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Lesson M04.L03: Planned vs Actual Expenditure and Aggregate Demand

Module: Macroeconomics in the Short-Run: The Basic Keynesian Model Level: intro Duration: 30 minutes Learning Objective: Distinguish planned from actual expenditure; describe inventory adjustment as the mechanism driving output toward equilibrium; draw the Keynesian cross diagram. Data as of: 2024 Provenance: OpenStax Macro 3e | MIT OCW 14.02

Explanation

A cornerstone of the Keynesian model is the distinction between planned expenditure and actual expenditure.

Planned expenditure (PE) is the amount households, firms, and governments intend to spend on goods and services. It is determined by income and autonomous spending decisions, and captured in our aggregate expenditure function:

PE = C + I_planned + G

Where C is consumption (from the consumption function), I_planned is planned investment by firms, and G is government spending.

Actual expenditure always equals GDP by accounting identity (every dollar of output must be purchased by someone). However, if firms produce more than households actually want to buy, the unsold goods pile up in inventories (stockrooms, warehouses). Conversely, if demand exceeds production, inventories are drawn down.

Inventory adjustment is the key mechanism: - If output > planned expenditure → inventories rise unexpectedly → firms reduce production next period → output falls - If output < planned expenditure → inventories fall unexpectedly → firms increase production → output rises - If output = planned expenditure → inventories stable → equilibrium: no pressure to change output

The Keynesian Cross is the diagram that shows this process: - The 45° line represents all points where actual output = actual expenditure (income = spending) - The planned expenditure line (PE) is flatter than 45° (slope = MPC < 1) - Equilibrium is where PE crosses the 45° line

At equilibrium: Y* = PE — output equals planned spending, inventories are stable, and there is no pressure for output to change.

Worked Example

Given: - Autonomous consumption a = $500 billion - MPC = 0.80 - Planned investment I = $200 billion (autonomous — does not vary with Y) - Government spending G = $300 billion (autonomous)

Step 1 — Write the planned expenditure function: PE = C + I + G C = 500 + 0.80Y PE = (500 + 0.80Y) + 200 + 300 PE = 1,000 + 0.80Y

Step 2 — Find equilibrium output (set Y = PE): Y = 1,000 + 0.80Y Y − 0.80Y = 1,000 0.20Y = 1,000 Y = 1,000 ÷ 0.20 = $5,000 billion*

Step 3 — Verify (check PE at Y = 5,000): PE = 1,000 + 0.80 × 5,000 = 1,000 + 4,000 = $5,000 billion ✓

Step 4 — What happens if firms produce $5,500 billion instead? PE at Y = 5,500: PE = 1,000 + 0.80 × 5,500 = 1,000 + 4,400 = \(5,400 billion Output (\)5,500B) > PE ($5,400B) → unplanned inventory build-up of $100B → Firms cut back production → output moves back toward $5,000B ✓

Common Misconception

Misconception: In the Keynesian model, equilibrium means the economy is at full employment.

Correction: Keynesian equilibrium is defined as the point where planned expenditure equals output — inventories are stable and firms have no incentive to change production. This equilibrium can occur below full employment. This is the central Keynesian insight: an economy can be stuck in a stable but sub-optimal state with persistent unemployment, if aggregate demand is insufficient to generate full-employment output. Policy is needed to shift the PE line upward.

Practice Prompts

  1. Autonomous consumption is $400B, MPC is 0.75, planned investment is $150B, and government spending is $250B. Write the PE function and find equilibrium output. → Answer: PE = (400 + 0.75Y) + 150 + 250 = 800 + 0.75Y. Equilibrium: Y = 800 + 0.75Y → 0.25Y = 800 → Y* = $3,200 billion.

  2. Using the same parameters, if current output is $3,600B, what happens to inventories and what direction does output move? → Answer: PE at Y = 3,600: PE = 800 + 0.75 × 3,600 = 800 + 2,700 = \(3,500B. Output (\)3,600B) > PE ($3,500B) → inventories rise by $100B (unplanned) → firms cut production → output falls back toward $3,200B.

  3. What is the role of the 45° line in the Keynesian cross diagram? → Answer: The 45° line shows all points where income (Y, on the horizontal axis) equals expenditure (on the vertical axis). It represents the accounting identity that actual expenditure always equals actual output. Equilibrium is found where the PE line crosses the 45° line — because only at that intersection does planned expenditure equal output, so there is no unplanned inventory change pushing output up or down.

Visual — Planned Expenditure and Inventory Adjustment

Keynesian cross: planned expenditure vs output Output / income, Y Expenditure 45° line PE = A + MPC·Y Autonomous spending intercept E Y* Above Y*: inventories fall, firms raise output Below Y*: inventories rise, firms cut output

Figure: Equilibrium occurs where planned expenditure equals output. If output is too high, inventories accumulate and firms cut production; if output is too low, inventories run down and firms expand production.

Further Resources