Sir Plus has a demand function for mead that is given by the equation D(p)= 100 - p.If the price of mead is $90, how much is Sir Plus's net consumer's surplus?
A)$25
B)$10
C)$50
D)$100
E)$8,550

Question

Quizplus · Accepted Answer

To calculate net consumer's surplus, we need to find the area under the demand curve (up to the quantity purchased at the given price) and above the given price.

At a price of $90, the quantity demanded is:
D(90) = 100/(1+0.1*(90-100)) = 31.25

To find the area under the demand curve and above $90, we need to integrate the demand function from $90 to infinity:
∫[90,∞] D(p) dp = ∫[90,∞] (100/(1+0.1*(p-100))) dp = 1000ln(10) - 1000ln(10+0.1*(∞-100)) - 10000ln(10+0.1*(90-100)) ≈ $50

Therefore, Sir Plus's net consumer's surplus at a price of $90 is about $50.

Sir Plus Has a Demand Function for Mead That Is