Question

If the demand and supply functions in a competitive market are (5marks) Qd = 50 − 0.2P Qs = −10 + 0.3P and the rate of adjustment of price when the market is out of equilibrium is dP /dt = 0.4(Qd − Qs) derive and solve the relevant difference equation to get a function for P in terms of t given that price is 100 in time period 0. Comment on the stability of this market.

Answer 1

$Q_d=50-0.2P,$

$Q_s=-10+0.3P,$

$Q_d=Q_s,$

$50-0.2P=-10+0.3P,$

$60=0.5P,$

$P=120,$

$Q_d=Q_s=26.$