# The expenditure-output, or Keynesian cross, model

Use a diagram to analyze the relationship between aggregate expenditure and economic output in the Keynesian model.

## Key points

• The expenditure-output model, or Keynesian cross diagram, shows how the level of aggregate expenditure varies with the level of economic output.
• The equilibrium in the diagram occurs where the aggregate expenditure line crosses the 45-degree line, which represents the set of points where aggregate expenditure in the economy is equal to output, or national income.
• Equilibrium in a Keynesian cross diagram can happen at potential GDP—or below or above that level.

## The expenditure-output, or Keynesian Cross, model

The fundamental ideas of Keynesian economics were developed before the aggregate demand/aggregate supply, or AD/AS, model was popularized. From the 1930s until the 1970s, Keynesian economics was usually explained with a different model, known as the expenditure-output approach.
This approach is strongly rooted in the fundamental assumptions of Keynesian economics. It focuses on the total amount of spending in the economy, with no explicit mention of aggregate supply or of the price level. Although, it is possible to draw some inferences about aggregate supply and price levels based on the diagram.

## The axes of the expenditure-output diagram

The expenditure-output model determines the equilibrium level of real gross domestic product, or GDP, by the point where the total or aggregate expenditures in the economy are equal to the amount of output produced.
If you take a look at the diagram below, you'll see that the axes of the Keynesian cross diagram presented show real GDP on the horizontal axis as a measure of output and aggregate expenditure on the vertical axis as a measure of spending.
The aggregate expenditure-output model shows aggregate expenditures on the vertical axis and real GDP on the horizontal axis. A vertical line shows potential GDP where full employment occurs.
Image credit: Figure 1 in "The Expenditure-Output (or Keynesian Cross) Model" by OpenStaxCollege, CC BY 4.0
Remember that GDP can be thought of in several equivalent ways—it measures both the value of spending on final goods and also the value of the production of final goods. All sales of the final goods and services that make up GDP will eventually end up as income for workers, managers, and investors and owners of firms. The sum of all the income received for contributing resources to GDP is called national income, $\text{Y}$ on the diagram above. When talking about the expenditure-output model, it is sometimes useful to refer to real GDP as national income. Both axes are measured in real—inflation-adjusted—terms.

## The potential GDP line and the 45-degree line

The Keynesian cross diagram contains two lines that serve as conceptual guideposts to orient the discussion. The first is a vertical line showing the level of potential GDP. Potential GDP means the same thing here that it means in the AD/AS diagrams. It refers to the quantity of output that the economy can produce with full employment of its labor and physical capital.
The second conceptual line on the Keynesian cross diagram is the 45-degree line, which starts at the origin and reaches up and to the right. A line that stretches up at a 45-degree angle represents the set of points $(1, 1)$, $(2, 2)$, $(3, 3)$, and so on, where the measurement on the vertical axis is equal to the measurement on the horizontal axis.
In this diagram, the 45-degree line shows the set of points where the level of aggregate expenditure in the economy, measured on the vertical axis, is equal to the level of output or national income in the economy, measured by GDP on the horizontal axis.
When the macroeconomy is in equilibrium, it must be true that the aggregate expenditures in the economy are equal to the real GDP—because by definition, GDP is the measure of what is spent on final sales of goods and services in the economy. Thus, the equilibrium calculated with a Keynesian cross diagram will always end up where aggregate expenditure and output are equal—which will only occur along the 45-degree line.

## The aggregate expenditure schedule

The final ingredient of the Keynesian cross or expenditure-output diagram is the aggregate expenditure schedule, which shows the total expenditures in the economy for each level of real GDP. The intersection of the aggregate expenditure line with the 45-degree line—at point $\text{E0}$ in the diagram above—shows the equilibrium for the economy because it is the point where aggregate expenditure is equal to output or real GDP.
You can learn how the aggregate expenditure schedule is built here. But in this article, we'll work with already completed aggregate expenditure schedules.

## Equilibrium in the Keynesian cross model

With the aggregate expenditure line in place, the next step is to relate it to the two other elements of the Keynesian cross diagram.
The point where the aggregate expenditure line crosses the 45-degree line will be the equilibrium for the economy. It is the only point on the aggregate expenditure line where the total amount being spent on aggregate demand equals the total level of production. In the diagram below, this point of equilibrium, $\text{E0}$, happens at 6,000.
This Keynesian cross diagram shows equilibrium at a real GDP of $6,000. Potential GDP in this example is$7,000, so the equilibrium occurs at a level of output or real GDP below the potential GDP level.
Image credit: Figure 7 in "The Expenditure-Output (or Keynesian Cross) Model" by OpenStaxCollege, CC BY 4.0
Equilibrium is a point of balance where no incentive exists to shift away from that outcome. To understand why the point of intersection between the aggregate expenditure function and the 45-degree line is a macroeconomic equilibrium, let's take a look at the diagram below.
Consider what would happen if an economy found itself to the right of the equilibrium point $\text{E}$, say at point $\text{H}$ where output is higher than the equilibrium. At point $\text{H}$, the level of aggregate expenditure is below the 45-degree line, showing that the level of aggregate expenditure in the economy is less than the level of output. As a result, at point $\text{H}$, output is piling up unsold—not a sustainable state of affairs.
A Keynesian cross diagram shows three situations—one where output is greater than aggregate expenditure, one where aggregate expenditure is equal to output and one where output is less than aggregate expenditure.
Image credit: Figure 8 in "The Expenditure-Output (or Keynesian Cross) Model" by OpenStaxCollege, CC BY 4.0
On the other hand, consider the situation where the level of output is at point $\text{L}$ where real output is lower than the equilibrium. In this case, the level of aggregate demand in the economy is above the 45-degree line, indicating that the level of aggregate expenditure in the economy is greater than the level of output. When the level of aggregate demand has emptied the store shelves, it cannot be sustained either. Firms will respond by increasing their level of production.
So, the equilibrium must be the point where the amount produced and the amount spent are in balance, at the intersection of the aggregate expenditure function and the 45-degree line.

## Summary

• The expenditure-output model, or Keynesian cross diagram, shows how the level of aggregate expenditure varies with the level of economic output.
• The equilibrium in the diagram occurs where the aggregate expenditure line crosses the 45-degree line, which represents the set of points where aggregate expenditure in the economy is equal to output, or national income.
• Equilibrium in a Keynesian cross diagram can happen at potential GDP—or below or above that level.

## Review questions

• What is on the axes of an expenditure-output diagram?
• What does the 45-degree line show?

## Critical-thinking questions

• What does it mean when the aggregate expenditure line crosses the 45-degree line? In other words, how would you explain the intersection in words?
• Which model, the AD/AS or the expenditure-output model model, better explains the relationship between rising price levels and GDP? Why?