Final answer:
The price elasticity of demand at a price of $60 for a product with the demand curve Q = 50 - 0.5P is approximately equal to -2, indicating that the demand is relatively elastic.
Step-by-step explanation:
The elasticity of demand measures the responsiveness of quantity demanded to changes in price. It is calculated by dividing the percentage change in quantity demanded by the percentage change in price. In this case, the demand curve is given by Q = 50 - 0.5P, and we want to find the price elasticity of demand at a price of $60.
First, we need to calculate the percentage change in quantity demanded when the price changes from $60 to $70. Using the demand curve equation, we find that the quantity demanded at a price of $60 is Q = 50 - 0.5(60) = 20. The quantity demanded at a price of $70 is Q = 50 - 0.5(70) = 15. Therefore, the percentage change in quantity demanded is ((15 - 20) / ((20 + 15) / 2)) * 100 = -33.33%.
Next, we need to calculate the percentage change in price. The price change is $70 - $60 = $10. Therefore, the percentage change in price is ($10 / (($60 + $70) / 2)) * 100 = 16.67%.
Finally, we can calculate the price elasticity of demand by dividing the percentage change in quantity demanded (-33.33%) by the percentage change in price (16.67%). The price elasticity of demand at a price of $60 is -33.33% / 16.67% = -1.9996, which is approximately equal to -2. Therefore, at a price of $60, the demand is relatively elastic.