What Is Keynesian Cross?
The Keynesian cross is a fundamental model in macroeconomics, specifically within Keynesian economics, that illustrates how the equilibrium level of real gross domestic product (GDP) is determined by the intersection of aggregate expenditure and aggregate output80, 81. This model, also known as the expenditure-output model, helps to visualize the relationship between total spending in an economy and the total goods and services produced79. The Keynesian cross is based on the premise that in the short run, product adjusts to meet the level of aggregate demand78.
History and Origin
The Keynesian cross diagram is a core component of the macroeconomic theories advanced by British economist John Maynard Keynes. It encapsulates central ideas from his seminal 1936 work, "The General Theory of Employment, Interest, and Money". Keynes's work emerged during the Great Depression, a period marked by high unemployment and economic stagnation, which challenged the prevailing classical economic thought that markets would automatically ensure full employment77.
Keynes argued that aggregate demand, rather than aggregate supply, was the primary driver of economic activity, and that insufficient demand could lead to prolonged periods of unemployment75, 76. The Keynesian cross was later popularized as a teaching tool by Paul Samuelson in his influential textbook, Economics: An Introductory Analysis. This model became a dominant approach in macroeconomics from the 1930s to the 1970s, providing a theoretical basis for government policies aimed at achieving full employment73, 74.
Key Takeaways
- The Keynesian cross graphically represents the equilibrium where total aggregate expenditure equals real GDP.71, 72
- It highlights the importance of aggregate expenditure (spending by households, businesses, and government) in determining national income and output.69, 70
- The model suggests that an economy can achieve equilibrium at levels below or above potential GDP, indicating the possibility of recessionary or inflationary gaps.67, 68
- It forms the basis for understanding the multiplier effect, where initial changes in spending lead to larger changes in overall economic output.65, 66
- The Keynesian cross is a foundational concept in fiscal policy analysis, demonstrating how government spending and taxation can influence economic activity.64
Formula and Calculation
The Keynesian cross model establishes equilibrium where aggregate expenditure (AE) equals total output or income (Y). This relationship is expressed by the fundamental identity:
Aggregate expenditure (AE) is the sum of four components: consumption (C), planned investment (I), government spending (G), and net exports (NX). Therefore, the formula for aggregate expenditure is:
Substituting this into the equilibrium condition, we get:
Each component can be further defined:
- ( Y ): Represents total income or output in the economy, typically measured as real GDP.63
- ( C ): Represents consumption expenditure by households, often a function of disposable income.62
- ( I ): Represents investment expenditure by businesses. In simple Keynesian models, this is often assumed to be exogenous (predetermined).60, 61
- ( G ): Represents government spending on goods and services. This is also often treated as exogenous in the basic model.58, 59
- ( NX ): Represents net exports, calculated as exports (X) minus imports (M).57
Interpreting the Keynesian Cross
The Keynesian cross is interpreted through a diagram with real GDP (output/income) on the horizontal axis and aggregate expenditure on the vertical axis55, 56. A 45-degree line, originating from the origin, represents all points where aggregate expenditure equals aggregate output (AE = Y)53, 54. This line signifies the equilibrium condition where what is produced in the economy is exactly equal to what is being spent52.
The aggregate expenditure line, which represents C + I + G + NX, typically slopes upward because consumption, a major component, increases with income50, 51. The equilibrium in the economy occurs at the point where the aggregate expenditure line intersects the 45-degree line48, 49.
If the economy's output is below this equilibrium point, aggregate expenditure exceeds output, leading to a depletion of inventories. Businesses respond by increasing production, which raises income and employment, moving the economy towards equilibrium. Conversely, if output is above the equilibrium, aggregate expenditure is less than output, causing inventories to accumulate. Businesses will then reduce production, leading to lower incomes and employment, moving the economy back to equilibrium45, 46, 47. The model demonstrates that the economy naturally adjusts towards this equilibrium point44.
Hypothetical Example
Consider a simplified economy where:
- Consumption (C) = (100 + 0.75Y_d), where (Y_d) is disposable income ((Y - T))
- Investment (I) = 300 (assumed fixed)
- Government Spending (G) = 200 (assumed fixed)
- Taxes (T) = 0 (for simplicity)
- Net Exports (NX) = 0 (for simplicity, closed economy)
In this scenario, aggregate expenditure (AE) is (C + I + G + NX).
So, (AE = (100 + 0.75Y) + 300 + 200 + 0).
(AE = 600 + 0.75Y).
To find the equilibrium output (Y), we set AE = Y:
(Y = 600 + 0.75Y)
(Y - 0.75Y = 600)
(0.25Y = 600)
(Y = 600 / 0.25)
(Y = 2400)
In this hypothetical economy, the equilibrium level of output, where total spending equals total production, is 2,400 units. If output were below 2,400, say 2,000, then AE would be (600 + 0.75(2000) = 600 + 1500 = 2100). Since AE (2,100) > Y (2,000), businesses would increase production. If output were above 2,400, say 2,800, then AE would be (600 + 0.75(2800) = 600 + 2100 = 2700). Since AE (2,700) < Y (2,800), businesses would reduce production, eventually bringing the economy back to equilibrium at 2,400.
