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.)

Question

Consumers' and Producers' Surplus

 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 = −0.2x² + 200

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+7x+100

Answer 1

-.2x^2 + 200 = .1x^2 + 7x + 100

.3x^2 + 7x -100 = 0

x = -7/.6 + (1/.6)sqr(49+120) = -70/6 + (10/6)sqr169

=(-70+130)/6 = 60/6 = 10

x=10

p=-.2(100) +200 = $180

p=-1(100)+70 +100 = $180

consumer surplus = integral of -.2x^2 +200-180 = (-.2/3)x^3 +20x evaluated at 10

200-(2/30)1000 = 200-(2/3)100 = $133

producer surplus = integral of 180 -(.1x^2 +7x +100) = -[(1/30)x^3+(7/2)x^2 +100x] +180x evaluated at 10: -[100/3 +350+ 1000] +1800 = 800-350-33=$417