In our simple Keynesian model, all else equal, any change in National Income can be traced to changes in autonomous spending or taxes:

                       1                         -mpc   

DY = D A ( 1 - mpc ) + DTa ( 1 - mpc )

If the mpcequals 0.8, the spending multiplier equals 5 and the tax multiplier equals -4. Thus, DY = DA(5) + DTa(-4). If government spending and taxes each grow by $20 billion, income also rises by $20 billion: $20 billion ¢ (5) plus $20 billion ¢ (-4) equals $20 billion.

 

            We can generalize: Equal changes in autonomous government spending and taxes cause income to change in the same direction and by the same amount. The applicable multiplier, termed the balanced-budget multiplier, always equals one because it reflects the numerical sum of the autonomous spending and tax multipliers:

 

                 1                   - mpc                     1 - mpc                  

 ( 1 - mpc ) + (  1 - mpc )  =  (  1 - mpc  ) =  1

Reviewing Table 3 in the body of this chapter should help convince you why, if both government purchases and taxes are increased by $1, then equilibrium income will rise by exactly $1.

 

            More realistic assumptions than those we have used underpin the sophisticated econometric models used to forecast national economic activity. For example, how income affects taxes, investment, and government outlays is recognized. Although serious forecasting models are mathematically more complex than those considered here, the approaches are similar: Assumptions about the behavior of various economic agents are used to predict National Income and Output.

 

Table 3  Round-by-Round Effects of $100 Billion Increases in Spending, Taxing, and the Balanced Budget  (billions of dollars)
Effect	(1) $100 billion In extra government spending	(2) $100 billion in extra autonomous taxes	(3) $100 billion in extra taxes and purchases
Round 1: Initial effect of change on income	$100	0	100
Round 2: induced spending	80	- 80	0
Round 3: induced spending	64	- 64	0
Round 4 through all subsequent rounds	256	- 256	0
Total Change	500	- 400	100
Multiplier   (mpc= 0.8)	5.00	-4.00	1.00
Note: Each $1 increase in government purchases creates $1 in new income in Round 1, but each $1 in new taxes does not influence first-round income. In Round 2, each $1 in new government purchases has caused the person whose income was increased to spend $0.80, but this is offset by the reduced spending of $0.80 caused by each $1 in new taxes. Moreover, the effects of the new spending and taxing offset each other in all subsequent rounds. Thus, only Round 1 spending has any net effect on income, and the balanced-budget multiplier equals one.