Question

Assume MPC = 0.75. If an initial fiscal restraint of $100 billion is desired, by how much must

a. government spending be reduced?
b. taxes be raised?

Answer 1

To achieve an initial fiscal restraint of $100 billion, government spending needs to be reduced by $300 billion and taxes need to be increased by $33.33 billion.

Step-by-step explanation:

To determine how much government spending needs to be reduced in order to achieve an initial fiscal restraint of $100 billion, we need to calculate the spending multiplier. The spending multiplier (MPC) is the reciprocal of the marginal propensity to consume (MPC). The formula to calculate the spending multiplier is MPC/(1 - MPC). In this case, the given MPC is 0.75. So, the spending multiplier is 0.75/(1 - 0.75) = 3.

To calculate the reduction in government spending, we multiply the desired fiscal restraint ($100 billion) by the spending multiplier. Therefore, the reduction in government spending is $100 billion x 3 = $300 billion.

To determine how much taxes need to be raised to achieve the same fiscal restraint, we can use the spending multiplier as well. Since taxes are an inverse of government spending, we need to divide the desired fiscal restraint ($100 billion) by the spending multiplier. Therefore, the increase in taxes is $100 billion/3 = $33.33 billion.

Answer 2

To determine the changes in government spending and taxes needed to achieve a fiscal restraint of $100 billion, we can use the concept of the fiscal multiplier, which relates changes in government spending or taxes to changes in the overall economy.

The fiscal multiplier (M) can be calculated using the formula:

\[ M = \frac{1}{1 - MPC} \]

Given that the marginal propensity to consume (MPC) is 0.75, we can calculate the fiscal multiplier:

\[ M = \frac{1}{1 - 0.75} = 4 \]

a. To achieve a fiscal restraint of $100 billion, the reduction in government spending (\( \Delta G \)) can be calculated using the formula:

\[ \Delta G = \frac{\text{desired fiscal restraint}}{\text{fiscal multiplier}} \]

\[ \Delta G = \frac{\$100 \text{ billion}}{4} = \$25 \text{ billion} \]

Therefore, government spending must be reduced by $25 billion.

b. Similarly, the increase in taxes (\( \Delta T \)) can be calculated using the same formula:

\[ \Delta T = \frac{\text{desired fiscal restraint}}{\text{fiscal multiplier}} \]

\[ \Delta T = \frac{\$100 \text{ billion}}{4} = \$25 \text{ billion} \]

Therefore, taxes must be raised by $25 billion.

In summary:
a. Government spending must be reduced by $25 billion.
b. Taxes must be raised by $25 billion.