Model Answer
0 min readIntroduction
Market equilibrium, a cornerstone of economic analysis, describes a state where supply equals demand. However, the stability of this equilibrium – its tendency to return to balance after a shock – is a complex issue. Two prominent frameworks for analyzing this stability are the Marshallian and Walrasian approaches. Alfred Marshall’s partial equilibrium analysis focuses on individual markets, while Léon Walras’s general equilibrium analysis considers the entire economy simultaneously. Understanding the stability conditions within each framework, and their interrelation, is vital for comprehending the dynamics of price determination and resource allocation.
Marshallian Stability Condition
The Marshallian stability condition, rooted in partial equilibrium analysis, focuses on the responsiveness of quantity demanded and supplied to price changes. It states that for an equilibrium to be stable, the price elasticity of demand and supply must be less than unity (in absolute value) at the equilibrium point. Mathematically, |Ed| < 1 and |Es| < 1. This implies that as price deviates from equilibrium, the change in quantity demanded and supplied will be proportionally smaller, pushing the market back towards equilibrium. This is often visualized using a cobweb diagram where the curves intersect at a stable point.
Walrasian Stability Condition
Walrasian stability, based on general equilibrium analysis, relies on the concept of tâtonnement – a ‘groping’ process where prices are adjusted based on excess demand or supply in all markets simultaneously. The Walrasian stability condition requires that the Jacobian matrix of excess demand functions be negative definite. This means that any deviation from equilibrium will trigger price adjustments that move the economy back towards equilibrium in all markets. This condition is more stringent than the Marshallian one, as it considers the interconnectedness of all markets.
Comparing Marshallian and Walrasian Stability
The key difference lies in the scope of analysis. Marshallian stability is a local condition, applicable to a single market, assuming other markets remain unaffected. Walrasian stability, on the other hand, is a global condition, considering the entire economy.
| Feature | Marshallian Stability | Walrasian Stability |
|---|---|---|
| Scope | Partial Equilibrium (Single Market) | General Equilibrium (Entire Economy) |
| Condition | |Ed| < 1 and |Es| < 1 | Jacobian of Excess Demand is Negative Definite |
| Assumptions | Ceteris Paribus | Interdependence of all markets |
| Complexity | Relatively Simple | Mathematically Complex |
Does Marshallian Stability Imply Walrasian Stability?
No, the existence of Marshallian stability does not necessarily ensure Walrasian stability. Marshallian stability only guarantees stability in a single market, holding everything else constant. However, in a general equilibrium framework, changes in one market can ripple through the entire economy, potentially destabilizing the system. The negative definiteness of the Jacobian matrix requires a more comprehensive and stringent condition than simply having elasticities less than one in individual markets.
Does Walrasian Stability Imply Marshallian Stability?
Yes, if Walrasian stability holds, then Marshallian stability will also hold in each individual market. If the entire system is stable, it implies that each individual market within that system must also be stable. The Walrasian condition encompasses the Marshallian condition as a special case. However, satisfying Marshallian stability in all markets does not guarantee Walrasian stability due to the potential for complex interactions and feedback loops across markets.
In essence, Walrasian stability is a stronger condition that requires a more coordinated and comprehensive adjustment process than Marshallian stability.
Conclusion
In conclusion, while both Marshallian and Walrasian stability conditions aim to determine the equilibrium of a market, they differ significantly in their scope and underlying assumptions. Marshallian stability is a necessary but not sufficient condition for Walrasian stability. The latter, being a more comprehensive and rigorous framework, provides a more realistic assessment of market stability in a complex, interconnected economy. Understanding these nuances is crucial for effective economic policymaking and analysis.
Answer Length
This is a comprehensive model answer for learning purposes and may exceed the word limit. In the exam, always adhere to the prescribed word count.