To answer the questions given, let’s approach them step-by-step. We were initially given computational results and had to extract information from them.
#### Part a) Calculation of Price Elasticity of Demand
For each group, the price elasticity of demand (PED) is calculated using the formula:
[tex]\[ \text{Price Elasticity of Demand (PED)} = \frac{\%\text{ Change in Quantity Demanded}}{\%\text{ Change in Price}} \][/tex]
Let’s define and calculate percent changes first.
For Business Travelers:
- Initial price ([tex]\(P_1\)[/tex]): \[tex]$800
- New price (\(P_2\)): \$[/tex]250
- Initial quantity ([tex]\(Q_{d1}\)[/tex]): 500
- New quantity ([tex]\(Q_{d2}\)[/tex]): 250
Calculate the percentage change in price:
[tex]\[
\%\Delta P = \frac{P_2 - P_1}{P_1} \times 100 = \frac{250 - 800}{800} \times 100 = \frac{-550}{800} \times 100 = -68.75\%
\][/tex]
Calculate the percentage change in quantity demanded:
[tex]\[
\%\Delta Q_d = \frac{Q_{d2} - Q_{d1}}{Q_{d1}} \times 100 = \frac{250 - 500}{500} \times 100 = \frac{-250}{500} \times 100 = -50\%
\][/tex]
Calculate PED for business travelers:
[tex]\[
\text{PED} = \frac{-50\%}{-68.75\%} = 0.727
\][/tex]
For Vacationers:
- Initial price ([tex]\(P_1\)[/tex]): \[tex]$800
- New price (\(P_2\)): \$[/tex]250
- Initial quantity ([tex]\(Q_{d1}\)[/tex]): 1900
- New quantity ([tex]\(Q_{d2}\)[/tex]): 1800
Calculate the percentage change in price:
We use the same percentage change in price as above since the prices are the same.
[tex]\[
\%\Delta P = -68.75\%
\][/tex]
Calculate the percentage change in quantity demanded:
[tex]\[
\%\Delta Q_d = \frac{Q_{d2} - Q_{d1}}{Q_{d1}} \times 100 = \frac{1800 - 1900}{1900} \times 100 = \frac{-100}{1900} \times 100 = -5.26\%
\][/tex]
Calculate PED for vacationers:
[tex]\[
\text{PED} = \frac{-5.26\%}{-68.75\%} = 0.0765
\][/tex]
#### Part b) Explanation for Different Elasticities
The reason why vacationers and business travelers have different elasticity values lies in their differing sensitivities and necessities for travel.
1. Business Travelers:
- Business travels are often time-sensitive and less flexible. Most companies may not significantly alter travel plans based on changes in ticket prices, leading to inelastic demand.
2. Vacationers:
- Vacationers generally have more flexibility in terms of travel dates and destinations. High competition in the travel market and the option to delay, change, or cancel travel plans based on ticket prices makes their demand more elastic.
Conclusion: The elasticity comparison shows that business travelers exhibit lower elasticity (0.727) versus vacationers (0.0765), indicating that business travel is less sensitive to price changes compared to vacation travel.
