3. 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 total 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 initial total expenditure line has a slope of 0.5 and passes through the point (100, 100).

The second economy's MPC is 0.75. Therefore, its initial total expenditure line has a slope of 0.75 and passes through the point (100, 100).

Now, suppose there is a decrease of $20 billion in investment in each economy.

Place a green line (triangle symbol) on each of the previous graphs to indicate the new total expenditure line for each economy. Then place a 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 it.)

Now, confirm your graphical analysis algebraically using the oversimplified multiplier formula: Multiplier - -MPC For the first economy, with an MPC of 0.5, the effect of the $20 billion decrease in investment is as follows: Change in Equilibrium Output = Change in Total Expenditure x Multiplier X X Using the same method, the multiplier for the second economy isMPC-0.5 200 45-Degree Line A 180 New AE Line 160 140 120 New Equilibrium TOTAL EXPENDITURE (Billions of dollars) 100 80 60 AE Line 40 20 0 0 20 40 60 80 100 120 140 160 180 200 REAL GDP (Billions of dollars)MPC=0.75 200 45-Degree Line A 180 New AE Line 160 140 120 New Equilibrium 100 TOTAL EXPENDITURE (Billions of dollars) 80 60 40 AE Line 20 0 0 20 40 60 80 100 120 140 160 180 200 REAL GDP (Billions of dollars)