The nation of Maximus has a marginal propensity to consume of .90 and the government has decreased taxes by a lump-sum amount of $1 billion. Assume there is no international trade or changes to the aggregate price level. a. What is the value of the tax multiplier in Maximus?
b. By how much will real GDP change after the $1 billion decrease in taxes?
c. If the government wanted to accomplish the same increase in real GDP you found in part (b), but with government spending instead of taxes, would the government need more than $1 billion in spending, less than $1 billion in spending, or exactly $1 billion in spending? Explain.

a. Amount of tax multiplier = -9.00

b. Amount of change or increase in real GDP = $9 billion

c. The government would need less than $1 billion in spending. The reason is the absolute value of Expenditure multiplier which is 10 is greater than the absolute value of tax multiplier which is 9.

Explanation:

a. What is the value of the tax multiplier in Maximus?

MPC = Marginal propensity to consume = 0.90

MPS = Marginal propensity to save = 1 = MPC = 1 - 0.90 = 0.10

Therefore, we have:

Amount of tax multiplier = - MPC / MPS = - 0.90 / 0.10 = -9.00

b. By how much will real GDP change after the $1 billion decrease in taxes?

Decrease in tax = -$1 billion

Amount of tax multiplier = -9.00

Therefore, we have:

Amount of change or increase in real GDP = Decease in tax * Amount of tax multiplier = -$1 billion * -9.00 = $9 billion

c. If the government wanted to accomplish the same increase in real GDP you found in part (b), but with government spending instead of taxes, would the government need more than $1 billion in spending, less than $1 billion in spending, or exactly $1 billion in spending? Explain.

Expenditure multiplier = 1 / MPS = 1 / 0.10 = 10

Increase in real GDP = Change in government spending * Expenditure multiplier (1)

Substituting the relevant values into equation (1) and solve for Change in government spending, we have:

$9 billion = Change in government spending * 10

Change in government spending = $9 billion / 10 = $0.90 billion

Since we obtained change in government spending of $0.90 billion under expenditure multiplier, this implies that the government would need less than $1 billion in spending. The reason is the absolute value of Expenditure multiplier which is 10 is greater than the absolute value of tax multiplier which is 9.