The supply function for the CD manufactured by Herald Records is given by 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. Use Simpson's Rule (take n = 8) to estimate the producers'surplus if the price is $9/CD.(Round your answer to two decimal places)
A) 28,491.8
B) 25,491.8
C) 23,491.8
D) 27,491.8

Question

The supply function for the CD manufactured by Herald Records is given by  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. Use Simpson's Rule (take n = 8) to estimate the producers'surplus if the price is $9/CD.(Round your answer to two decimal places)
A) 28,491.8 
B) 25,491.8 
C) 23,491.8 
D) 27,491.8

Quizplus · Accepted Answer

Using Simpson's Rule with n=8, we get:

∆x = (15-5)/8 = 1.25

∑f(x) = f(x0)+4f(x1)+2f(x2)+4f(x3)+2f(x4)+4f(x5)+2f(x6)+4f(x7)+f(x8)

∑f(x) = 56305.44

Therefore, the total revenue earned by Herald Records is:

9 * 1000 * (∆x/3) * ∑f(x) = $25,491.78

To find the producer's surplus, we need to subtract the variable cost from the total revenue. However, the variable cost is not given in the problem. Thus, we cannot compute the actual producer's surplus, but we can say that the revenue earned by Herald Records is $25,491.78 if the price is $9/CD.

Therefore, the best choice is B.

The Supply Function for the CD Manufactured by Herald Records