Posted by **Mia** on Friday, April 25, 2014 at 9:47pm.

The demand function for a certain brand of CD is given by

p = −0.01x^2 − 0.2x + 12

where p is the unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. The supply function is given by

p = 0.01x^2 + 0.5x + 3

where p is the unit price in dollars and x stands for the quantity that will be made available in the market by the supplier, measured in units of a thousand. Determine the producers' surplus if the market price is set at the equilibrium price. (Round your answer to the nearest dollar.)

- !math (4) -
**Kuai**, Saturday, April 26, 2014 at 12:26am
0.01x^2 + 0.5x + 3 = −0.01x^2 − 0.2x + 12

0.02^2 + 7x -9 = 0

2x^2 + 70x -900 =0

2(x^2 + 35x -450) = 0

2(x -10)(x + 45)=0

x = 10

x = -45

Solving gives x=10

This is the equilibrium quantity

Plug 10 into either demand or supply function to get equilibrium price = 9

Consumer surplus:

ʃ (−0.01x^2 − 0.2x + 12 )dx on [0,10] - 10*9

(-.01/3x^3/3 -.2x^2/3 + 12x on [0,10] - 90

-10/3 - 20/3 + 120- 90 = 20

Producer surplus:

10*9 -ʃ (0.01x^2 + 0.5x + 3)dx on [0,10]

90 - ((.01/3)x^3 + .5x^2/2 + 3x)) on [0,10]

90 - ( 10/3 + 25+ 30)

90 -175/3 = 31.67

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