The Mesa Redbirds football team plays in a stadium with a seating capacity of 80,000. However,
during the past season, attendance averaged only 50,000. The average ticket price was $30. If
price elasticity is −4, what price would the team have to charge in order to fill the stadium? If the
price were to be decreased to $27 and the average attendance increased to 60,000, what is the
price elasticity?
Well, it seems like the Mesa Redbirds football team needs to do some seat-filling magic! To determine the price they would have to charge in order to fill the stadium, we need to consider the price elasticity of -4.
Now, if the team wants to increase attendance from an average of 50,000 to the full capacity of 80,000, they need to bump up their price in such a way that it doesn't scare away fans.
Since the price elasticity is -4, we can use the formula: Elasticity = (% Change in Quantity Demanded) / (% Change in Price)
To calculate the required price, let's figure out the percentage change in quantity demanded:
(% Change in Quantity Demanded) = (80,000 - 50,000) / (50,000) = 60%
Now, let's substitute the values into the elasticity formula and solve for the % change in price:
-4 = 60% / (% Change in Price)
(% Change in Price) = 60% / -4 = -15%
To fill the stadium, the team would have to decrease their ticket price by 15% (since the percentage change in price is negative). So, if the average ticket price is currently $30, they would need to charge approximately $25.50 to fill the stadium.
Now, let's move on to the next scenario - decreasing the price to $27 and increasing the attendance to 60,000. To find the price elasticity, we can use the same formula:
Elasticity = (% Change in Quantity Demanded) / (% Change in Price)
The percentage change in quantity demanded would be: (60,000 - 50,000) / 50,000 = 20%
And the percentage change in price: ($30 - $27) / $30 = 10%
Therefore, the price elasticity in this scenario would be: 20% / 10% = 2
So, there you have it! The price elasticity in the second scenario would be 2. Now, I hope the Mesa Redbirds can use these insights to fill their stadium and score some winning touchdowns!
To find the price the team would have to charge in order to fill the stadium, we need to calculate the price elasticity of demand. The formula for price elasticity is given by:
Price elasticity = (% change in quantity demanded) / (% change in price)
We are given the following information:
Seating capacity = 80,000
Average attendance = 50,000
Average ticket price = $30
Price elasticity = -4
To find the price that would fill the stadium, we can set the quantity demanded (attendance) equal to the seating capacity:
Quantity demanded = Seating capacity
Let's assume that the price the team needs to charge to fill the stadium is P.
To find P, we set up the following equation:
Quantity demanded = Seating capacity = P * (1 + (% change in quantity demanded) / 100)
The percentage change in quantity demanded can be calculated using the price elasticity formula:
Price elasticity = (% change in quantity demanded) / (% change in price)
Rearranging the formula, we can solve for the percentage change in quantity demanded:
% change in quantity demanded = Price elasticity * (% change in price)
Using the given price elasticity of -4:
% change in quantity demanded = -4 * (% change in price)
Now, we can substitute the given values:
80,000 = P * (1 + (-4 * (% change in price) / 100))
Next, we can substitute the information provided in the second part of the question:
Average attendance = 60,000
Price = $27
To find the new price elasticity, we use the same formula as before:
Price elasticity = (% change in quantity demanded) / (% change in price)
Rearranging the formula, we can solve for the percentage change in quantity demanded:
% change in quantity demanded = Price elasticity * (% change in price)
Using the values:
Price elasticity = ? (to be calculated)
% change in price = (Price - Old Price) / Old Price = ($27 - $30) / $30 = -0.10
Now, we can use the information provided to calculate the new price elasticity:
Price elasticity = (% change in quantity demanded) / (% change in price)
Price elasticity = (60,000 - 50,000) / (50,000 * -0.10)
Let's calculate the values.
To find out what price the team would have to charge in order to fill the stadium, we need to calculate the price elasticity of demand and use it to determine the optimal price.
Price elasticity of demand measures how responsive quantity demanded is to changes in price. It is calculated using the formula:
Price Elasticity = (% Change in Quantity Demanded) / (% Change in Price)
In this case, we know that the price elasticity is -4, which means that a 1% increase in price will result in a 4% decrease in quantity demanded, and vice versa.
First, let's calculate the percentage change in quantity demanded. The average attendance increased from 50,000 to 80,000, which is an increase of 30,000. To find the percentage change, we divide this by the initial attendance:
Change in Quantity Demanded = (80,000 - 50,000) = 30,000
Percentage Change in Quantity Demanded = (30,000 / 50,000) * 100% = 60%
Now, using the price elasticity formula, we can solve for the change in price:
-4 = (60% / Change in Price)
Solving for Change in Price:
Change in Price = 60% / -4 = -15%
Therefore, to fill the stadium, the team would have to decrease the ticket price by 15%.
Next, let's calculate the price elasticity when the price is decreased to $27 and the attendance increases to 60,000.
The change in price is:
Change in Price = ($27 - $30) / $30 = -10%
The change in quantity demanded is:
Change in Quantity Demanded = (60,000 - 50,000) = 10,000
Percentage Change in Quantity Demanded = (10,000 / 50,000) * 100% = 20%
With these values, we can calculate the new price elasticity:
Price Elasticity = (20% / -10%) = -2
Therefore, when the price is decreased to $27 and the attendance increases to 60,000, the price elasticity is -2.