As the original answer stated, the change is negligible in compared with the equilibrium GDP. The general process is quite simple, though. The value of the real GDP increases or decreases by the expenditures multiplied by the multiplier, because the autonomous expenditures result in that amount of additional economic activity.

Therefore, for every dollar that is spent through autonomous expenditures, in this scenario, the GDP will rise by 5 dollars. The reason for this is that autonomous expenditures generates more economic activity (the money you spend at Macy's in the mall goes to someone's pocket, who then has more money to spend at Jamba Juice in the same mall).

The overlying principle is that if the prices remains the same (relatively speaking), the economic activity increases whenever there is an influx of cash, and the multiplier quantifies that increase.

I wonder if you have made a mistake in typing this question. A change in autonomous expenditures of less than $1 ($.30) will have a negligible effect on GDP when the previous equilibrium GDP is $12 trillion. The actual change in GDP would be $1.50, which is not a real change in GDP. I will discuss how to answer this question so you can plug in a different number and find the right answer.

There are three factors in this question that matter. First, it is important that we know that the short run aggregate supply curve (SRAS) is horizontal. That means that there will be no increase in the price level when consumption rises. Second, it is important that we know that the current equilibrium GDP is $12 trillion. That will be our starting point and we will add any increase to that figure. Finally, it is important to know that the multiplier is 5. We will need to multiply the change in autonomous expenditures by 5 to get the change in real GDP.

For example, then, if autonomous expenditures increase by $1 billion, GDP will actually rise by $5 billion and the new RGDP will be $12.005 trillion. If autonomous expenditures increase by $10 billion, RGDP will actually rise by $50 billion and the new equilibrium RGDP will be $12.05 trillion. If the change in autonomous expenditures is $.3 trillion, then the actual increase is $.15 trillion and your new equilibrium RGDP is $12.15 trillion.

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