Macroeconomics MPC Govt increases spending what is initial impact of real GDP and what is total impact of real gdp?

Question

Assume the MPC is 0.70. If the government increases spending on schools by $20 billion, what is the value of the initial impact on real GDP? What is the value of the total impact on Real GDP?

Answer 1

The initial impact on real GDP is simply the increase in government spending. Therefore, if the government increases spending by $20 billion, the initial impact on real GDP is +$20 billion.

The spending multiplier (k) is given by the formula: k = 1 / (1 - MPC)

Given that the MPC is 0.70: k = 1 / (1 - 0.70) = 1 / 0.30 ≈ 3.33

The total impact on real GDP is the initial increase in spending multiplied by the spending multiplier:

Total Impact = Initial Impact × k

Total Impact = $20 billion × 3.33 = $66.6 billion.