(Solved): The multiplier and the MPC: Consider two dosed economies that are identical except for their margin ...

The multiplier and the MPC: Consider two dosed economies that are identical except for their marginal propensity to consume (MPC). Each economy is currently in equilibrium with real GDP and aggregate expenditure equal to \( \$ 100 \) billion, as shown by the black points on the following two graphs. Neither economy has taxes that change with income. The grey lines show the 45 -degree line on each graph. The first economy's MPC is \( 0.5 \). Therefore, its inlial aggregate expenditure line has a slope of \( 0.5 \) and passes through the point ( 200,100\( ) \). The second economy's MpC is \( 0.75 \). Therefore, its initial aggregate expenditure line has a slope of \( 0.75 \) and passes through the point (100, 100 ). New, suppose there is a decrease of \( \$ 20 \) bltion in investment in each economy. Pisce a green line (triangle symbol) en each of the previous graphs to indicate the new aggregafe expenditure fine for each economy. Then pisce a black point (pius symbol) on each graph showing the new level of eqwibbrium output. (Wint: You can sce the slope and vertical aris intercept of a fine on the graph by selecting it.) Aplia Homework: Aggregate Demand \( M P C=0.75 \) In the first economy (with MPC \( =0.5 \) ), the \( \$ 20 \) billion decrease in investment causes equilibrium output to decrease by billion. In the second economy (with \( M P C=0.75 \) ), the \( \$ 20 \) billion decrease in investment causes equilibrium output to decrease by bilion. Therefore, a lower MPC is associated with a multigiler. Now, confirm your graphical analysis algebraically using the formula for the simple spending multipler: Multiplier \( =\frac{1}{12 \text { MRC }} \) For the first economy with an MPC of \( 0.5 \), the effect of the \( \$ 20 \) balion decrease in investment becomes the following: Using the same method, the inutiplier for the second economy is