# The Spending Multiplier and Changes in Government Spending

### Learning Objectives

- Determine how government spending should change to reach equilibrium, or full employment (using the income-expenditure model)

Recall that macro equilibrium in the income-expenditure model is found at the point where the level of GDP, or national income, equals aggregate expenditure. The formula for the aggregate expenditure is

Aggregate Expenditure = C + I + G + (X – M).

Finally, note that this example includes income taxes; thus, people consume out of disposable income (or take-home pay). This is shown in the consumption equation below, which deducts taxes before spending.### Exercise: Expansionary Fiscal policy

Suppose the model is given by:Y = National income

T = Taxes = 0.3Y

C = Consumption = 200 + 0.9 (Y – T)

I = Investment = 600

G = Government spending = 1,000

X = Exports = 600

Y = Imports = 0.1 (Y – T)

**Step 1.** Calculate the initial equilibrium for this economy (where Y = AE).

Y | = | 200 + 0.9(Y – 0.3Y) + 600 + 1000 + 600 – 0.1(Y – 0.3Y) |

Y – 0.63Y + 0.07Y | = | 2400 |

0.44Y | = | 2400 |

Y | = | 5454 |

**Step 2.** Assume that the full employment level of output is 6,000. What level of government spending would be necessary to reach that level? Since initial output is 5,454, GDP needs to be increased by 6,000 - 5,454 = 556. What increase in government spending (while incorporating the spending multiplier) will achieve this?

6000 = 200 + 0.9(6000 – 0.3(6000)) + 600 + G + 600 – 0.1(6000 – 0.3(6000))

**Step 3.** Solve this problem arithmetically. The answer is: G = 1,240. In other words, increasing government spending by 240, from its original level of 1,000, to 1,240, would raise output to the full employment level of GDP.

### Watch It

Watch the following video for a similar example.### Try It

https://assessments.lumenlearning.com/assessments/7579### Licenses and Attributions

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