An economic model for the supply S(P) and demand D(P) of a product at a market price

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An economic model for the supply S(P) and demand D(P) of a product at a market price of P is given by

D(P) = 2 - P S(P) == + P

and D(P+1) = S(P)

(so that supply lags behind demand by 1 time unit). Show that

P+1 = (P - 1) and deduce that P=1+(-)'(Po - 1)

Find the particular solution of the recurrence relation corresponding to P0 = 0.8 and sketch it in a cobweb diagram. What is the steady state price of the product?

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