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7. The multiplier and the MPC Consider two closed 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 ine on each graph The first economy MPCI0.5. Therefore, its initial aggregate expenditure line has a slope of 0.5 and passes through the point (100, 100) The second economy's MPCI 0.70. Therefore, its initial aggregate expenditure tine has a slope of 0.70 and passes through the point (100, 100), Now, suppose there is a decrease of $30 billion in Investment in each economy, a Place Greenline triangle symbol) on each of the previous graphs to indicate the new aggregate expenditure line for each economy. The place black point (plus symbol) on each graph showing the new level of equilibrium output. (Hint: You can see the slope and vertical axis intercept of a line on the graph by selecting E.) MPC+0.5 45-Degree Line 200 180 New AE Line 160 140 New Equilibrium 120 AGGREGATE EXPENDITURE (Billions of dollars) 100 60 AE Line 40 20 0 160 180 200 0 20 40 60 80 100 120 140 REAL GDP (Billions of dollars) MPC=0.70 200 45-Degree Line 180 New AE Line 160 140 New Equilibrium 120 AGGREGATE EXPENDITURE (Billions of dollars) 100 80 20 40 AE Line 20 D 0 0 20 40 180 200 60 80 100 120 140 160 REAL GDP (Billions of dollars) In the first economy (with MPC = 0.5), the $30 billion decrease in investment causes equilibrium output to decrease by S billion. In the second economy (with MPC = 0.70), the $30 billion decrease in investment causes equilibrium output to decrease by billion. Therefore, a lower MPC is associated with a multiplier Now, confirm your graphical analysis algebraically using the formula for the simple spending multipler: Multiplier For the first economy with an MPC of 0.5, the effect of the $30 billion decrease in investment becomes the following: Change in Equilibrium Output - Change in Aggregate Expenditure X Multiple X Using the same method, the multiplier for the second economy is