Economics – Equilibrium, Output Gaps and Paradox of Thrift

🎯 Learning Objectives

Distinguish between equilibrium output and full-employment output
Identify a deflationary gap and an inflationary gap
Understand the paradox of thrift
Explain why the desire to save more can lead to less actual saving

🏭 Full Employment and the Output Gap

What is full-employment output (YF)_F)?

🔑 Definition

Full-employment output (YF_F) ) is the maximum output the economy can produce when all factors are fully employed.

This is the supply side of the economy — its potential.

Output Gap

Output gap = Y_F - Y*

The difference between full-employment output and equilibrium output

State	Condition	Meaning
Positive output gap	Y_F > Y*	Unemployment — economy below potential
Negative output gap	Y_F < Y*	Inflationary pressure — excess demand
Full employment	Y_F = Y*	Optimal equilibrium

📉 Deflationary Gap

Deflationary gap = increase in AD needed to reach Y_F

Deflationary gap = (Y_F - Y*) / k

📝 Example: Calculating the Deflationary Gap

Given: Y* = 1,000, Y_F = 1,200, MPC = 0.75

Solution:

Output gap = 1,200 − 1,000 = 200

Multiplier k = 1/(1−0.75) = 4

Deflationary gap = 200/4 = 50

Autonomous expenditure must rise by 50 to reach full employment.

📈 Inflationary Gap

Inflationary gap = decrease in AD needed to reach Y_F

Inflationary gap = (Y* - Y_F) / k

⚠️ What happens with an inflationary gap?

Demand exceeds productive capacity
The economy cannot supply all the demand
Result: Rising prices (inflation)
In our model prices are fixed, so this gap is problematic

🔄 Paradox of Thrift

💡 The Paradox

When households decide to save more at every income level, output falls, and in the end total saving may not increase at all.!

How does this work?

Households want to save more → they reduce consumption
C₀ falls → AD curve shifts down
Aggregate demand falls → output falls (multiplier effect!)
Income falls → although they want to save more per shekel, they have fewer shekels

Final saving depends on investment!

At equilibrium: \(S_p = I\)

🔑 Why Is It a Paradox?

At the individual level: if I save more, my wealth grows
At the economy level: if everyone saves more, national income falls
What is true for the individual is not necessarily true for the economy!

📝 Numerical Example

Initial state: C = 200 + 0.8Y, I = 100 (autonomous), no taxes or government

AD = 200 + 0.8Y + 100 = 300 + 0.8Y

Y* = 300/(1-0.8) = 300/0.2 = 1,500

C = 200 + 0.8×1,500 = 1,400

Sp = Y - C = 1,500 - 1,400 = 100 = I

Now people want to save more: C = 150 + 0.8Y

AD = 150 + 0.8Y + 100 = 250 + 0.8Y

Y* = 250/0.2 = 1,250

C = 150 + 0.8×1,250 = 1,150

Sp = 1,250 - 1,150 = 100 = I

🎯 Result: Output fell from 1,500 to 1,250, but saving remained 100!

⚠️ Condition for the Paradox

The paradox holds when investment is autonomous (independent of output).

If \(I = I_0 + bY\) (induced investment), saving can change.

📊 Summary: Comparison of States

State	Symptoms	Solution
Deflationary gap	Unemployment, under-utilised resources	Expansionary policy (↑G, ↓T)
Inflationary gap	Price pressure, excess demand	Contractionary policy (↓G, ↑T)
Full employment	Full utilisation, stability	Maintain the situation