If MPC is .07 and a decrease in the interest rate causes investment spending to increase by $4 billion, using the simple spending multiplier what impact does the change have on real GDP? 

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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-.7) = 1/.3 = 3.3

This means that every dollar of change in investment spending will result in a $3.3 change in GDP.  In this case, however, investment is increasing so GDP will increase as well.  The equation is

Change in GDP = Change in investment x multiplier.

Using the numbers you have given us and the multiplier we have calculated:

Change in GDP = $4 billion x 3.3 = $13.2 billion.

This means that GDP will increase by $13.2 billion as a result of this increase in investment.  In this example, there is a very low multiplier because the MPC is low.  That means that people are saving more money instead of using it for consumption.  This limits the impact of the increase in investment.

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