Question

What would a 10 percent increase in the price of movie tickets mean for the quantity demanded of a movie theater if the price elasticity of demand was \(0.1,0.5,1.0\), and \(5.0\) ?

Short answer

Answer: For a price elasticity of demand of 0.1, the quantity demanded would decrease by 1%; for 0.5, it would decrease by 5%; for 1.0, it would decrease by 10%; and for 5.0, it would decrease by 50%.

Step-by-step solution

Understand the Elasticity of Demand Formula

The price elasticity of demand (PED) formula can be written as: \(PED = \frac{Percentage\ Change\ in\ Quantity\ Demanded}{Percentage\ Change\ in\ Price}\) We will use this formula to find the percentage change in quantity demanded for each given elasticity value.

Calculate the Percentage Change in Price

The exercise states that there is a 10 percent increase in the price of movie tickets. We need this value to calculate the percentage change in quantity demanded. The percentage change in price is \(10\%\).

Calculate the Percentage Change in Quantity Demanded for Each Elasticity Value

We will now use the PED formula to find the corresponding percentage change in the quantity demanded for each given elasticity value. For each value of the price elasticity of demand, we have: \(PED = \frac{Percentage\ Change\ in\ Quantity\ Demanded}{Percentage\ Change\ in\ Price} \Rightarrow Percentage\ Change\ in\ Quantity\ Demanded = PED \times Percentage\ Change\ in\ Price\) Let's calculate the percentage change in quantity demanded for each given elasticity value. 1. For PED \(= 0.1\), we have: \(Percentage\ Change\ in\ Quantity\ Demanded = 0.1 \times 10\% = 1\%\) 2. For PED \(= 0.5\), we have: \(Percentage\ Change\ in\ Quantity\ Demanded = 0.5 \times 10\% = 5\%\) 3. For PED \(= 1.0\), we have: \(Percentage\ Change\ in\ Quantity\ Demanded = 1.0 \times 10\% = 10\%\) 4. For PED \(= 5.0\), we have: \(Percentage\ Change\ in\ Quantity\ Demanded = 5.0 \times 10\% = 50\%\)

Interpret the Results

Here are the results for the percentage change in quantity demanded for each given price elasticity of demand value: 1. For PED \(= 0.1\), the quantity demanded decreases by \(1\%\). 2. For PED \(= 0.5\), the quantity demanded decreases by \(5\%\). 3. For PED \(= 1.0\), the quantity demanded decreases by \(10\%\). 4. For PED \(= 5.0\), the quantity demanded decreases by \(50\%\). As we can see, as the price elasticity of demand increases, the percentage change in quantity demanded becomes larger. This means that the demand for movie tickets becomes more sensitive to changes in price as the elasticity value increases.