The demand function for a certain brand of CD is given by p =(-0.01x^2-0.2x+10)

Question

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

p =(-0.01x^2-0.2x+10) where p is the wholesale 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 + 0.2x + 4)

where p is the unit wholesale 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 wholesale market price is set at the equilibrium price. (Round your answer to the nearest dollar.)

Explanation / Answer

level of producer surplus is shown by the area above the supply curve and below the market price.

demand = supply

(-0.01x^2-0.2x+10) =  (0.01x^2 + 0.2x + 4)

0.02x^2 - 0.4x - 6 = 0

0.01x^2 - 0.2x - 3 = 0

we get x = 30

p = (0.01x^2 + 0.2x + 4) = (0.01*30 + 0.2*30+ 4 ) = 10.3

Prodcures surplus = integral( 10.3 - ( (0.01x^2 + 0.2x + 4)) dx ) from 0 to 30

= integral ( ( 6.3 - 0.01x^2-0.2x)) fro 0 to 30

= 9

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