# The Spending Multiplier in the Income-Expenditure Model

## What you’ll learn to do: explain why the expenditure multiplier happens and how to calculate its size

Recall that a major finding of Keynesian economics is that spending is powerful. Not only does GDP change when aggregate expenditure changes, but GDP changes more than proportionately, so that a smaller change in expenditure causes a larger change in GDP. In this section, you'll explore the multiplier effect using logic, graphs and algebra. You'll also learn what makes the multiplier effect larger or smaller and how to compute that using the income-expenditure model.### Learning Objectives

- Explain and demonstrate the multiplier graphically using the income-expenditure model

\displaystyleSp\ending Multiplier=\frac{1}{(\text{MPS} )}

## Showing the Spending Multiplier Graphically Using the Income-Expenditure Model

We can show the expenditure multiplier graphically using the income-expenditure model. The original level of aggregate expenditure is shown by the AE_{0}line and yields an equilibrium level of GDP at Y

_{0}. Consider an increase in AE to AE

_{1}, which is shown by a parallel shift in the AE line. This could be caused by an increase in autonomous consumption, investment, government spending or net exports. The vertical distance between the two AE lines is the increase in aggregate expenditure. The new equilibrium level of GDP occurs at Y

_{1}. It should be clear that the increase in GDP from Y

_{0}to Y

_{1}is greater than the increase in expenditure from AE

_{0}to AE

_{1}.

The spending multiplier is defined as the ratio of the change in GDP (

**Δ**Y) to the change in autonomous expenditure (

**Δ**AE). Since the change in GDP is greater change in AE, the multiplier is greater than one. Suppose the equilibrium level of GDP is $700 billion. If government spending increases by $50 billion, GDP rises from is $700 billion (at Y

_{0}) to Y

_{1}$800 billion (at Y

_{1}). Thus, the change in GDP is $800 - $700 = $100 billion. In this example, the multiplier would be $100/$50 = 2.