is approximately Therefore, if the government decides 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.Explanation / Answer
(a) DI = Y - 40
In equilibrium, Y = C + I + G
Y = 100 + 0.75 x (Y - 40) + 80 + 50
Y = 230 + 0.75Y - 30
(1 - 0.75)Y = 200
0.25Y = 200
Y = 800
Aggregate output demanded = $800 billion
(b) Spending multiplier = 1 / (1 - MPC) = 1 / (1 - 0.75) = 1 / 0.25 = 4
As government spending increases by $10 billion, aggregate output increases by $10 billion x 4 = $40 billion
(c) DI = 0.95 x Y
Y = 100 + 0.75 x (0.95Y) + 80 + 50
Y = 230 + 0.7125Y
(1 - 0.7125)Y = 230
0.2875Y = 230
Y = 800
Aggregate output = $800 billion
(d) With 5% tax,
C = 100 + 0.7125Y
MPC = 0.7125
Spending multiplier = 1 / (1 - 0.7125) = 1 / 0.2875 = 3.5
As government spending rises by $10 billion, aggregate output rises by $10 billion x 3.5 = $35 billion
(d) Increase in government spending has larger effect under a Fixed tax of $40 billion.