The quantity demanded x (in units of a hundred) of the Mikado miniature cameras

Question

The quantity demanded x (in units of a hundred) of the Mikado miniature cameras per week is related to the unit price p (in dollars) by p = -0.2x^2 + 80 and the quantity x (in units of a hundred) that the supplier is willing to make available in the market is related to the unit price p (in dollars) by p = 0.1x^2 + x + 40. If the market price is set at the equilibrium price, find the consumers? surplus and the producers? surplus. (Round your answers to the nearest dollar.) consumer?s surplus $ _____________ producer?s surplus $ ____________

Explanation / Answer

P(consumer)=p(suppliers) at equlibrium

-0.2x2 + 80=0.1x2 + x+40

0.3x2 +x-40=0

x=1.6153*100=161.53 units

p(consumer)=-0.2(1.6153*1.6153)+80=$79

p(suppilers)=0.1(1.6153*1.6153)+1.6153+40= $42

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