Asked by David Benjamin on Jun 03, 2024

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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

Consumer's Surplus

The difference between the total amount consumers are willing and able to pay for a good or service and the total amount they actually pay.

Demand Function

The demand function is a mathematical representation that describes the quantity of a good that consumers are willing and able to purchase at various prices.

Mead

A drink made by the fermentation of honey and water, often enhanced with the addition of fruits, spices, grains, or hops to create an alcoholic beverage.

  • Extract and elucidate consumer surplus from demand equations.
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ZK
Zybrea KnightJun 07, 2024
Final Answer :
C
Explanation :
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.