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
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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