Walrasian versus Marshallian
Dynamics

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A little care will lead us to notice that the Marshallian and Walrasian stability conditions are not the same. For the Walrasian, it must be that 1/b < 1/a; for the Marshallian, it must be that b > a for stability. If the slope of the demand curve is negative and that of the supply curve is positive, is in the standard case, then the system is stable in both the Walrasian and Marshallian senses. Similarly, if we have the extreme opposite of an upward-sloping demand and a downward-sloping supply curve, then it is unstable in both the Walrasian and Marshallian senses.

The question of issue now is what happens when both curves slope in the same way. Here, Walrasian and Marshallian stability part ways. Suppose both curves are upward-sloping. Then the system is Walrasian-stable if demand is steeper than supply, but then it is Marshallian unstable. This is shown in Figure 5a. In contrast, the system is Walrasian-unstable but Marshallian-stable if supply is steeper than demand, as shown in Figure 5b.

Fig. 5a - W-Stable, M-Unstable

Fig. 5b - W-Unstable, M-Stable

If both curves are downward-sloping, then the system is Walrasian-stable and Marshallian-unstable if supply is absolutely steeper than demand (Figure 8a); and Walrasian-unstable and Marshallian-stable if demand is absolutely steeper than supply (Figure 8b).

Fig. 6a - W-Stable, M-Unstable

Fig. 6b - W-Unstable, M-Stable

We can summarize the results in the following table:

Demand slope

Supply slope

Walrasian

Marshallian

-

+

Stable

Stable

+

-

Unstable

Unstable

+ steep

+ flat

Stable

Unstable

+ flat

+ steep

Unstable

Stable

-flat

-steep

Stable

Unstable

-steep

- flat

Unstable

Stable

 

 


 

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