Step 1: Define the demand function and market equilibrium.
The demand function is given as:
At market equilibrium, the price and quantity are and , respectively.
Step 2: Find the price at .
Substitute into the demand function to find the price:
Thus, the price at equilibrium is , which matches the given information.
Step 3: Consumer Surplus Formula.
The consumer surplus is the area between the demand curve and the price level up to the equilibrium quantity. The formula for consumer surplus is:
Where:
- The base is the quantity .
- The height is the difference between the maximum price consumers are willing to pay at and the equilibrium price .
Step 4: Calculate the maximum price consumers are willing to pay at .
Substitute into the demand function:
Thus, the maximum price consumers are willing to pay when is .
Step 5: Calculate the consumer surplus.
Now, substitute the values into the consumer surplus formula:
Final Answer: