If the demand and supply functions in a competitive market are Q d = 26 0.4P and Q s = 4 + 0.6P and the rate of adjustment of price when the market is out of equilibrium is dPdt = 0.32(Q d, Q s) .…

If the demand and supply functions in a competitive market are $Q_d=26-0.4P$ and $Q_s=4+0.6P$ and the rate of adjustment of price when the market is out of equilibrium is $\frac{dP}{dt}=0.32(Q_d,Q_s)$. a) Calculate the maximum profit by using graphical or simplex method. b) Derive and solve the differential equation to get a function for $p$ in terms of $t$ given that the price is 40 in time period zero. Comment on the stability of the market.