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

Question

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 + 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 $

producers surplus $

Answer 1

equilibrium price = 760 when x=80

just set .1x^2 +x +40 = -.2x^2 +80, and solve for x

the left side is the supply curve, the right side is the demand curve

they intersect at (80, 760) the equilibrium point

for consumer surplus find the area above P=760 and the demand curve

for producer surplus find the area below P=760 and the supply curve.