Answer to Question #245634 in Microeconomics for Ndanu

Question

1)   With regard to achievement of stability of equilibrium in an isolated market assume that the market for string beans is found to have a lagged supply response such that the demand and supply function may be written as

D_t = aP_t + b

S_t = AP _t-1 + B

Required: Derive the conditions for dynamic stability of equilibrium

Answer 1

Given:

$Dt = aPt + b\\ St = APt-1 + BDt=aPt+b$

At the equilibrium level,

$Dt = St\\ aPt + b = APt-1 + B .....(1)Dt=St$

If the equilibrium is stable it implies that the price level in all the periods is equal to the stable prices, i.e P*.

$=>aP ∗ +b=AP ∗ +B.....(2)$

Subtracting 1 from 2 we get,

$a (P^* - Pt) = A(P^* - Pt-1)\\ aP1 = AP2a(P ∗ −Pt)=A(P ∗ −Pt−1)$

Where P1 = Deviation of Pt from P*

P2 = Deviation of Pt-1 from P*

$\frac{P_1}{P_2} = \frac{A}{a}$ , where $\frac{A}{a}$ is a constant denoted by C

$\frac{P_1}{P_2} =C P 2 ​ P 1 ​ ​ =C$