E XERCISES FOR C HAPTER 5
6.4 The multiplier: Changes in aggregate expenditure and equi- equi-librium output
6.4. The multiplier: Changes in aggregate expenditure and equilibrium output 137
producers of commodities including iron ore, copper, metallurgical coal, base metals, natural gas, and crude oil have faced declining demand for their products and lower prices and rising inven-tories. Producers responded by lowering production to try to reduce excess inventory. In general terms, when the economy is producing more than current aggregate expenditure, unwanted inven-tories build up and output is cut back.
Hence, when output is below the equilibrium level, firms raise output. When output is above the equilibrium level, firms reduce output. At the equilibrium output Ye, firms sell their current output and there are no unplanned changes to their inventories. Firms have no incentive to change output.
Equilibrium output and employment
In the examples of short-run equilibrium we have discussed, output is at Ye with output equal to planned expenditure. Firms sell all they produce, and households and firms buy all they plan to buy. But it is important to note that nothing guarantees that equilibrium output Ye is the level of potential output YP. When wages and prices are fixed, the economy can end up at a short-run equilibrium below potential output with no forces present to move output to potential output.
Furthermore, we know that, when output is below potential output, employment is less than full and the unemployment rate u is higher than the natural rate un. The economy is in recession and by our current assumptions neither price flexibility nor government policy action can affect these conditions.
6.4 The multiplier: Changes in aggregate expenditure and
Figure 6.8: The effect of a rise in autonomous expenditure
Y=AE
A0
AE0= A0+ (c − m)Y A0+ ∆A
AE1= A0+ ∆A + (c − m)Y
AE
Real GDP
Y0 Y1
∆Y
∆A
45◦
A rise in autonomous expenditure∆A shifts AE up to AE1. Equilibrium GDP rises by a larger amount from Y0to Y1.
When autonomous expenditure rises, firms increase output, increasing their payments for factor inputs to production. Households have higher income and increase their consumption expenditure (cY ) and imports (m∆Y ). Firms increase output again to meet this increased demand, further in-creasing household incomes. Consumption and imports rise further. This is a first and important example of interdependency and feedback in a basic model. A change in autonomous expenditure, either positive or negative, changes income which in turn causes a change in induced expenditure.
Equilibrium income changes by the change in autonomous expenditure plus the change in induced expenditure.
6.4. The multiplier: Changes in aggregate expenditure and equilibrium output 139
Figure6.8shows that an upward shift in the AE function increases equilibrium income by a finite amount, but by a larger amount than the vertical rise in the AE line. This is because(c − m), the slope of AE, is less than unity, giving the AE line a lower slope than the 45◦ line. Households increase their expenditure when incomes rise, but they increase expenditure by less than the rise in income. Equilibrium moves from Y0to Y1. Equilibrium output rises more than the original rise in investment,∆Ye> ∆A, but does not rise without limit.
A fall in autonomous expenditure would have the opposite effect. AE would shift down and equi-librium income would decline by more than the fall in A.
Themultiplieris a concept used to define the change in equilibrium output and income caused by a change in autonomous expenditure. If A is autonomous expenditure:
The multiplier=∆Y
∆A (6.3)
Multiplier (∆Y /∆A): the ratio of the change in equilibrium income Y to the change in autonomous expenditure A that caused it.
We can also show the change in equilibrium output caused by a rise in autonomous investment expenditure using the earlier simple numerical example we used earlier. In Table 6.4 initial au-tonomous expenditure is 100, induced expenditure is 0.5Y and initial equilibrium is Y = 200.
Then autonomous expenditure increases, as in column (3) by 25 to a new level of 125. Induced expenditure is still 0.5Y . Aggregate expenditure in column (6) rises as a result of increase in both autonomous and induced expenditure.
Table 6.4: The effect of a rise in autonomous expenditure on equilibrium GDP
Initial New Initial New
GDP Autonomous Autonomous Induced Aggregate Aggregate
(Y ) Expenditure Expenditure Expenditure Expenditure Expenditure (A0= 100) (A1= 125) (c − m)Y = 0.5Y (AE = 100 + 0.5Y ) (AE1= 120 + 0.5Y )
(1) (2) (3) (4) (5) (6)
175 100 - 87.5 187.5 187.5
200 100 - 100 200 200
225 125 112.5 237.5
237.5 125 118.75 243.5
243.5 125 121.75 246.75
246.75 125
– 125
250 125 125 250
300 125 150 275
The initial increase in aggregate expenditure illustrated is from 200 to 237.5 made up of an increase in autonomous expenditure of 25 and in induced expenditure of 0.5× 25 = 12.5. However GDP(Y ) is only 225 and planned expenditure is accommodated by a decrease in inventories of 12.5. This unintended fall in inventories is an incentive to increase production to take advantage of higher than expected sales. The incentive exists until producers increase output and income to 250. Aggregate expenditure rises as income increases until equilibrium is reached at Y = 250. At that point actual inventory investment meets producer plans.
The change in autonomous expenditure by 25 caused an increase in equilibrium income by 50.
The multiplier, defined as the change in equilibrium income caused by a change in autonomous expenditure∆Y/∆A = 2.
You can construct a diagram like Figure 6.8 using the numerical values for GDP and aggregate expenditure in Table6.4and a 45◦line to show equilibrium Ye= 200. Example Box6.2at the end of the chapter illustrates the multiplier effect of a change in autonomous expenditure on equilibrium income using simple algebra.
The size of the multiplier
The multiplier is a number that tells us how much equilibrium output changes as a result of a change in autonomous expenditure. The multiplier is bigger than 1 because a change in autonomous expenditure changes income and sets off further changes in induced expenditure. The marginal propensity to spend on domestic output(c − m) determines the induced expenditure.