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/week is related to the unit price p (in dollars) by p = ?0.2x2 + 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 = 0.1x2 + 2.2x + 56 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.) consumers' surplus producers' surplus

Explanation / Answer

in equilibrium:

so Dx=Sx

-0.2x^2+80= 0.1x^2+2.2x +56

so x=6

corresonding to that Sx=

now for that p(x)=72.8

so consumer surplus=> integrate(0to72.8)(-0.2x^2+80)- (6*72.8)

=19897.9-436.8

= 19461

and producer's surlpus= 6*72.8-integrate(0to72.8)(0.1x2 + 2.2x + 56)dx

=22331

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