Very confused on how to figure these out.
Suppose that the following table shows the weekly visits to an amusement park as a function of the daily admission fee charged:
#visits daily fee
200 $50
400 $40
600 $30
800 $20
1000 $10
What is the price elasticity of demand when the daily fee is $20? When the daily fee is $40?
What is the elasticity of demand at the price which maximizes total revenue?
What price maximizes total revenue?
What is the arc price elasticity between the prices of $40 and $20 per day?
To calculate the price elasticity of demand, we need to use the formula:
Price Elasticity of Demand = Percentage change in Quantity Demanded / Percentage change in Price
Let's calculate the price elasticity of demand at different daily fees and find the price that maximizes total revenue.
1. Price elasticity of demand when the daily fee is $20:
First, let's find the percentage change in Quantity Demanded:
Percentage change in Quantity Demanded = (800 - 600) / 600 = 200 / 600 = 1/3
Next, let's find the percentage change in Price:
Percentage change in Price = ($20 - $30) / $30 = -10 / $30 = -1/3
Now we can calculate the price elasticity of demand:
Price Elasticity of Demand = (1/3) / (-1/3) = 1 / -1 = -1
Therefore, the price elasticity of demand when the daily fee is $20 is -1.
2. Price elasticity of demand when the daily fee is $40:
First, let's find the percentage change in Quantity Demanded:
Percentage change in Quantity Demanded = (600 - 400) / 400 = 200 / 400 = 1/2
Next, let's find the percentage change in Price:
Percentage change in Price = ($40 - $30) / $30 = 10 / $30 = 1/3
Now we can calculate the price elasticity of demand:
Price Elasticity of Demand = (1/2) / (1/3) = 3/2
Therefore, the price elasticity of demand when the daily fee is $40 is 3/2.
3. Elasticity of demand at the price that maximizes total revenue:
To find the price that maximizes total revenue, we need to look for the price with unitary price elasticity, which corresponds to maximum revenue. In other words, we need to find the price at which the price elasticity of demand is equal to 1.
Looking at the table, we can see that the price elasticity of demand is close to 1 when the daily fee is around $30. Therefore, the elasticity of demand at the price that maximizes total revenue is approximately 1.
4. Price that maximizes total revenue:
The price that maximizes total revenue is the one with unitary price elasticity. From the previous calculation, we found that the price that maximizes total revenue is approximately $30.
5. Arc price elasticity between the prices of $40 and $20:
The arc price elasticity formula is the same as the regular price elasticity formula, but it takes into account the average quantities and prices between two points.
Let's calculate the arc price elasticity between the prices of $40 and $20:
Percentage change in Quantity Demanded = (1000 - 600) / ((600 + 1000) / 2) = 400 / 800 = 1/2
Percentage change in Price = ($40 - $20) / (($20 + $40) / 2) = 20 / 30 = 2/3
Arc Price Elasticity of Demand = (1/2) / (2/3) = 3/4
Therefore, the arc price elasticity between the prices of $40 and $20 per day is 3/4.
To find the price elasticity of demand, you need to use the formula:
Price Elasticity of Demand (PED) = (% change in quantity demanded) / (% change in price)
Let's go through each question step by step:
1. What is the price elasticity of demand when the daily fee is $20? When the daily fee is $40?
To calculate the price elasticity of demand at a specific price, you need to compare the change in quantity demanded relative to the change in price. Let's look at the specific table entries:
When the daily fee decreases from $30 to $20, the quantity demanded increases from 600 to 800 visits. So, the change in quantity demanded is (800 - 600) = 200 visits.
The change in price is ($20 - $30) = -$10.
Now you can calculate the price elasticity of demand for $20 using the formula:
PED = (200 / 600) / (-10 / 30)
Similarly, for the daily fee at $40, you compare the change in quantity demanded between $30 and $40 and calculate the price elasticity of demand.
2. What is the elasticity of demand at the price which maximizes total revenue?
To find the elasticity of demand at the price that maximizes total revenue, you need to calculate the revenue for each price and determine which one is maximized. Revenue is calculated by multiplying the quantity demanded by the price.
Calculate the revenue for each price point and compare them to find the price that results in the highest revenue.
3. What price maximizes total revenue?
To find the price that maximizes total revenue, you need to calculate the revenue for each price point and determine which one is maximized. Revenue is calculated by multiplying the quantity demanded by the price.
Calculate the revenue for each price point and determine which price results in the highest revenue.
4. What is the arc price elasticity between the prices of $40 and $20 per day?
The arc price elasticity measures the average price elasticity of demand between two different price points. To calculate the arc price elasticity, you use the average percentage change in quantity demanded divided by the average percentage change in price.
To find the arc price elasticity between $40 and $20 per day, you compare the change in quantity demanded and the change in price between these two points.
Calculate the percentage change in quantity demanded and the percentage change in price between $40 and $20, and then use these values in the formula to calculate the arc price elasticity.