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.)

MPC=0.5New AE LineNew Equilibrium020406080100120140160180200200180160140120100806040200TOTAL EXPENDITURE (Billions of dollars)REAL GDP (Billions of dollars)45-Degree LineAE Line

MPC=0.75New AE LineNew Equilibrium020406080100120140160180200200180160140120100806040200TOTAL EXPENDITURE (Billions of dollars)REAL GDP (Billions of dollars)45-Degree LineAE Line

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 MPC = 0.75), the $20 billion decrease in investment causes equilibrium output to decrease by

billion. Therefore, a higher MPC is associated with a multiplier.

Now, confirm your graphical analysis algebraically using the oversimplified multiplier formula:

MultiplierMultiplier

==

11MPC11MPC

For the firsteconomy, with an MPC of 0.5, the effect of the $20 billion decrease in investment is as follows:

ChangeinEquilibriumOutputChangeinEquilibriumOutput	==	ChangeinTotalExpenditureChangeinTotalExpenditure		MultiplierMultiplier
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Using the same method, the multiplier for the secondeconomy is .