The MPC is .89 and the government has cut spending by $4 billion.  Using the simple multiplier how does this cut affect the real GDP?  

In order to understand what impact this action has on gross domestic product (GDP), we must first determine what the multiplier is in this situation.  The formula for the multiplier is

Spending multiplier = 1/(1-MPC).

Since you have given us the MPC (marginal propensity to consume), we can calculate the multiplier.  Using the figure given for MPC, we have the equation

Spending multiplier = 1/(1-.89) = 1/.11 = 9.1

This means that every dollar of change in government spending will result in a $9.1 change in GDP.  The reason for this is that every dollar the government spends gets re-spent in the economy.  For example, if the government pays a worker $1,000 in a week, that worker will go out and spend some amount of that (determined by the MPC) on goods and services.  The people he or she buys from will do the same.  This will continue on and on, creating a multiplier effect.

In this case, however, the government is cutting spending so GDP will go down.  The equation is

Change in GDP = Change in spending x multiplier.

In this case, it is

Change in GDP = -$4 billion x 9.1 = -$36.4 billion.

This means that GDP will decrease by $36.4 billion as a result of this spending cut.