To determine the price elasticity of demand, we analyze how the quantity demanded of a product changes in response to a change in its price. In this scenario, a pizza company's lunch special is priced at $6, with a weekly demand of 1,400 specials. When the price is lowered to $5, the demand increases to 2,000 specials. The price elasticity of demand (PED) can be calculated using the formula:

Price Elasticity of Demand (PED) = \(\frac{\%\text{ Change in Quantity Demanded}}{\%\text{ Change in Price}}\)

First, we calculate the percentage change in quantity demanded. The formula for percentage change is:

\(\%\text{ Change} = \frac{\text{New} - \text{Original}}{\text{Original}} \times 100\)

For quantity demanded:

New quantity = 2,000

Original quantity = 1,400

Percentage change in quantity demanded = \(\frac{2,000 - 1,400}{1,400} = \frac{600}{1,400} \approx 0.429\) or 42.9%.

Next, we calculate the percentage change in price:

New price = $5

Original price = $6

Percentage change in price = \(\frac{5 - 6}{6} = \frac{-1}{6} \approx -0.167\) or -16.7%.

Since we are interested in the absolute value for elasticity, we take the positive value of the price change, which is 0.167.

Now, substituting these values into the elasticity formula gives:

PED = \(\frac{0.429}{0.167} \approx 2.569\).

This indicates that the demand is elastic, meaning that the quantity demanded is quite responsive to price changes. However, it is important to note that the elasticity can yield different results depending on the direction of the price change due to the original values used in the calculations. To achieve consistency, it is advisable to use the average of the original and new values in the denominator for both quantity and price changes.

In summary, the price elasticity of demand is a crucial concept in understanding consumer behavior in response to price changes, and using averages in calculations can provide a more reliable measure of elasticity.