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Lesson M04.L05: Recessionary and Inflationary Gaps

Module: Macroeconomics in the Short-Run: The Basic Keynesian Model Level: intro Duration: 30 minutes Learning Objective: Identify and illustrate recessionary and inflationary output gaps in the Keynesian cross; calculate the required policy change to close each gap. Data as of: 2024 Provenance: OpenStax Macro 3e | RBA Education | MIT OCW 14.02

Explanation

In the Keynesian cross, the economy reaches equilibrium where planned expenditure equals output. But that equilibrium is not necessarily at full-employment output (Y_fe) โ€” the level of GDP consistent with the natural rate of unemployment (NAIRU).

Two types of output gap can exist:

1. Recessionary gap (deflationary gap): Equilibrium output (Y) is below full-employment output (Y_fe). - Actual unemployment > NAIRU - The economy is underperforming; there is spare capacity - Workers and capital are idle - Policy prescription: increase* aggregate demand (expansionary fiscal or monetary policy)

Recessionary gap = Y_fe โˆ’ Y (a positive number when Y < Y_fe)

2. Inflationary gap: Equilibrium output (Y) is above full-employment output (Y_fe). - Actual unemployment < NAIRU - The economy is "overheating"; demand exceeds the economy's sustainable productive capacity - Upward pressure on wages and prices โ€” inflation risk - Policy prescription: reduce* aggregate demand (contractionary fiscal or monetary policy)

Inflationary gap = Y โˆ’ Y_fe (a positive number when Y > Y_fe)

Closing the gap with policy: Because of the multiplier, you do not need to increase government spending by the full size of the gap. The required change in autonomous spending (ฮ”A) to close a gap equals:

ฮ”A = Gap รท Multiplier = Gap ร— (1 โˆ’ MPC)

In other words, a small change in government spending (or investment, or taxes) gets amplified by the multiplier to close a larger output gap.

Worked Example

Given: - Full-employment output: Y_fe = $2,000 billion - Current equilibrium output: Y = $1,700 billion - MPC = 0.75 - Multiplier: k = 1 รท (1 โˆ’ 0.75) = 4*

Step 1 โ€” Identify the gap: Y < Y_fe โ†’ Recessionary gap Gap = Y_fe โˆ’ Y = 2,000 โˆ’ 1,700 = $300 billion

Step 2 โ€” Calculate required increase in government spending to close the gap: ฮ”G = Gap รท k = 300 รท 4 = $75 billion

Step 3 โ€” Verify: New equilibrium: ฮ”Y = k ร— ฮ”G = 4 ร— 75 = \(300B increase New Y* = 1,700 + 300 = **\)2,000B = Y_fe** โœ“

Step 4 โ€” Now suppose instead Y* = \(2,200B (inflationary gap):** Gap = Y* โˆ’ Y_fe = 2,200 โˆ’ 2,000 = **\)200 billion inflationary gap Required reduction in spending: ฮ”G = โˆ’(200 รท 4) = โˆ’$50 billion (cut government spending by \(50B) New Y* = 2,200 โˆ’ 200 = **\)2,000B = Y_fe** โœ“

Australian context (2022โ€“23): Following massive COVID stimulus, Australia's economy ran with an estimated inflationary gap: unemployment fell to 3.5% (below NAIRU โ‰ˆ 4.5%) and inflation surged to 7.8% (Dec 2022). The RBA responded with aggressive interest rate increases (from 0.1% to 4.35% by late 2023) to reduce aggregate demand and close the inflationary gap โ€” a real-world example of contractionary policy in action.

Common Misconception

Misconception: To close a $300 billion recessionary gap, the government must spend $300 billion.

Correction: Thanks to the multiplier, the government needs to spend only a fraction of the gap. With a multiplier of 4, a $75 billion increase in spending generates a $300 billion increase in equilibrium output. The multiplier amplifies the initial spending through successive rounds of income and expenditure. Understanding this allows policymakers to calculate precisely how much stimulus is needed โ€” and avoid over- or under-shooting.

Practice Prompts

  1. Full-employment output is $1,500B. Equilibrium output is $1,200B. MPC = 0.80. What type of gap exists, what is its size, and how much must government spending increase to close it? โ†’ Answer: Y < Y_fe โ†’ recessionary gap of \(300B. Multiplier = 1 รท (1โˆ’0.80) = 5. Required ฮ”G = 300 รท 5 = **\)60 billion increase*.

  2. Full-employment output is $2,500B. Current equilibrium is $2,700B. MPC = 0.75. Identify the gap and calculate the required policy change to close it. โ†’ Answer: Y > Y_fe โ†’ inflationary gap of \(200B. Multiplier = 1 รท (1โˆ’0.75) = 4. Required ฮ”G = โˆ’(200 รท 4) = **โˆ’\)50 billion* (reduce government spending or raise taxes to reduce demand by $50B).

  3. In Australia in 2022, why did the RBA raise interest rates rather than cut government spending to close the inflationary gap? โ†’ Answer: Monetary policy (raising the cash rate) is faster to implement and more flexible than fiscal policy โ€” interest rate decisions can be made monthly by the RBA board, whereas changing government spending requires parliamentary approval and budget processes. Higher interest rates increase borrowing costs, reducing household consumption and business investment, shifting the PE line downward and closing the inflationary gap. The speed and flexibility of monetary policy make it the preferred first-response tool for short-run stabilisation in Australia.

Visual โ€” Recessionary and Inflationary Gaps in the Keynesian Cross

Output gaps relative to full employment \(Y_{fe}\) Output / income, Y Expenditure PEโ‚‚ PEโ‚ 45ยฐ line Y_fe Recessionary equilibrium Inflationary equilibrium Recessionary gap Inflationary gap

Figure: When planned expenditure intersects the 45ยฐ line below \(Y_{fe}\), the economy has a recessionary gap. When it intersects above \(Y_{fe}\), the economy has an inflationary gap.

Further Resources