Answer to Question #244522 in Microeconomics for james

Question

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 2 Dt = aPt + b St = AP t-1 + B

Required: Derive the conditions for dynamic stability of equilibrium

Answer 1

Given:

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

At the equilibrium level,

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

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,

$a (P^* - Pt) = A(P^* - Pt-1)\\ aP1 = AP2$

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

$\frac{P_1}{P_2} =C$