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, D is disposable income, I is investment, and G is government purchases: C=40+0.9∗DIG=80I=201. 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 the real GDP. Aggregate output demanded is $500 billion (True/False).2. Suppose the government decides to increase spending by $10 billion without raising taxes. Because the expenditure multiplier is 10 (True/False), this will increase the economy's aggregate output demanded by $100 billion (True/False).3. Now, suppose that the government switches to an income tax, which is the type of variable tax, of 20%. Because consumers retain only 80% of each additional dollar of income, disposable income is now 0.80∗Y. In this case, the economy's aggregate output demanded is $500 billion (True/False).4. Given an income tax of 20%, the expenditure multiplier is approximately 3.6 (True/False). 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 (True/False).5. A $10 billion increase in government purchases will have a larger effect on output under a fixed tax of $100 billion (True/False).

1. Aggregate output demanded is $500 billion. True.

Aggregate Demand (Y) = C + G + I

Y = 40+0.9∗DI + 80 + 20

Y = 40 + 0.9 ∗ (Y−100) + 80 + 20

Y = 50 + 0.9Y

0.1Y = 50

Y = $500 billion

2. Suppose the government decides to increase spending by $10 billion without raising taxes. Because the expenditure multiplier is 10. True.

Expenditure Multiplier = 1 / ( 1 - Marginal Propensity to Consume)

Marginal Propensity to Consume = 0.9 as per the Consumption function.

= 1/ ( 1 - 0.9)

= 10

2. b. this will increase the economy's aggregate output demanded by $100 billion. True.

Change in Aggregate output = Increase in government expenditure * expenditure multiplier

= 10 billion * 10

= $100 billion

3. ... In this case, the economy's aggregate output demanded is $500 billion . True.

Aggregate Demand (Y) = C + G + I

Y = 40+0.9∗DI + 80 + 20

Y = 40 + 0.9 ∗ (0.80∗Y) + 80 + 20

Y = 140 + 0.72Y

0.28Y = 140

Y = $500 billion

4. Given an income tax of 20%, the expenditure multiplier is approximately 3.6. True.

As a result of the new tax, the MPC will become;

= 0.9 * ( 0.80 * Y)

= 0.72Y.

Expenditure Multiplier = 1 / ( 1 - Marginal Propensity to Consume)

= 1/ ( 1 - 0.72)

= 3.57

= 3.6

4. b. 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. True.

Change in Aggregate output = Increase in government expenditure * expenditure multiplier

= 10 billion * 3.6

= $36 billion

5. A $10 billion increase in government purchases will have a larger effect on output under a fixed tax of $100 billion. True.

When the tax was fixed, an increase in Government purchases of $10 billion resulted in an increase in Aggregate output of $100 billion. When the Government switched to income taxes however, a $10 billion increase in Government spending led to a significantly lesser increase in Aggregate output of $36 billion.