The quantity demanded x in units of a hundred of the Mikado

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 = -0.2x^2 + 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 = 0.1x^2 + 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 producer\'s surplus $

Solution

p = -0.2x^2+80
p = 0.1x^2+x+40

equate both price to find equilibrium value of x
0.1x^2+x+40 = -0.2x^2+80
0.3x^2 + x - 40 = 0

solving above equation we get, x= 10 and x=-13.33

x can\'t be negative, so x =10

for consumer:
p = -0.2x^2+80
   = -0.2*(10)^2+80
   = $ 60 <----Answer

for supplier:
p = 0.1x^2+x+40
   = 0.1*(10)^2+80
   = $ 90 <----Answer