Marshallian and Walrasian stability analysis :Indian Economic Service

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Marshallian and Walrasian Stability Analysis

1. Introduction

Market stability is a fundamental concept in economics that determines how prices and quantities adjust when there is disequilibrium (excess demand or supply). Two primary approaches to analyzing market stability are:

✔ Marshallian Stability – Based on the adjustment of quantity in response to price changes.
✔ Walrasian Stability – Based on the adjustment of prices in response to excess demand or supply.

These concepts are crucial in microeconomic theory, general equilibrium analysis, and market dynamics.

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2. Marshallian Stability Analysis

📌 Definition

Marshallian stability, developed by Alfred Marshall, focuses on quantity adjustments when a market is out of equilibrium. If there is excess supply, firms reduce production; if there is excess demand, firms increase production until equilibrium is restored.

🔹 Key Characteristics

✔ Adjustment occurs through quantity changes.
✔ Firms react to market signals (demand and supply conditions).
✔ Assumes that price remains fixed in the short run, while quantity adjusts.

📊 Graphical Representation

• X-axis → Quantity (Q)
• Y-axis → Price (P)
• Demand (D) and Supply (S) curves intersect at equilibrium (E).
• If quantity is too high (Q₂), firms reduce output to return to equilibrium.
• If quantity is too low (Q₁), firms increase output.

📌 Example:

• If farmers produce too much wheat, leading to excess supply, some reduce production in the next season, restoring balance.

🔹 Stability Condition

Marshallian stability occurs if: dQdP<0\frac{dQ}{dP} < 0

i.e., an increase in price leads to a decrease in quantity supplied, ensuring equilibrium restoration.

🔹 Advantages

✔ Realistic for Short-Run Analysis – Many firms adjust quantity faster than price.
✔ Applicable to Competitive Markets – Firms respond to demand fluctuations by changing output.

🔹 Disadvantages

❌ Ignores Price Adjustments – Prices are not always rigid; markets often adjust through price changes.
❌ Less Relevant for Services & Monopolies – Many sectors cannot quickly adjust quantity.

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3. Walrasian Stability Analysis

📌 Definition

Walrasian stability, developed by Léon Walras, focuses on price adjustments when there is disequilibrium. Instead of firms changing output, the price changes until demand and supply are equal.

🔹 Key Characteristics

✔ Adjustment occurs through price changes.
✔ The market mechanism is driven by tatonnement (trial and error process).
✔ Assumes instantaneous adjustment of prices to clear the market.

🔹 Walrasian Tatonnement Process

The auctioneer mechanism (Walrasian tatonnement) works as follows:
1️⃣ If excess demand (shortage) exists → Price increases.
2️⃣ If excess supply (surplus) exists → Price decreases.
3️⃣ This process continues until equilibrium is reached.

📊 Graphical Representation

• X-axis → Quantity (Q)
• Y-axis → Price (P)
• If price is too high (P₂) → Surplus → Prices fall.
• If price is too low (P₁) → Shortage → Prices rise.
• Price adjusts until P = Pe (equilibrium price).

📌 Example:

• In stock markets, if a company’s share price is too high, fewer investors buy, leading to a price drop. If the price is too low, demand rises, pushing the price up.

🔹 Stability Condition

Walrasian stability requires: dPdQ>0\frac{dP}{dQ} > 0

i.e., when price increases, quantity demanded decreases, ensuring stability.

🔹 Advantages

✔ More Realistic for Modern Markets – Many industries adjust prices before quantity.
✔ Works Well in Financial & Auction Markets – Stock prices change quickly in response to demand shifts.

🔹 Disadvantages

❌ Assumes Instantaneous Price Adjustments – In reality, prices do not change instantly.
❌ Ignores Production Constraints – Some industries cannot rapidly change output.

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4. Comparison: Marshallian vs. Walrasian Stability

Feature	Marshallian Stability	Walrasian Stability
Adjustment Mechanism	Quantity adjusts to reach equilibrium.	Prices adjust to reach equilibrium.
Main Focus	Firm’s production decisions.	Market price changes.
Key Assumption	Prices are fixed in the short run.	Quantity remains unchanged during price adjustment.
Process	Firms reduce/increase output based on demand.	Auctioneer mechanism adjusts prices.
Best Applied To	Goods markets with flexible production.	Financial and auction markets where prices adjust rapidly.
Example	Farmers reduce wheat production if there is excess supply.	Stock prices fall when there is low demand.

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5. Conclusion

✔ Marshallian Stability is useful for competitive markets where firms adjust output to balance supply and demand.
✔ Walrasian Stability is relevant for financial markets and auctions, where price changes restore equilibrium.
✔ The choice between the two models depends on market structure, time frame, and pricing flexibility.