Find the consumer surplus at the equilibrium point.(I keep using the formula listed below but get a completely different answer from what the book says. I am a visual person so please show me step by step so I can see where I went wrong.
D(x)=(x-6)^2 ; x=3
Formula: D(x)-QP
The Answer according to the book is $36
To calculate the consumer surplus at the equilibrium point, let's go through the steps using the provided formula:
Step 1: Start with the demand function, D(x). In this case, D(x) = (x-6)^2.
Step 2: Set the quantity, x, equal to the equilibrium point, which is given as x = 3.
Step 3: Calculate the price corresponding to the equilibrium quantity using the demand function. Remember that the price, p, is given as the inverse of the demand function. So, p = D(x) = (3-6)^2 = 9.
Step 4: Calculate the consumer surplus using the formula D(x) - p.
Now, let's substitute the values into the formula:
Consumer Surplus = D(x) - p
Consumer Surplus = (x-6)^2 - 9
Consumer Surplus = (3-6)^2 - 9
Consumer Surplus = (-3)^2 - 9
Consumer Surplus = 9 - 9
Consumer Surplus = 0
Based on the calculations, the consumer surplus at the equilibrium point is $0, not $36 as mentioned in the book.
Please recheck your calculations or the formula provided in the book to ensure accuracy.