A movie theater
finds that when it prices tickets
at $9
,
the theater
sells 250
per day
.
When the price is reduced to $8
,
the theater
sells 300
per day
.
Based on this information, use the average-values formula to find the price elasticity of demand for tickets
.
Provide the absolute value of the price elasticity of demand.
Part 2
A.1.55
1.55
B.1.80
1.80
C.0.56
0.56
D.0.65
0.65
To calculate the price elasticity of demand (PED), we use the formula:
PED = (∆Q / ∆P) * (P / Q)
Where:
∆Q = change in quantity demanded
∆P = change in price
P = average price
Q = average quantity demanded
Using the given information, ∆Q = 300 - 250 = 50, ∆P = $8 - $9 = -$1, P = ($8 + $9) / 2 = $8.50, and Q = (250 + 300) / 2 = 275.
Substituting these values into the formula, we get:
PED = (50 / -1) * (8.50 / 275)
= -50 * 0.0309
= -1.545
The absolute value of the price elasticity of demand is 1.545.
To calculate the price elasticity of demand, you can use the average-values formula:
Elasticity = (Q2 - Q1) / [(Q1 + Q2)/2] / (P2 - P1) / [(P1 + P2)/2]
Where:
Q1 = Initial quantity sold (250)
Q2 = New quantity sold (300)
P1 = Initial price ($9)
P2 = New price ($8)
Let's plug in the values and calculate:
Elasticity = (300 - 250) / [(250 + 300) / 2] / (8 - 9) / [(9 + 8) / 2]
Simplifying the equation:
Elasticity = 50 / (275 / 2) / (-1) / (17 / 2)
Elasticity = 50 / 137.5 / (-1) / 8.5
Elasticity = 50 / (-116.18)
Elasticity ≈ -0.43
The absolute value of the price elasticity of demand is 0.43.
To find the price elasticity of demand using the average-values formula, we need to calculate the percentage change in quantity demanded and the percentage change in price.
The percentage change in quantity demanded can be calculated using the formula:
(Change in quantity demanded / Initial quantity demanded) * 100
In this case, the change in quantity demanded is 50 (300 - 250) and the initial quantity demanded is 250.
(50 / 250) * 100 = 20%
The percentage change in price can be calculated using the formula:
(Change in price / Initial price) * 100
In this case, the change in price is -1 (8 - 9) and the initial price is 9.
(-1 / 9) * 100 = -11.11%
Now, we can use the average-values formula to find the price elasticity of demand:
Price elasticity of demand = (Percentage change in quantity demanded / Percentage change in price)
Price elasticity of demand = 20% / -11.11%
Price elasticity of demand = -1.8
Therefore, the absolute value of the price elasticity of demand is 1.8.
The correct answer for Part 2 is B. 1.80.