Douglas A. Ruby
Revised: 02/06/2003

Aggregate Demand

Macroeconomic Policy

The Accelerator

Macroeconomic Principles

Macroeconomic Theory
Aggregate Expenditure,
the Spending Multiplier and Income Determination

Using the methods of National Income Accounting, one method of calculating nominal GDP (YN) was through the expenditure approach such that:

NGDP = ΣPiQi = YNominal

or

YNominal = C + I + G + NX

where the variables on the right-hand side represent the four expenditure categories that make up GDP. What is important is that certain expenditure decisions are proportional to the level of income such that as aggregate income increases, expenditure increases by some fraction of this income change. We can think in terms of this expression representing an equilibrium condition (Ye) such that for one unique level of income, expenditure is exactly equal to that level of income:

Ye : Aggregate Income = Aggregate Expenditure

We will begin with consumption expenditure 'C' as being proportional to disposable income (gross income less taxes paid) with the proportional relationship being defined by the marginal propensity to consume 'b':

C = Co + b(Y-T), 0 < b < 1

Tax revenue 'T' is defined to be some fraction of income via the tax rate 't':

T = tY, 0 < t < 1

For algebraic simplicity we will define the other expenditure categories; investment 'I', government 'G', and net exports 'NX' as being autonomous with respect to income (i.e., spending decisions independent of the level of national income). We will summarize this via a single variable 'Ao' known as autonomous expenditure:

Ao = Co + Io + Go + NXo

Thus, the expenditure equation can be written as:

Y = Co + b(Y-tY) + Io + Go + NXo

or

Ye : Y = Ao + b(1-t)Y

as shown in the diagram below:

Figure 1, Aggregate Expenditure

Solving for 'Ye', the equilibrium value of income, we have

Ye = α'[Ao],

where α' = 1 / [1-b(1-t)] and represents, what is commonly known as, the simple spending multiplier.

The Multiplier
Any time new spending is introduced into the economy (or if spending is removed), it will cause GDP (and other measures of national income) to change by some multiple of that spending shock. This takes place through the multiplier process in aggregate spending largely via changes in consumption expenditure. For example, suppose that the marginal propensity to spend (changes in spending induced by changes in income) is equal to 0.50

Expenditure = Ao + 0.75(Y - 0.333Y)

=Ao + 0.50Y

Given our equilibrium condition: Y = AE (Aggregate Expenditure)

Y = Ao + 0.50Y

Since [1-b(1-t)] < 1, the spending multiplier α' will be greater than one such that:

Ye = 2.0[Ao] and ΔYe = 2.0[ΔAo]

Figure 2, An Autonomous Spending Shock

note: [Y1 - Y0] = 2.0[A'o - Ao]

 Interactive Graph -- Product Market Equilibrium

In the interactive diagram below, autonomous expenditure Ao is equal to \$5,000 (billion).
1) You may use your mouse to drag any slider to simulate changes to 'Autonomous Consumption Exp.', 'the Tax Rate', 'Govt. Exp.', 'Investment Exp.' or 'Net Export Exp.'.
2) Press the 'Income Adjustment' button to see the change to a new equilibrium.
3) Press 'Reset' to start over.

The Process
An initial change in autonomous spending (for example, a shock in the form of an increase in government spending) of \$20 (billion) is received as income by some person or business in the aggregate economy. This spending translates into an increase in income for that person who, given the propensity to spend, will increase his expenditure by \$10 . This \$10 in additional spending is received by someone else as income who spends 50% of that amount.

 --> iteration ΔIncome ΔExpenditure 0 Δ Ao= \$20 (billion) 10 : : : n 0.001 - Total Change in Income: 40 (billion)

The spending flows through the aggregate economy such that when we total up all of the increases in income we find that aggregate income has increased by \$40 billion -- 2.0 times the initial spending shock. This is known as the multiplier process. Try it using different values of the MPC, tax rate, and Autonomous spending shock in the table below:

 Interactive Table -- the Spending Multiplier

1) You may adjust the value for the Change in Autonomous Expenditure,
Marginal Propensity to Consume (MPC), or Tax Rates: by clicking on the boldfaced numbers in the appropriate number box. Just click on any of these three numbers and enter a new value.
2) Note the following:
• \$-50,000.00 < Change in Ao < \$50,000.00,
• 0.010 < MPC < 1.00
• 0.010 < Tax Rate < 1.00
3) Press the Spending button to display the process.
4) Press Reset to start over.

Concepts for Review:
• Aggregate Income
• Aggregate Expenditure
• Autonomous Consumption
• Autonomous Expenditure
• Equilibrium Income
• Marginal Propensity to Consume
• Spending Multiplier