Let’s take a simple example to understand this multiplier effect. Assume that the government increases its spending by $100. Assume that the tax rate and MCP for those who receive this money is 30% and 90%. So, a $100 increase in government spending increases income by $100*(1-0.30) = $70. From this disposable income of $70, people will spend $70 *0.90 = $63. This $63 will become income for other people, and their disposable income will be $63*(1-0.30) = $44.1, out of which they will spend $44.1*0.90 = $39.69. This process will continue till the additionally created disposable income becomes close to zero.
The actual increase in aggregate demand due to increased spending can be calculated using the fiscal multiplier.
Fiscal Multiplier = 1/(1-MCP(1-t))
Where, t is the tax rate.
With t = 30% and MCP = 90%, the Fiscal multiplier will be:
Fiscal multiplier = 1/(1-0.90*(1-0.30)) = 2.7
With a fiscal multiplier of 2.7, a $100 increase in spending will increase the aggregate demand by $270.
As you can see, fiscal multiplier is directly related to MCP and inversely related to the tax rate.
Balanced Budget Multiplier
When the government increases spending, it may also want to increase taxes to balance its budget. If the spending is increased by $100, then it may also increase the taxes by $100 to offset the increase in spending. However, even the taxes have a multiplier effect on the aggregate demand. With an MCP of 90%, when the taxes are increased by $100, the aggregate demand will initially reduce by $100*0.90 = $90. This again will have multiple iterations, and the total decrease in aggregate demand will be $100*0.9*2.7 = $243.
So, a $100 increase in spending and taxes each will have a net effect of increase in aggregate demand by $27 ($270 - $243). This means that the balanced budget multiplier is positive. The government can increase the taxes a little more to make the net increase in aggregate demand zero.
