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 income and planned 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 planned expenditure line has a slope of 0.5 and passes through the point (100, 100).

The second economy's MPC is 0.70. Therefore, its initial planned expenditure line has a slope of 0.70 and passes through the point (100, 100).

Now, suppose there is a decrease of $30 billion in planned investment in each economy.

Place a green line (triangle symbol) on each of the preceding graphs to indicate the new planned expenditure line for each economy. Then place a black point (plus symbol) on each graph showing the new level of equilibrium income. (Hint: You can see the slope and vertical axis intercept of a line on the graph by selecting it.)

MPC=0.5 200 45-Degree Line A 180 PLANNED EXPENDITURE (Billions of dollars) New AE Line 160 140 120 New Equilibrium 100 80 60 AE Line 40 20 0 0 20 40 60 80 100 120 140 160 180 200 REAL INCOME (Billions of dollars)MPC=0.70 200 45-Degree Line A 180 PLANNED EXPENDITURE (Billions of dollars) 160 New AE Line 140 120 New Equilibrium 100 80 60 40 AE Line 20 0 0 20 40 60 80 100 120 140 160 180 200 REAL INCOME (Billions of dollars)In the rst economy (with MPC = 0.5), the $30 billion decrease in planned investment causes equilibrium income to decrease by $ billion. In the second economy (with MPC = 0.70), the $30 billion decrease in planned investment causes equilibrium income to decrease by $ billion. Therefore, a higher MPC is associated with a V multiplier. Now, confirm your graphical analysis algebraically using the formula for the multiplier: l 1 MPC Multiplier = For the first economy with an MPC of 0.5, the effect of the $30 billion decrease in planned investment becomes the following: Change in Equilibrium Real Income Change in Planned Expenditure X Multiplier VX V VX v Using the same method, the multiplier for the second economy is v