Suppose the price of widgets rises from $7 to $9 and consumption of widgets falls from 25 widgets a month to 15 widgets. Calculate your price elasticity of demand of widgets. What can you say about your price elasticity of demand of widgets? Is it Elastic, Inelastic, or Unitary Elastic? Why? Use the Midpoint formula and please show your work
To calculate the price elasticity of demand using the midpoint formula, we need to determine the percentage change in quantity demanded and the percentage change in price.
The percentage change in quantity demanded can be calculated using the following formula:
% Change in Quantity Demanded = [(new quantity - old quantity) / (midpoint quantity)] * 100
The percentage change in price can be calculated using a similar formula:
% Change in Price = [(new price - old price) / (midpoint price)] * 100
Let's calculate these values step by step:
Old quantity = 25 widgets
New quantity = 15 widgets
Midpoint quantity = (Old quantity + New quantity) / 2 = (25 + 15) / 2 = 20 widgets
% Change in Quantity Demanded = [(15 - 25) / 20] * 100 = -50%
Old price = $7
New price = $9
Midpoint price = (Old price + New price) / 2 = ($7 + $9) / 2 = $8
% Change in Price = [($9 - $7) / $8] * 100 = 25%
Now, we can calculate the price elasticity of demand using the midpoint formula:
Price Elasticity of Demand = % Change in Quantity Demanded / % Change in Price
Price Elasticity of Demand = (-50% / 25%) = -2
The absolute value of the price elasticity of demand is 2. Therefore, the price elasticity of demand for widgets is 2.
In terms of interpretation, the price elasticity of demand tells us how responsive the quantity demanded is to a change in price.
When the price elasticity of demand is greater than 1 (in absolute value), it is considered elastic. This means that a change in price will result in a proportionally larger change in quantity demanded. In this case, the price elasticity of demand for widgets is 2, which is greater than 1, indicating that the demand for widgets is elastic.