compute the price elasticity of demand for paint and show calculations? If a gallon of paint went from 3.00 to 3.50 a gallon and the usage of paint drops from 35 gallons a month to 20 gallons a month.
To compute the price elasticity of demand for paint, we need to use the formula:
Price Elasticity of Demand = (% Change in Quantity Demanded) / (% Change in Price)
Step 1: Calculate the percentage change in quantity demanded:
Quantity Demanded (Initial) = 35 gallons
Quantity Demanded (Final) = 20 gallons
% Change in Quantity Demanded = (Quantity Demanded (Final) - Quantity Demanded (Initial)) / Quantity Demanded (Initial)
% Change in Quantity Demanded = (20 - 35) / 35 = -15 / 35
Step 2: Calculate the percentage change in price:
Price (Initial) = $3.00
Price (Final) = $3.50
% Change in Price = (Price (Final) - Price (Initial)) / Price (Initial)
% Change in Price = (3.50 - 3.00) / 3.00 = 0.50 / 3.00
Step 3: Plug the values into the formula to find the price elasticity of demand:
Price Elasticity of Demand = (% Change in Quantity Demanded) / (% Change in Price)
Price Elasticity of Demand = (-15/35) / (0.50/3.00)
Price Elasticity of Demand = -0.4286 / 0.1667
Price Elasticity of Demand ≈ -2.5714
The price elasticity of demand for paint is approximately -2.5714.