If the demand and supply functions in a competitive market, Business Economics

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If the demand and supply functions in a competitive market

Question: If the demand and supply functions in a competitive market are

Q_d = 35 - 0.5P and Q_s = -4 + 0.8P

and the rate of adjustment of price when the market is out of equilibrium is

dP = 0.25(Q_d - Q_s)
dt

derive and solve the relevant differential equation to get a function for P in terms of t given that price is 37 in time period 0. Comment on the stability of this market.

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