III. The Multiplier

• The multiplier is the amount by which a change in autonomous expenditure is magnified or multiplied to determine the change in equilibrium expenditure and real GDP.
• When there is an autonomous change in a component of expenditure such as investment, additional changes in aggregate expenditure are set in motion. Because of the feedback between real GDP and consumption expenditure, the total change in real GDP is larger than the initial change in autonomous expenditure.
• The multiplier effect operates for a decrease as well as an increase in autonomous expenditure.

Why is the Multiplier Greater Than 1?

An increase in autonomous expenditure increases real GDP and the increase in real GDP induces an additional increase in aggregate expenditure (primarily an increase in consumption expenditure). Each additional increase in aggregate expenditure increases real GDP further, leading to yet further increases in aggregate expenditure. The process converges because the increase in aggregate expenditure is smaller at each step of the process.

The Multiplier and the Marginal Propensities to Consume and Save

• The change in real GDP can be divided into the change in induced expenditure plus the change in autonomous expenditure, DY = DN + DA, where Y is real GDP, N is induced expenditures, and A is autonomous expenditure. The slope of the AE curve = DN÷DY, so DN = (slope of AE curve)´ DY. Using this equality in the previous formula shows DY = (slope of AE curve)´ DY + DA. Solving for the change in GDP, DY, gives DY = ´ DA. This last result shows that the multiplier equals . In the previous figure, the slope of the AE curve is 0.8, so the multiplier is 5.0.
• If there are no imports or income taxes, the slope of AE curve equals the MPC so the multiplier equals or, equivalently, .
• The size of the multiplier depends on the MPC and the MPS. The smaller the MPC or, equivalently, the larger the MPS, the smaller the increase in expenditure at each step of the multiplier process and so the smaller the multiplier.

The Effect of Imports and Income Taxes on the Multiplier; Business Cycle Turning Points

• Imports and income taxes both mean that the increase in expenditure on domestic production will be smaller at each step of the multiplier process and so the multiplier is smaller.
• An unexpected decrease in autonomous expenditure is signaled by a buildup of unplanned inventories. The buildup in inventories sets the multiplier process in motion that decreases aggregate expenditure and real GDP so that a recession follows.
• An unexpected increase in autonomous expenditure is signaled by an unwanted depletion of inventories. The depletion in inventories sets the multiplier process in motion and an expansion follows.

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