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  Stability of Equilibrium, Static stability and Dynamic Stability

Stability of Equilibrium:

1. Static Stability:

a) Walrasian Adjustment Process:

If excess demand (supply) exists, the market price will go up (down).

Excess supply (demand) price above (below) equilibrium price

ED(P) = D(P) − S(P) - Excess Demand Function

(dED(P)/dP)< 0

(Try to depict diagrams with stable and unstable conditions).

b) Marshallian Adjustment Process:

Housing market has very steep supply curve. It’s rigid to adjust price to eliminate any existence of excess demand or supply.

EDP(Q) = PD − PS = d(Q) − s(Q) : Excess Demand Price Function

(dEDP (Q)/dQ)<0

(Try to depict diagrams with stable and unstable conditions).

2. Dynamic Stability:

a. Discrete time (Cobweb Process):

Dt = −aPt + b (demand) (1)
St = αPt−1 − β (supply) (2) ( a, b,α ,β are all positive numbers).

Equilibrium condition implies that Dt = St .

So we get aPt +αPt−1 − b − β = 0 (3). And finally, rewriting w.r.t. Pt ,

Pt= −(α/a) *Pt-1+ (b+ β)/a

b. Continuous time (Differential Equation):

|slope of supply| >| slope of demand| (condition for dynamic stability)

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