Difficulty: Intermediate | Prerequisites: Section 8.1 (consumption function, MPC/MPS, planned vs. actual investment)
Source: Principles of Macroeconomics, Case/Fair, 8e – Chapter 8, Section 8.2
Tags: equilibrium output, planned aggregate expenditure, unplanned inventory, saving equals investment, Keynesian cross, income-expenditure model, leakages, injections
Section 8.1 gave you the consumption function and the distinction between planned and actual investment. This section puts those pieces together to answer a central question: at what level of output is the economy in balance? "Balance" here means that firms are selling exactly what they planned to produce, with no surprise build-up or drawdown of inventories. If spending exceeds output, shelves empty and firms ramp up production. If output exceeds spending, goods pile up and firms cut back. The equilibrium is where neither adjustment is needed. This is the core of the Keynesian cross model, and it is the framework onto which fiscal policy (Chapter 9) will be layered.
The economy is in equilibrium when planned aggregate expenditure equals aggregate output (Y = AE). At that point, planned investment equals actual investment and unplanned inventory change is zero. Below equilibrium, inventories fall and firms expand; above it, inventories rise and firms contract.
Equilibrium output
The level of aggregate output (income) at which planned aggregate expenditure equals aggregate output: Y = AE. In simple terms, it is the output level where everything produced gets bought as planned.
Planned aggregate expenditure (AE)
Total planned spending: AE = C + planned I (in the simple model with no government or foreign sector). This is what all the buyers in the economy intend to spend.
Unplanned inventory investment
The gap between aggregate output and planned aggregate expenditure. When Y > AE, inventories accumulate unexpectedly (positive unplanned inventory). When Y < AE, inventories fall unexpectedly (negative unplanned inventory).
Leakages
Income that is not spent on domestic goods and services. In the simple model, saving is the only leakage. Think of it as money "leaking out" of the spending stream.
Injections
Spending that enters the economy from outside the household consumption stream. In the simple model, planned investment is the only injection.
Saving-investment approach
An alternative way to find equilibrium: set saving equal to planned investment (S = I). Since Y = C + S and AE = C + I, requiring Y = AE is the same as requiring S = I.
Equilibrium requires Y = C + planned I (no government, no foreign sector).
Equivalently, S = planned I.
At equilibrium, there is no unplanned inventory change. Actual investment equals planned investment.
Output above equilibrium (Y > AE): firms produce more than people want to buy. Unsold goods stack up as unplanned inventory. Firms respond by cutting production. Output falls toward equilibrium.
Output below equilibrium (Y < AE): spending exceeds production. Inventories are drawn down unexpectedly. Firms respond by increasing production. Output rises toward equilibrium.
The AE line plots planned expenditure against output. Its intercept is autonomous spending (autonomous C + planned I), and its slope is the MPC.
The 45-degree line shows all points where AE = Y.
Equilibrium is where the AE line crosses the 45-degree line.
At output levels to the left of the crossing, the AE line is above the 45-degree line: spending exceeds output, inventories fall, output rises.
At output levels to the right, the AE line is below the 45-degree line: output exceeds spending, inventories rise, output falls.
In the simple model: leakage = saving; injection = planned investment.
At equilibrium, leakages equal injections (S = I).
Above equilibrium, saving exceeds planned investment (leakages > injections), so income contracts.
Below equilibrium, planned investment exceeds saving (injections > leakages), so income expands.
Given C = a + bY and I = I₀ (a constant), set Y = C + I:
Y = a + bY + I₀
Y − bY = a + I₀
Y(1 − b) = a + I₀
Y = (a + I₀) / (1 − b)*
Example: C = 100 + 0.8Y, I = 50.
Y = (100 + 50) / (1 − 0.8) = 150 / 0.2 = 750.
Using the saving-investment approach: S = −a + (1 − b)Y. Set S = I:
−a + (1 − b)Y = I₀
Y = (a + I₀) / (1 − b), which is the same result.
The inventory mechanism is the engine that drives the economy toward equilibrium.
Unplanned inventory increases signal overproduction. Firms cut output.
Unplanned inventory decreases signal excess demand. Firms raise output.
This process continues until planned spending matches output.
If planned investment falls, the AE line shifts downward.
Equilibrium output decreases. The decrease in output is larger than the initial drop in investment (this is the multiplier effect, covered fully in Section 8.3).
