The demand function for a certain brand of CD is given by: p = 0.01x2 0.2x + 8 w

Question

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

p = 0.01x2 0.2x + 8

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 for the CDs is given by

p = 0.01x2 + 0.08x + 2.5

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

demand function = surplus function

0.01x2 0.2x + 8 =  0.01x2 + 0.08x + 2.5

Solve for x

So, x=11

Demand at x=11 ; 4.59

Supply at x=11 ; 3.49

Producer surplus = 1/2(3.49)(8-4.59) = 6

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