CONSUMER AND PRODUCER SURPLUS

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 = −0.2x² + 160

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 + 5x + 80.

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	$

ANSWER IS NOT $133 AND $317

Answer 1

set the supply and demand curves equal. that gives x=10 and P=140

take the integral of the demand curve minus 140 to get 20x-(x^3)/15. evaluate at x=10. That gives 133 1/3 for consumer surplus. Round off to $133

take the integral of 140 minus the supply curve to get 60x minus (5/2)x^2 - (1/30)x^3. evaluate at x=10. producer surplus = 316 2/3. Round off: $317