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

he 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 + 220 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 + 8x + 110.

Answer 1

equilibrium price = $185.47

equilibrium quantity demanded and supplied: x=8.525 or 852.5

construct right triangles with base = x

heights = y intercepts + or - equilibrium price

= $185.47 per 100x or 852 1/2 units

CS = area of the right triangle above the horizontal price line

PS = area of the right triangle below the horizontal price line

while that geometric approach would work if the supply and demand curves were linear

in this case they're quadratic, yet the quadratic term when integrated is relatively small

and the PS is very close to the actual amount when calculated as the area of a right triangle

$42,628 versus $42,605

for a closer more exact answer use integral calculus

CS is much smaller and the geometric calculation not as close, but in the same general range

do the geometry and triangles to check the integral answer