Final answer:
The consumer surplus at market equilibrium with a price of $83 is calculated by finding the area of the triangle above the equilibrium price and below the demand curve. The maximum price consumers would be willing to pay is $108, and the quantity demanded at $83 is 50 units. The consumer surplus is $625.
Step-by-step explanation:
To calculate the consumer surplus at market equilibrium for the given demand equation q = 10 √(108-p), we first need to find the maximum price that consumers would be willing to pay for the product.
This price occurs when the quantity demanded, q, is zero. Setting q to zero and solving for p gives us :
0 = 10 √(108-p)
=> √(108-p) = 0
=> 108-p = 0
=> p = 108
The maximum price consumers would be willing to pay is $108.
Now, we know that the market equilibrium price is $83, and the quantity at that price can be found by substituting p with 83 in the demand equation:
q = 10 √(108-83)
= 10 √25
= 10 * 5
= 50
The quantity demanded at price $83 is 50 units.
To find the consumer surplus, we calculate the area of the triangle that forms above the market price and below the demand curve.
The base of the triangle is the difference between the maximum price consumers are willing to pay ($108) and the market equilibrium price ($83), which is $108 - $83 = $25. The height of the triangle is the quantity demanded at the equilibrium price, which is 50.
Therefore, the consumer surplus is:
Consumer Surplus = 0.5 * base * height
= 0.5 * 25 * 50
= 0.5 * 1250
= $625