Final answer:
The price elasticity of demand is calculated to be 1.67, which is greater than one, indicating that the demand for the good is considered elastic.
Step-by-step explanation:
If a good's price falls from 50 to 40 and as a result the per-period quantity demanded increases from 30 to 40 units, we can determine the type of elasticity by calculating the price elasticity of demand. The formula for this calculation is the percentage change in quantity demanded divided by the percentage change in price. The percentage change in quantity demanded is ((40 - 30) / 30) * 100 = 33.33%, and the percentage change in price is ((50 - 40) / 50) * 100 = 20%. Thus, the price elasticity of demand is 33.33% / 20% = 1.67.
Since the calculated elasticity is greater than one, we conclude that the price elasticity is greater than one, indicating a high responsiveness to changes in price, meaning that the demand for this good is considered elastic.