Final answer:
The consumers' surplus is 0 dollars for both cases.
Step-by-step explanation:
To find the consumers' surplus, we need to calculate the area between the demand curve and the equilibrium quantity. In this case, the equilibrium quantity is 40 pounds. Substituting this value into the demand equation, we can find the equilibrium price:
p = √(18,201 - 413x) = √(18,201 - 413(40)) = √(18,201 - 16,520) = √681 = 26.09
The consumers' surplus is the area between the price (26.09) and the equilibrium price (26.09) multiplied by the quantity (40 pounds):
Consumers' surplus = (26.09 - 26.09) * 40 = 0
Therefore, the consumers' surplus is 0 dollars.
To find the consumers' surplus if the equilibrium price is 17 dollars, we need to find the equilibrium quantity. Substituting the price into the demand equation, we can solve for x:
17 = √(18,201 - 413x)
Squaring both sides, we get:
289 = 18,201 - 413x
413x = 17,912
x = 43.36
The consumers' surplus is the area between the price (17) and the equilibrium price (17) multiplied by the quantity (43.36 pounds):
Consumers' surplus = (17 - 17) * 43.36 = 0
Therefore, the consumers' surplus is 0 dollars.