Homework Question: From the model above you can see that government purchases (G) are counter-cyclical, that is, G increased as national income decreases. If you compare this specification of G with one that has a constant level of government spending (for example, G0 = 300), how would the value of the expenditure multiplier differ?

A: If government purchases are used as a stabilization tool, the size of the expenditure multiplier should be lower than if the level of government spending is fixed. In the model of the expenditure sector above, the slope of the [C + I + G+ X] line is c1 = 0.5, and therefore, the size of the expenditure multiplier = 1/.5 or 2. However, if the government purchases are defined as G0 = 300 instead, then the slope of the [C + I + G+ X] line changes to c2 = 0.6 and the size of the expenditure multiplier is 2.5.

Could you please explain how they arrived at this answer (notably why are the slopes .5 and .6 respectively)? Thank you!