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Demanded Price of a Commodity

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Q thousand units of the commodity will be demanded at a price of p = D(q) dollars per unit, while q thousand units will be supplied by producers when the price is p = S(q).

D (q) = 65 - q^2

S (q) = (1/3)q^2 + 2q + 5q)

a) Find the equilibrium price P (where supply equals demand)

b) Find the consumer's surplus and the producer's surplus at equilibrium.

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(a) At equilibrium, D(q) = S(q)

65 - q^2 = (1/3)q^2 + 2q + 5

(4/3)q^2 + 2q - 60 = 0 or 4q^2 + 6q - 180 = 0

2q^2 + 3q - 90 = 0

(q - 6)(2q + 15) = 0

q = ...

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