Change in Q=5000-3000=2000
change in P=300-200=100
original Q =3000
original P =300
Q/P×p1+p2/q1+q2
2000/100*500/8000
=1.25

Calculating the Price Elasticity of Demand using the Arc Elasticity Method

To calculate the price elasticity of demand using the arc elasticity method, we need to follow a few steps:

Step 1: Determine the initial price and quantity values
- Initial price (P1) = 300 rupees
- Initial quantity demanded (Q1) = 3000 plate settings

Step 2: Determine the final price and quantity values
- Final price (P2) = 200 rupees
- Final quantity demanded (Q2) = 5000 plate settings

Step 3: Calculate the percentage change in price (ΔP)
- ΔP = (P2 - P1) / [(P1 + P2) / 2]
- ΔP = (200 - 300) / [(200 + 300) / 2]
- ΔP = -100 / 250
- ΔP = -0.4

Step 4: Calculate the percentage change in quantity demanded (ΔQ)
- ΔQ = (Q2 - Q1) / [(Q1 + Q2) / 2]
- ΔQ = (5000 - 3000) / [(3000 + 5000) / 2]
- ΔQ = 2000 / 4000
- ΔQ = 0.5

Step 5: Calculate the price elasticity of demand (PED)
- PED = ΔQ / ΔP
- PED = 0.5 / -0.4
- PED ≈ -1.25

Interpretation of the Price Elasticity of Demand

The price elasticity of demand (PED) for silverware using the arc elasticity method is approximately -1.25. This value indicates that the demand for plate settings is elastic.

Explanation:
When the price of plate settings is reduced from 300 to 200 rupees, the quantity demanded increases from 3000 to 5000 plate settings. The negative value of PED (-1.25) indicates that the demand for plate settings is responsive to changes in price.

Interpretation of Elastic Demand:
Since PED is greater than 1 (in absolute value), the demand for silverware is considered elastic. This means that a decrease in price leads to a proportionally larger increase in quantity demanded. In this case, the 33.33% reduction in price (from 300 to 200 rupees) results in a 66.67% increase in quantity demanded (from 3000 to 5000 plate settings).

Implications for the Department Store:
The department store can benefit from the elastic demand for silverware by offering sales and discounts. Lowering the price of plate settings increases the store's revenue as the increase in quantity demanded more than compensates for the reduction in price. However, it is important for the store to consider the cost implications and profitability when determining the extent of price reductions. Additionally, the store can use this information to make informed decisions about pricing strategies and promotions to maximize sales and profits.