Practical Applications
The Keynesian cross serves as a foundational tool for understanding and implementing macroeconomic policy, particularly fiscal policy. It helps economists and policymakers predict the impact of government interventions on economic output and employment42, 43.
During economic downturns or recessions, the model suggests that there may be insufficient aggregate demand to maintain full employment. In such situations, the government can intervene by increasing its spending or cutting taxes to boost aggregate demand40, 41. For instance, increased government expenditure on public projects not only creates jobs directly but also stimulates demand for related goods and services, leading to a broader increase in economic activity through the multiplier effect39. This approach aims to move the economy towards a new equilibrium with higher output and employment38.
Conversely, in periods of economic expansion with rising inflation, Keynesian theory suggests using contractionary fiscal policies, such as increasing taxes or reducing government spending, to cool down an overheating economy37. The Keynesian cross thus provides a simplified framework for analyzing how government actions can help stabilize economic cycles36.
Limitations and Criticisms
Despite its foundational role, the Keynesian cross model has several limitations and has faced criticisms. One key critique is its assumption of a closed economy, meaning it does not fully account for the impacts of international trade, exports, or imports34, 35. While some versions incorporate net exports, the basic model often simplifies or omits them, which can limit its applicability to open economies32, 33.
Another limitation is its assumption that prices and wages are fixed, overlooking potential inflationary effects that can arise from increased demand30, 31. The model primarily focuses on output adjustments in response to demand changes and does not explicitly include the price level28, 29. Critics also argue that the model does not consider how changes in aggregate expenditure might influence interest rates, which can, in turn, affect investment27.
Furthermore, some critics argue that the Keynesian cross is excessively aggregative, focusing heavily on macroeconomic variables like aggregate demand and supply while potentially neglecting the complexities of individual markets or microeconomic foundations26. While useful for demonstrating basic income-expenditure dynamics, it is a simplified representation that does not capture all the intricate mechanisms of a real economy. For example, some economists argue that the model ignores the supply side of the economy, assuming that supply will always meet demand as long as the economy operates below full employment25.
Keynesian Cross vs. IS-LM Model
The Keynesian cross and the IS-LM model are both fundamental tools in macroeconomics, but they operate at different levels of complexity. The Keynesian cross, as discussed, is a simpler model that focuses on the goods market equilibrium, where aggregate expenditure equals output23, 24. It does not explicitly include interest rates or the money market22. Its primary purpose is to illustrate the determination of equilibrium income and the impact of changes in autonomous spending, such as government expenditure or investment21.
In contrast, the IS-LM model extends the analysis by integrating both the goods market (represented by the IS curve) and the money market (represented by the LM curve)19, 20. The IS curve is derived from the Keynesian cross, showing combinations of interest rates and output where the goods market is in equilibrium17, 18. The LM curve represents combinations of interest rates and output where the money market is in equilibrium16. By combining these two curves, the IS-LM model determines the simultaneous equilibrium levels of national income and the interest rate, providing a more comprehensive view of macroeconomic interactions, including the role of monetary policy14, 15. While the Keynesian cross offers a straightforward depiction of demand-driven output, the IS-LM model offers a more nuanced framework by incorporating financial markets and showing how fiscal and monetary policy interact.
FAQs
What is the significance of the 45-degree line in the Keynesian cross?
The 45-degree line in the Keynesian cross diagram represents all points where aggregate expenditure (total spending) in the economy is equal to the total output or national income. It serves as a visual representation of the equilibrium condition (AE = Y).12, 13
How does the Keynesian cross explain unemployment?
The Keynesian cross suggests that equilibrium can occur at a level of output below potential GDP, implying that the economy can be in a state of stable equilibrium with unemployment. This happens when the aggregate expenditure is insufficient to generate full employment.10, 11
What is the role of government spending in the Keynesian cross model?
Government spending is a component of aggregate expenditure in the Keynesian cross model. An increase in government spending directly boosts aggregate demand, shifting the aggregate expenditure line upward and leading to a higher equilibrium level of income and output, demonstrating the multiplier effect.8, 9
Does the Keynesian cross account for inflation?
The basic Keynesian cross model assumes fixed prices and wages, and thus does not explicitly account for inflation. While it can illustrate how aggregate demand exceeding potential GDP might create an "inflationary gap," it doesn't detail the mechanisms of price level changes.6, 7
What is the marginal propensity to consume (MPC) in relation to the Keynesian cross?
The marginal propensity to consume (MPC) is the slope of the consumption function and thus influences the slope of the aggregate expenditure line. A higher MPC means that a larger portion of additional income is spent on consumption, leading to a steeper aggregate expenditure line and a larger multiplier effect in the model.4, 5
How does investment appear in the Keynesian cross?
In the simplest Keynesian cross model, investment is often treated as exogenous, meaning it's assumed to be a fixed amount not directly influenced by current income levels. It is a component of aggregate expenditure, and changes in planned investment can shift the aggregate expenditure line.1, 2, 3