By how much would government spending have to increase to achieve the goal in the following scenario?
Suppose that the MPC = 0.8 and that $14 trillion of real GDP is currently being demanded. The government wants to increase real GDP demanded to $15 trillion at the given price level.
First, we need to determine the amount of the recessionary gap that exists in this economy. Since the real GDP at the current time is $14 trillion, and since the government wants a real GDP of $15 trillion, then there is a recessionary gap of $1 trillion. This means that the government needs to increase its spending enough to create $1 trillion more of aggregate demand.
Now that know that, we need to determine what the multiplier is. Each dollar of government spending has an impact on aggregate demand that is affected by the multiplier. The formula for the government spending multiplier is
Multiplier = 1/(1 – MPC)
We know that the MPC is .8, so we know that
Multiplier = 1(1-.8) = 1/.2 = 5
The spending multiplier, then, is 5, meaning that every dollar spent by the government adds $5 to aggregate demand. All that is left then is to calculate the amount of government spending needed. The equation is
Change in government spending x multiplier = change in aggregate demand.
Given what we know, this becomes
Change in government spending x 5 = $1 trillion.
We divide both sides by 5 and we get
Change in government spending = $200 billion.
Therefore, we know that the government must increase spending by $200 billion to close the recessionary gap in this scenario.