Asked by David Benjamin on Jun 03, 2024
Verified
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.
Verified Answer
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.
Learning Objectives
- Extract and elucidate consumer surplus from demand equations.
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