The recessionary gap is the difference between what the government desires and what is currently demanded. Since the government wants $15 trillion, and there is currently a demand of $14 trillion, there is a $1 trillion recessionary gap.

Now, to overcome this recessionary gap, we have to multiply it by the economic multiplier, which is the amount of change in the economy every dollar spent by the government will create. This is calculated by the following equation: 1/(1-MPC). We know the MPC is 0.8. Therefore, the multiplier is 1/(1-0.8) = 5.

To calculate the spending necessary, then, we know that we need a certain amount spent which, when multiplied by 5, will equal the $1 trillion recessionary gap. If you divide $1 trillion dollars by the multiplier, 5, you will get the amount of government spending needed to increase the GDP demanded—which is $200 billion.

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.