We can use the midpoint formula to calculate the price elasticity of demand:
Price elasticity of demand = [(Q2 - Q1) / ((Q2 + Q1) / 2)] / [(P2 - P1) / ((P2 + P1) / 2)]
where:
Q1 = initial quantity demanded = 15,000
Q2 = new quantity demanded = 20,000
P1 = initial price = P100
P2 = new price = P90
Plugging in these values, we get:
Price elasticity of demand = [(20,000 - 15,000) / ((20,000 + 15,000) / 2)] / [((90 - 100) / ((90 + 100) / 2))]
Price elasticity of demand = [(5,000 / 17,500)] / [(-10 / 95)]
Price elasticity of demand = -0.2857 / -0.1053
Price elasticity of demand = 2.71
Since the absolute value of price elasticity of demand is greater than 1, the demand is considered elastic. This means that the percentage change in quantity demanded is greater than the percentage change in price. In other words, consumers are very sensitive to price changes for Bluetooth speakers, and a small decrease in price leads to a large increase in the quantity demanded.