Show price elasticity of demand for Company XYZ’s product.

Using the following data:

Price Quantity
2000 5.00 100

2001 5.25 115

2002 5.50 150

2003 6.00 198

Calculate endpoint elasticity from 2000 to 2003 over the entire period.

Use the arc convention and the traditional percent change calculations.

Show work and compare results.

Finally, is this a typical situation?

To calculate the price elasticity of demand for Company XYZ's product using endpoint elasticity, we need to calculate the percent change in quantity demanded and the percent change in price. Then we can divide the percent change in quantity demanded by the percent change in price to get the elasticity value.

Step 1: Calculate the percent change in quantity demanded.
Percent change in quantity demanded = (New quantity - Old quantity) / Old quantity * 100

For the given data:
Percent change in quantity demanded from 2000 to 2003 = (198 - 100) / 100 * 100 = 98%

Step 2: Calculate the percent change in price.
Percent change in price = (New price - Old price) / Old price * 100

For the given data:
Percent change in price from 2000 to 2003 = (6.00 - 5.00) / 5.00 * 100 = 20%

Step 3: Calculate the price elasticity of demand.
Price elasticity of demand = Percent change in quantity demanded / Percent change in price

For the given data:
Price elasticity of demand from 2000 to 2003 = 98% / 20% = 4.9

Now, let's compare the results with the traditional percent change calculations using the arc convention.

Step 1: Calculate the midpoint quantity and the midpoint price.
Midpoint quantity = (Old quantity + New quantity) / 2 = (100 + 198) / 2 = 149
Midpoint price = (Old price + New price) / 2 = (5.00 + 6.00) / 2 = 5.50

Step 2: Calculate the percent change in quantity demanded using the midpoint values.
Percent change in quantity demanded = (New quantity - Old quantity) / Midpoint quantity * 100

For the given data:
Percent change in quantity demanded from 2000 to 2003 = (198 - 100) / 149 * 100 ≈ 66.44%

Step 3: Calculate the percent change in price using the midpoint values.
Percent change in price = (New price - Old price) / Midpoint price * 100

For the given data:
Percent change in price from 2000 to 2003 = (6.00 - 5.00) / 5.50 * 100 ≈ 18.18%

Step 4: Calculate the price elasticity of demand using the midpoint percent changes.
Price elasticity of demand = Percent change in quantity demanded / Percent change in price

For the given data:
Price elasticity of demand from 2000 to 2003 ≈ 66.44% / 18.18% ≈ 3.65

Comparing the two results:
Using the endpoint elasticity method, the elasticity is 4.9, while using the traditional percent change calculations with the arc convention, the elasticity is approximately 3.65. The two approaches yield slightly different results, but they are in the same range.

As for whether this situation is typical, it depends on the specific circumstances. Generally, a price elasticity of demand greater than 1 indicates relatively elastic demand, meaning that a change in price leads to a proportionally larger change in quantity demanded. In this case, both elasticity values (4.9 and 3.65) demonstrate the product's demand is quite elastic. However, it's worth noting that the elasticity value can vary depending on factors like consumer preferences, availability of substitutes, and market conditions.