The demand for a good is given by QD = 750 – 0.4P. What is consumer surplus at a price of $80?
To find the consumer surplus at a price of $80, we need to understand what consumer surplus is and how to calculate it using the given demand equation.
Consumer surplus refers to the difference between what consumers are willing to pay for a product or service and what they actually have to pay. In other words, it measures the benefit or value that consumers receive from purchasing a good at a given price.
To calculate consumer surplus, we need two pieces of information: the demand equation and the price at which we want to evaluate the consumer surplus.
Given the demand equation: QD = 750 – 0.4P, where QD represents the quantity demanded and P represents the price, we can substitute the price of $80 into the equation to find the corresponding quantity demanded.
QD = 750 - 0.4P
QD = 750 - 0.4($80)
QD = 750 - 32
QD = 718
So, at a price of $80, the quantity demanded is 718.
Now, to calculate consumer surplus, we need to find the difference between the maximum value consumers are willing to pay (represented by the demand equation) and the actual price they have to pay. In this case, the maximum value consumers are willing to pay is the value from the demand equation when QD is equal to the quantity demanded at the given price.
To find the maximum value consumers are willing to pay (Pmax), we need to solve for P in the demand equation when QD is equal to 718.
QD = 750 - 0.4P
718 = 750 - 0.4P
Subtracting 718 from both sides gives:
32 = 0.4P
Dividing both sides by 0.4, we get:
P = 80
Therefore, the maximum value consumers are willing to pay (Pmax) at a quantity demanded of 718 is $80 (which is the given price in this case).
To calculate consumer surplus, subtract the actual price paid ($80) from the maximum value consumers are willing to pay ($80):
Consumer Surplus = Pmax - P
Consumer Surplus = $80 - $80
Consumer Surplus = $0
So, at a price of $80, the consumer surplus is $0.