Changes in Aggregate Expenditures: The Multiplier

In the AE model, equilibrium is found at the level of real GDP at which the aggregate expenditures curve crosses the 45-degree line. It follows that a shift in the curve will change equilibrium real GDP. Here we will examine the magnitude of such changes.

Figure A Change in Autonomous Aggregate Expenditures Changes Equilibrium Real GDP begins with the aggregate expenditures curve shown in Figure Determining Equilibrium in the Aggregate Expenditures Model. Now suppose that planned investment increases from the original value of $1,100 billion to a new value of $1,400 billion – an increase of $300 billion. This increase in planned investment shifts the aggregate expenditures curve upward by $300 billion, all other things unchanged. Notice, however, that the new aggregate expenditures curve intersects the 45-degree line at a real GDP of $8,500 billion. The $300 billion increase in planned investment has produced an increase in equilibrium real GDP of $1,500 billion.

How could an increase in aggregate expenditures of $300 billion produce an increase in equilibrium real GDP of $1,500 billion? The answer lies in the operation of the multiplier. Because firms have increased their demand for investment goods (that is, for capital) by $300 billion, the firms that produce those goods will have $300 billion in additional orders. They will produce $300 billion in additional real GDP and, given our simplifying assumption, $300 billion in additional disposable personal income. But in this economy, each $1 of additional real GDP induces $0.80 in additional consumption. The $300 billion increase in autonomous aggregate expenditures initially induces $240 billion (= 0.8 × $300 billion) in additional consumption.

Figure A Change in Autonomous Aggregate Expenditures Changes Equilibrium Real GDP

An increase of $300 billion in planned investment raises the aggregate expenditures curve by $300 billion. The $300 billion increase in planned investment results in an increase in equilibrium real GDP of $1,500 billion.

 

The $240 billion in additional consumption boosts production, creating another $240 billion in real GDP. But that second round of increase in real GDP induces $192 billion (= 0.8 × $240) in additional consumption, creating still more production, still more income, and still more consumption. Eventually (after many additional rounds of increases in induced consumption), the $300 billion increase in aggregate expenditures will result in a $1,500 billion increase in equilibrium real GDP. Table The Multiplied Effect of an Increase in Autonomous Aggregate Expenditures shows the multiplied effect of a $300 billion increase in autonomous aggregate expenditures, assuming each $1 of additional real GDP induces $0.80 in additional consumption.

The size of the additional rounds of expenditure is based on the slope of the AE function, which in this example is simply the marginal propensity to consume. Had the slope been flatter (if the marginal propensity to consume were smaller), the additional rounds of spending would have been smaller. A steeper slope would mean that the additional rounds of spending would have been larger.

This process could also work in reverse. That is, a decrease in planned investment would lead to a multiplied decrease in real GDP. A reduction in planned investment would reduce the incomes of some households. They would reduce their consumption by the MPC times the reduction in their income. That, in turn, would reduce incomes for households that would have received the spending by the first group of households. The process continues, thus multiplying the impact of the reduction in aggregate expenditures resulting from the reduction in planned investment.

 

Table The Multiplied Effect of an Increase in Autonomous Aggregate Expenditures

Round of spending	Increase in real GDP (billions of dollars)
1	300
2	240
3	192
4	154
5	123
6	98
7	79
8	63
9	50
10	40
11	32
xcdf12	26
Subsequent rounds	+103
Total increase in real GDP	1,500