The balanced-budget multiplier measures the change in aggregate production triggered by an autonomous change in government taxes. This multiplier is useful in the analysis of fiscal policy changes that involves both government purchases and taxes.
The logic behind this multiplier comes from the government's budget, which includes both spending and taxes. In general, a balanced budget has an equality between spending and taxes. As such, the balanced-budget multiplier analyzes what happens when there is an equality between changes in government purchases and taxes, that is, actions that keep the budget "balanced."
In other words, the balanced-budget multiplier indicates the overall impact on aggregate production of a change in government purchases that is matched (that is, paid for) by an equivalent change in taxes. The balanced-budget multiplier, as such, is actually the sum of the expenditures multiplier (for government purchases) and the tax multiplier.
The balanced-budget multiplier is equal to one. The "positive" impact on aggregate production caused by a change in government purchases is largely, but not completely, offset by the "negative" impact of the change in taxes. The only part of the impact of the change in government purchases NOT offset by the change in taxes is the purchase of aggregate production made by the initial injection. Hence, the change in aggregate production is equal to the initial change in government purchases.
A Simple FormulationThe balanced-budget multiplier, like the expenditures multiplier and tax multiplier can come in several different varieties based on assumptions concerning the structure of the economy and what components are induced by aggregate production.
However, the value of the balanced-budget multiplier is the same whether consumption is the only induced expenditure or all components are assumed to be induced. The reason is that all of the "induced" changes in aggregate production caused by changes in government purchases are cancelled out by opposite changes in taxes. So it matters not what components are induced.
As such, here is the balanced-budget multiplier (m[bb]) based on the combination of the simple expenditures multiplier and the simple tax multiplier.
Where MPC is the marginal propensity to consume and MPS is the marginal propensity to save.
|m[bb] ||= ||1|
|+ ||- MPC|
|= ||1- MPC|
Why One?The most obvious and most important point is that the balanced-budget multiplier has a value of 1. This value indicates that the change in aggregate production is caused by the initial injection of government purchases. The subsequent changes in aggregate production that might be result as government purchases trigger cumulatively reinforcing induced changes in factor payments, income, and consumption are cancelled out by an opposite impact from the change in taxes.
Suppose, for example, that government purchases are increased by $1 trillion using fiscal policy designed to correct a business-cycle contraction. By itself, this $1 trillion government purchases increase would be expected to trigger a $4 trillion increase in aggregate production.
However, further suppose that this $1 trillion increase in government purchases is matched by, and paid for with, an equal $1 trillion increase in taxes. By itself, this $1 trillion increase in taxes is expected to trigger a $3 trillion decrease in aggregate production. The net impact on aggregate production of both changes is only $1 trillion, not $4 trillion. If a $4 trillion increase in aggregate production is needed to achieve full employment, then this strategy falls $3 trillion short.
Why does this happen?
The offset is only partial and there is a net impact on production due to the way taxes and government purchases affect aggregate expenditures. All $1 trillion of the government purchases act to increase aggregate expenditures. However, only $750 billion of the taxes (due to a marginal propensity to consume of 0.75) work their way through consumption to decrease aggregate expenditures.
- First, the increase in aggregate production triggered by the increase in government purchases is offset by a decrease in aggregate production triggered by the increase in taxes.
- Second, the increase in aggregate production stimulated by government purchases is only partially offset by the decrease aggregate production stimulated by taxes.
As such, there remains a net increase in aggregate expenditures of $250 billion. Evaluating this net increase of $250 billion using the simple expenditures multiplier of 4 identifies an increase in aggregate production of $1 trillion.
Is it just a coincidence that this net increase in aggregate production is exactly equal to the original change in government purchases (and taxes)?
Not at all.
Only the initial $1 trillion government purchase triggers an increase in aggregate production. Each subsequent round of increased consumption that would be otherwise induced by the multiplier process is offset by decreased consumption resulting by higher taxes. The only expenditure that does not go through the household sector and is not cancelled by taxes is the original government purchase.
Other MultipliersThe tax multiplier is one of several Keynesian multipliers. Two other related multipliers are expenditures multiplier and tax multiplier.
Two other multipliers arise from the financial, or money, side of the economy. They are the deposit expansion multiplier and the money multiplier. The deposit expansion multiplier measures the change in bank deposits caused by a change in bank reserves. The money multiplier measures the change in money caused by a change in bank reserves. Both are useful in the analysis of monetary policy.
- Expenditures Multiplier: The expenditures multiplier measures changes in aggregate production caused by changes in an autonomous expenditure. Like the tax multiplier this comes in several varieties, simple and complex, depending on which expenditures and other components are induced by aggregate production and income. It differs from the tax multiplier in that aggregate expenditures change by full amount of the autonomous change.
- Tax Multiplier: The tax multiplier measures changes in aggregate production caused by changes in taxes. Like the expenditures multiplier this comes in several varieties, simple and complex, depending on which expenditures and other components are induced by aggregate production and income. It differs from the expenditures multiplier in that aggregate expenditures change by less than the change in taxes.
BALANCED-BUDGET MULTIPLIER, AmosWEB Encyclonomic WEB*pedia, http://www.AmosWEB.com, AmosWEB LLC, 2000-2017. [Accessed: December 13, 2017].