If you are given this function: P=1000-40Q where P=price and Q=sales.....
How do you get the price elasticity of demand at a price that is $500?
At what price, if any is the price elasticity of demand equal to one?
To calculate the price elasticity of demand at a specific price, such as $500, you need to use the formula:
E = (% change in quantity demanded) / (% change in price)
Let's break down the steps to calculate the price elasticity of demand at $500:
Step 1: Determine the original quantity demanded at a specific price.
Plug in the price P = $500 into the demand function P = 1000 - 40Q and solve for Q.
$500 = 1000 - 40Q
Solving this equation, we get:
40Q = 1000 - $500
40Q = $500
Q = $500 / 40
Q = 12.5
So, at a price of $500, the quantity demanded is 12.5.
Step 2: Calculate the new quantity demanded after a change in price.
To calculate the percentage change in quantity demanded, you need to determine what the new quantity demanded is if the price changes slightly, both above and below $500.
For example, if the price slightly decreases to $490, you will calculate the new quantity demanded using the demand function P = 1000 - 40Q:
$490 = 1000 - 40Q
Solving for Q, we find:
40Q = 1000 - $490
40Q = $510
Q = $510 / 40
Q = 12.75
In this case, the new quantity demanded is 12.75.
Step 3: Calculate the percentage change in quantity demanded.
To calculate the percentage change, use the following formula:
% change in quantity demanded = (new quantity demanded - original quantity demanded) / original quantity demanded * 100
In this scenario, the calculation would be:
% change in quantity demanded = (12.75 - 12.5) / 12.5 * 100
% change in quantity demanded = 0.25 / 12.5 * 100
% change in quantity demanded = 2%
Step 4: Calculate the percentage change in price.
Since we are calculating the price elasticity of demand at a specific price, the price change would be zero. Therefore, the percentage change in price will also be zero.
Step 5: Calculate the price elasticity of demand.
Now that we have both the percentage change in quantity demanded (2%) and the percentage change in price (0%), we can use the formula:
E = (% change in quantity demanded) / (% change in price)
E = 2% / 0%
(Note that any division by zero is undefined, so the price elasticity of demand at a specific price of $500 in this case is undefined.)
Moving on to the second part of your question:
To find the price at which the price elasticity of demand is equal to one, you need to determine the price where the absolute value of the elasticity is equal to 1. In other words:
|E| = 1
Using the formula E = (% change in quantity demanded) / (% change in price), set |E| = 1 and solve for the price.
Let's assume the percentage change in quantity demanded is x and the percentage change in price is y. The formula becomes:
|E| = x / y
1 = x / y
To explain how to find the price at which the price elasticity of demand is equal to one, we would need additional information such as specific values for x and y. Without those values, we cannot determine the price at which the elasticity is equal to one.