Formula | Meaning |
|---|---|
Y* = (a + I₀) / (1 − MPC) | Equilibrium output (algebraic solution) |
Y = AE = C + I | Equilibrium condition (expenditure approach) |
S = I | Equilibrium condition (saving-investment approach) |
Unplanned inventory = Y − AE | Positive means excess output; negative means excess spending |
Actual I = Planned I + Unplanned inventory change | Always holds, by definition |
Example 1 – Table-based equilibrium (Table 8.3 from the textbook):
Output | Consumption | Planned I |
|---|---|---|
200 | 300 | 100 |
400 | 450 | 100 |
600 | 600 | 100 |
800 | 750 | 100 |
1,000 | 900 | 100 |
AE at 400 = 450 + 100 = 550. Output is 400, so unplanned inventory = 400 − 550 = −150.
AE at 1,000 = 900 + 100 = 1,000. Output = AE. Equilibrium is at Y = 1,000.
MPC = ΔC / ΔY = (450 − 300) / (400 − 200) = 150 / 200 = 0.75.
Example 2 – Algebraic equilibrium: C = 500 + 0.9Y, I = 400.
Y = (500 + 400) / (1 − 0.9) = 900 / 0.1 = 9,000.
Example 3 – Saving-investment approach: S = −200 + 0.2Y, I = 100.
Set S = I: −200 + 0.2Y = 100. So 0.2Y = 300, Y = 1,500.
When consumer confidence collapses (say, during a financial crisis), spending drops below output. Businesses see unsold goods stacking up on shelves and in warehouses. They cut orders, lay off workers, and reduce production. That is the adjustment mechanism this model describes. The 2008-09 recession is a textbook case: as spending fell, unplanned inventories surged, triggering sharp output cuts across manufacturing.
Students often think equilibrium means "the economy is doing well." It does not. Equilibrium just means output equals planned spending. The economy can be in equilibrium with high unemployment if spending is low.
Actual investment always equals saving (by accounting identity). But equilibrium requires planned investment to equal saving. This distinction catches a lot of students on exams.
An unplanned inventory increase does not mean planned investment went up. It means the opposite: firms could not sell everything they produced, so goods piled up beyond what they intended.
Equilibrium is not where saving equals zero. It is where saving equals planned investment.
Be prepared to find equilibrium from a table (locate the row where Y = C + I), from a graph (find where AE crosses the 45-degree line), and from equations (solve algebraically).
Know the direction of unplanned inventory change above and below equilibrium, and how firms respond.
The saving-investment approach (S = I) is an alternative route to the same equilibrium. Some exam questions force you to use it.
Watch for questions that test whether you know the difference between planned and actual investment. They only coincide at equilibrium.
At equilibrium, unplanned inventory change is ________. (zero)
True or false: If aggregate output exceeds planned spending, inventories fall. (False, inventories rise)
If C = 100 + 0.8Y and I = 50, equilibrium Y is ________. (750)
Firms react to unplanned inventory increases by ________ output. (reducing)
True or false: At equilibrium, planned investment equals actual investment. (True)
Q: In macroeconomics, equilibrium is defined as the point at which what two things are equal?
A: Planned aggregate expenditure equals aggregate output.
Q: If aggregate output is greater than planned aggregate spending, what happens to unplanned inventory investment?
A: It is positive. Output exceeds spending, so unsold goods accumulate.
Q: Using C = 500 + 0.9Y and I = 400, what is the equilibrium level of income?
A: Y = (500 + 400) / (1 − 0.9) = 900 / 0.1 = 9,000.
Q: If S = −200 + 0.2Y and I = 100, what is equilibrium income?
A: −200 + 0.2Y = 100, so 0.2Y = 300, Y = 1,500.
Q: When there is an unplanned drawdown of inventories, what do firms do?
A: They increase production, because the inventory decline signals that demand exceeds current output.
Q: Using the saving-investment approach, what is the equilibrium condition?
A: C + I = C + S, which simplifies to S = I (saving equals planned investment).
This section is the bridge between the consumption and saving functions (Section 8.1) and the multiplier (Section 8.3). Once you understand how equilibrium is determined, the multiplier shows you how far equilibrium shifts when planned investment or autonomous consumption changes. This framework also prepares you for Chapter 9, where government spending and taxes enter the model and create new leakages (taxes) and injections (government purchases).
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