Consider a small country that is closed to trade, so its net exports are equal t
ID: 1228103 • Letter: C
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 = 40 + 0.9 Times DI G = 80 I = 20 Assume that this economy initially has a fixed tax and that net taxes (taxes minus transfer payments) are $100 billion. Disposable income is then (Y - 100), where Y is real GDP. Aggregate output demanded is $800 billion. Suppose the government decides to increase spending by $10 billion without raising taxes. Because the expenditure multiplier is 10, this will increase the economy's aggregate output demanded by $100 billion. Now suppose that the government switches to an income tax, which is a type of variable tax, of 20%. Because consumers retain only 80% of each additional dollar of income, disposable income is now 0.80 Times Y. In this case, the economy's aggregate output demanded is $800 billion. Given an income tax of 20%, the expenditure multiplier is approximately 3.6. 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 $36 billion. A $10 billion increase in government purchases will have a larger effect on output under a fixed tax of $100 billion.Explanation / Answer
(a) DI = Y - 100
In equilibrium, Y = C + I + G
Y = 40 + 0.9 x (Y - 100) + 20 + 80
Y = 140 + 0.9Y - 90
(1 - 0.9)Y = 50
0.1Y = 50
Y = 500
Aggregate output demanded = $500 billion
(b) Spending multiplier = 1 / (1 - MPC) = 1 / (1 - 0.9) = 1 / 0.1 = 10
As government spending increases by $10 billion, aggregate output increases by $10 billion x 10 = $100 billion
(c) DI = 0.8 x Y
Y = 40 + 0.9 x (0.8Y) + 20 + 80
Y = 140 + 0.72Y
(1 - 0.72)Y = 140
0.28Y = 140
Y = 500
Aggregate output = $500 billion
(d) With 20% tax,
C = 40 + 0.72Y
MPC = 0.72
Spending multiplier = 1 / (1 - 0.72) = 1 / 0.28 = 3.6
As government spending rises by $10 billion, aggregate output rises by $10 billion x 3.6 = $36 bllion
(d) Increase in government spending has larger effect under a Fixed tax of $100 billion.