Suppose, the demand and supply functions for a commodity are:

qd = φ(pd)                                           (4.18)

and qs = Ψ(ps)                                   (4.19)

where pd and ps denote the demand price and supply price, respectively. It can be called the inverse of the demand and supply functions (4.18) and (4.19) the demand and supply curves.

Therefore, the equations of these curves would be:

pd = φ−1(qd)                                     (4.20)

and ps = Ψ−1(qs)                            (4.21)

Now define the excess demand price, F(q), as the difference between the demand price (pd) and the supply price (ps) at any q.

it can be written, therefore:

F(q) = pd−ps

= φ-1(qd) − Ψ-1(qs)                        (4.22)

The excess demand price F(q) may be positive or negative according as pd > ps or ps > pd. For exam­ple, in Fig. 4.7, at q = q1, F(q) = p1d − p1s is posi­tive and, at q = q2, F(q) = p2d – p2s is negative. The market is in equilibrium if at some q, pd = ps and F(q) = 0.

This has happened at q = q0 in Fig. 4.7. On the other hand, the market is not in equilibrium at any q if F(q) ≶ 0. For example, at q = q1 and at q = q2, F(q) is positive and negative respectively, and at both these quantities the market is not in equilibrium.

Marshallian Stability Condition:

The Marshallian stability condition is based on the behaviour assumption that producers will raise their output when F(q) > 0, i.e., when at output q, the buyers are offering a higher price than what the sellers are demanding (pd > ps), and the producers will lower their output when F(q) < 0, i.e., when at output q, the buyers are offering a price which is smaller than what the sellers are demanding (pd < ps).

Given this behaviour assumption, the market will be stable in the Marshallian sense if

i.e., if there is an inverse relation between q and F(q).

The logic behind the Marshallian stability condition (4.23) is this:

If F(q) is positive, the producers will raise their output (q) and as q rises F(q) would have to decrease, and, eventually, it would have to decrease to zero where the market equilibrium, again, would be restored.

On the other hand, if F(q) is negative, the producers will lower their output (q), and, as q decreases, F(q) would have to increase, and eventually, F(q) would have to be zero, where the market would again reach equilibrium. From (4.23),

Equations (4.23) and (4.24) give us the market stability condition in the Marshallian sense.

It is evident from (4.24) that the market would be stable if: