Management Assignment Sample
Q1:
Answer :Step 1: Understanding Price Elasticity of Demand (PED)
The price elasticity of demand (PED) measures the responsiveness of quantity demanded to a change in price. The formula for PED is:
PED=% Change in Quantity Demanded/ % Change in Price
Alternatively, it can be calculated using the following formula:
PED=(Q2−Q1)/(Q2+Q1)(P2−P1)/(P2+P1)PED = \frac{(Q_2 - Q_1) / (Q_2 + Q_1)}{(P_2 - P_1) / (P_2 + P_1)}PED=(P2−P1)/(P2+P1)(Q2−Q1)/(Q2+Q1)
Where:
- Q1Q_1Q1and Q2Q_2Q2 are the initial and new quantities of the product sold.
- P1P_1P1and P2P_2P2 are the initial and new prices.
Given the information:
- Initial price (P1P_1P1) = $50
- New price (P2P_2P2) = $60
- Initial quantity (Q1Q_1Q1) = 10,000 units
- New quantity (Q2Q_2Q2) = 8,000 units
Step 2: Calculate the Percentage Changes in Price and Quantity
Percentage change in price:
\frac{(P_2 - P_1)}{P_1} = \frac{60 - 50}{50} = \frac{10}{50} = 0.20 \quad \text{(or 20% increase)}
Percentage change in quantity demanded:
\frac{(Q_2 - Q_1)}{Q_1} = \frac{8,000 - 10,000}{10,000} = \frac{-2,000}{10,000} = -0.20 \quad \text{(or 20% decrease)}
Step 3: Calculate PED
Now we can calculate the price elasticity of demand:
PED=(Q2−Q1)/(Q2+Q1)(P2−P1)/(P2+P1)
=(8,000−10,000)/(8,000+10,000)(60−50)/(60+50)
PED = \frac{(Q_2 - Q_1) / (Q_2 + Q_1)}{(P_2 - P_1) / (P_2 + P_1)}
= \frac{(8,000 - 10,000) / (8,000 + 10,000)}{(60 - 50) / (60 + 50)}
PED=(P2−P1)/(P2+P1)(Q2−Q1)/(Q2+Q1)
=(60−50)/(60+50)(8,000−10,000)/(8,000+10,000) PED=−2,000/18,00010/110=−0.11110.0909=−1.22PED
= \frac{-2,000 / 18,000}{10 / 110} = \frac{-0.1111}{0.0909}
= -1.22PED=10/110−2,000/18,000=0.0909−0.1111=−1.22
The absolute value of PED is 1.22. This indicates that the demand is elastic since the absolute value is greater than 1.
Step 4: Interpretation and Decision
- Since the price elasticity of demand is greater than 1 (elastic), this means that the quantity demanded is highly responsive to price changes.
- In this case, a 20% increase in price results in a 20% decrease in quantity demanded, which implies that customers are quite sensitive to the price increase.
Step 5: Should the company raise its price?
To answer this question, we should consider the impact on revenue.
Revenue before the price change:
- Revenue1=P1×Q1=50×10,000=500,000\text{Revenue}_1 = P_1 \times Q_1 = 50 \times 10,000 = 500,000Revenue1=P1×Q1=50×10,000=500,000
Revenue after the price change:
- Revenue2=P2×Q2=60×8,000=480,000\text{Revenue}_2 = P_2 \times Q_2 = 60 \times 8,000 = 480,000Revenue2=P2×Q2=60×8,000=480,000
Although the company increases its price by 20%, the decrease in quantity demanded by 20% results in a reduction in total revenue from $500,000 to $480,000.
Conclusion:
Given the elastic demand (PED > 1), the company should not raise its price. A price increase leads to a proportionally larger decrease in quantity demanded, which causes a decrease in revenue. The company would be better off maintaining the current price or even considering price reductions to increase sales volume and total revenue.