Final answer:
To close a $400 billion recessionary gap with an MPC of 4/5, government spending should be increased by $80 billion, leveraging the multiplier effect.
Step-by-step explanation:
To close a recessionary gap where an economy is producing output $400 billion less than the natural level of output, fiscal policymakers would need to increase government spending. Given the marginal propensity to consume (MPC) of 4/5, the multiplier effect can be calculated as 1/(1 - MPC). Therefore, the multiplier is 1/(1 - 0.8) which equals 5. To close the $400 billion gap, the increase in government spending (change in G) should be less than the gap itself, due to the multiplier effect. The amount needed can be found by dividing the recessionary gap by the multiplier, so $400 billion / 5 = $80 billion. Hence, government spending must be increased by $80 billion to close the recessionary gap.
The appropriate response to a recessionary gap is for the government to increase spending to close the gap. In this case, the economy is producing $400 billion less than the natural level of output. To close this recessionary gap, the government should increase government spending by $400 billion. This increase in spending will shift the aggregate expenditure function up and lead to a new equilibrium at the potential level of GDP.