Consider the market for taxi rides in a particular metropolitan area.
a) Suppose that, when the price per mile increases by 40%, total miles demanded falls by 30%. Solve for the price elasticity of demand.
b) Is the demand for taxi rides elastic or inelastic (in this example)? Explain how you answer in part a) is relevant.
To solve for the price elasticity of demand, we need to use the formula:
Price Elasticity of Demand = Percentage Change in Quantity Demanded / Percentage Change in Price
a) In this case, we are given that the price per mile increases by 40% and total miles demanded falls by 30%.
Percentage Change in Quantity Demanded = -30%
Percentage Change in Price = 40%
Substituting these values into the formula, we get:
Price Elasticity of Demand = (-30% / 40%)
Simplifying this expression, we get:
Price Elasticity of Demand = -0.75
Therefore, the price elasticity of demand in this example is -0.75.
b) The demand for taxi rides can be classified as elastic or inelastic based on the absolute value of the price elasticity of demand.
If the absolute value of the price elasticity of demand is greater than 1, then the demand is considered elastic. This means that a change in price leads to a proportionately larger change in quantity demanded.
On the other hand, if the absolute value of the price elasticity of demand is less than 1, then the demand is considered inelastic. In this case, a change in price leads to a proportionately smaller change in quantity demanded.
In our example, the price elasticity of demand is -0.75. Since the absolute value of -0.75 is less than 1, the demand for taxi rides is considered inelastic.
This means that a 40% increase in price leads to a 30% decrease in total miles demanded, indicating that the demand for taxi rides is relatively less responsive to changes in price.