0.1x^2 + 8x + 110 = −0.2x^2 + 220
.3x^2 + 8x -110 = 0
3x^2 + 80x -1100 = 0
(3x + 110)(x-10) =0
x = -110/3
x = 10
This is the equilibrium quantity
Plug 10 into either demand or supply function to get equilibrium price = 200
Consumer surplus:
ʃ (-.2x^2+220)dx on [0,10] - 10*200
(-.2/3)x^3 + 220x on [0,10] - 2000
-200/3+ 2200- 2000 = 133.33
Producer surplus:
10*200 - ʃ (0.1x^2 + 2x + 110 )dx on [0,10]
2000 - (.1/3)x^3 + 4x^2 + 110x)) on [0,10]
2000 - (100/3 + 400 + 1100)
2000-4600/3 = 466.67
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 + 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 = 0.1x^2 + 8x + 110.
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 = ?
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