National Income Determination

National income determination is the process by which the equilibrium level of national income (GDP) is established in an economy. The Keynesian cross model (also called the 45-degree line model) provides a powerful visual and analytical framework for understanding this process. It was developed by Paul Samuelson (1948) as a pedagogical simplification of Keynes's (1936) General Theory, and it remains central to A-Level macroeconomics.

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The Keynesian Cross Model

The 45-Degree Line

The 45-degree line represents all points where planned aggregate expenditure (AE) equals actual output (Y):

• At every point on the 45-degree line, AE = Y
• This is the equilibrium condition — the economy is in balance when what firms produce equals what is planned to be spent

The Aggregate Expenditure Function

The aggregate expenditure function shows total planned spending at each level of national income:

AE = C + I + G + (X − M)

Using the Keynesian consumption function:

AE = [a + bYd] + I + G + (X − M)