Introduction:
To determine the original price of a commodity when the price elasticity of demand is given, we need to understand the concept of price elasticity of demand and how it relates to changes in price and quantity demanded. Price elasticity of demand measures the responsiveness of quantity demanded to changes in price.

Price Elasticity of Demand:
Price elasticity of demand is calculated using the formula:
Elasticity = (% change in quantity demanded) / (% change in price)

Given Information:
Price elasticity of demand = 0.71
Quantity demanded before the change = 20 units
Quantity demanded after the change = 15 units
New price = $10

Calculating the Percentage Change in Quantity Demanded:
Percentage change in quantity demanded = ((New quantity - Old quantity) / Old quantity) * 100
Percentage change in quantity demanded = ((15 - 20) / 20) * 100
Percentage change in quantity demanded = (-5 / 20) * 100
Percentage change in quantity demanded = -25%

Calculating the Percentage Change in Price:
Since the new price is given as $10 and the original price is unknown, we cannot calculate the percentage change in price. Therefore, we cannot directly determine the original price using the given information.

Interpreting Price Elasticity of Demand:
The price elasticity of demand value of 0.71 indicates that the commodity has an inelastic demand. Inelastic demand means that the quantity demanded is not very responsive to changes in price. In this case, a 1% increase in price would result in a less than 0.71% decrease in quantity demanded.

Conclusion:
Based on the given information, we cannot directly determine the original price of the commodity without knowing the percentage change in price. The price elasticity of demand only provides information about the responsiveness of quantity demanded to changes in price and does not give us the actual prices. To determine the original price, we need additional information such as the percentage change in price or the original quantity demanded at a specific price level.