Consumer Theory Or Behavior

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: