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)

Where:

• a = autonomous consumption
• b = MPC
• Yd = disposable income = Y − T
• I, G, X = treated as autonomous (independent of Y) in the simple model
• M = partly autonomous, partly induced (some imports depend on income)

Key Features of the AE Function

Feature	Explanation
Intercept	The sum of all autonomous spending: a + I + G + X − autonomous M. This is the level of planned spending when income is zero.
Slope	The marginal propensity to spend domestically out of national income. In a closed economy, this equals MPC. In an open economy with taxation, the slope is MPC(1 − t) − MPM, where t is the marginal tax rate.
Position	Any change in autonomous spending shifts the AE function up or down. A rise in G, I, X, or autonomous C shifts AE upward; a rise in autonomous T or M shifts AE downward.

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Equilibrium National Income

Equilibrium occurs where the AE function crosses the 45-degree line:

Condition	Meaning
AE = Y	Planned spending equals output — firms sell exactly what they produce
AE > Y	Planned spending exceeds output — unplanned depletion of inventories — firms increase production → Y rises
AE < Y	Output exceeds planned spending — unplanned accumulation of inventories — firms cut production → Y falls

The economy automatically moves towards equilibrium through the inventory adjustment mechanism:

1. If AE > Y → firms find inventories falling → they increase production → Y rises → convergence towards equilibrium
2. If AE < Y → firms find inventories rising → they cut production → Y falls → convergence towards equilibrium

Exam Tip: The inventory adjustment mechanism is the key to understanding how equilibrium is reached. Always explain this process in your answers — it shows that you understand the dynamics of the model, not just the static equilibrium condition.

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The Inflationary Gap and the Deflationary Gap

The Deflationary (Recessionary) Gap

A deflationary gap exists when equilibrium national income is below full employment national income (Yfe):

Feature	Explanation
Definition	The amount by which aggregate expenditure falls short of the level needed to achieve full employment
Cause	Insufficient aggregate demand — consumers, firms, and/or the government are not spending enough
Symptoms	Demand-deficient (cyclical) unemployment, spare capacity, low inflation or deflation
Solution (Keynesian)	Increase injections (raise G, cut T, lower interest rates) to shift AE upward and close the gap
Multiplier effect	The required increase in autonomous spending is smaller than the gap itself, because the multiplier amplifies the initial injection

Calculating the Required Injection

If the deflationary gap is £50 billion and the multiplier is 2:

Required injection = Gap / Multiplier = £50bn / 2 = £25bn

A £25bn increase in autonomous spending (e.g., government spending) would, via the multiplier, increase equilibrium national income by £50bn, closing the deflationary gap.

The Inflationary Gap

An inflationary gap exists when equilibrium national income exceeds full employment national income:

Feature	Explanation
Definition	The amount by which aggregate expenditure exceeds the level consistent with full employment
Cause	Excessive aggregate demand — spending exceeds the economy's productive capacity
Symptoms	Demand-pull inflation, labour shortages, overheating
Solution (Keynesian)	Reduce injections (cut G, raise T, raise interest rates) to shift AE downward and close the gap
Multiplier effect	The required reduction in autonomous spending is smaller than the gap, because the negative multiplier amplifies the initial withdrawal

Exam Tip: Be careful with the terminology. A "deflationary gap" is not about deflation per se — it is about output being below full employment. Similarly, an "inflationary gap" describes excess demand, not necessarily runaway inflation. Use the terms precisely.

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The Paradox of Thrift in the Keynesian Cross

The Keynesian cross illustrates the paradox of thrift (Keynes, 1936):

Step	What Happens
1	Households decide to save more → consumption falls
2	The AE function shifts downward (lower autonomous consumption or lower MPC)
3	Equilibrium national income falls (by a multiplied amount)
4	At the new, lower equilibrium, incomes are lower — so actual saving may not increase
5	The attempt to save more has reduced national income without necessarily increasing aggregate saving

This paradox is central to Keynesian economics: it shows that what is rational for individuals (saving for the future) can be collectively harmful (reducing national income and employment).

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Injections-Withdrawals Approach

An alternative way to determine equilibrium is the injections-withdrawals (J-W) approach:

Equilibrium condition: J = W

That is: I + G + X = S + T + M