In order to determine the change in the level of real Gross Domestic Product demanded, we will have to determine what the expenditure multiplier is and use that multiplier to find the impact of the reduction in government spending.
We know that the formula for finding the spending multiplier is
Multiplier = 1/(1 – MPC).
Since we have the MPC given in this question, it is easy to find the multiplier.
Multiplier = 1/(1-.9) = 1/.1 = 10.
So, the multiplier in this scenario is 10. That means that any change in government spending will change the level of real GDP demanded by 10 times the amount of the change.
We can then use the following equation to calculate the change in RGDP demanded.
Change in RGDP = change in government purchases x multiplier.
Change in RGDP = -$10 billion x 10
Change in RGDP = -$100 billion.
This means that the decrease in government spending ($10 billion) will reduce the amount of RGDP demanded by $100 billion.