you are a painter, and the price of a gallon of paint increases from $3.00 a gallon to $3.50 a gallon. your usage of paint drops from 35 gallons a month to 20 gallons a month. perform the following. compute the price elasticity of demand for paint and show your calculations. decide whether the demand for paint is elastic, unitary elastic, or inelastic. explain your reasoning and interpret your results.
To compute the price elasticity of demand, we will use the formula:
Price Elasticity of Demand = percentage change in quantity demanded / percentage change in price
First, let's calculate the percentage change in quantity demanded (Qd):
Percentage Change in Quantity Demanded = ((New Quantity Demanded - Old Quantity Demanded) / Old Quantity Demanded) * 100
New Quantity Demanded = 20 gallons
Old Quantity Demanded = 35 gallons
Percentage Change in Quantity Demanded = ((20 - 35) / 35) * 100 = (-15 / 35) * 100 = -42.86%
Next, let's calculate the percentage change in price (P):
Percentage Change in Price = ((New Price - Old Price) / Old Price) * 100
New Price = $3.50 per gallon
Old Price = $3.00 per gallon
Percentage Change in Price = (($3.50 - $3.00) / $3.00) * 100 = ($0.50 / $3.00) * 100 = 16.67%
Now, we can substitute the values into the price elasticity of demand formula:
Price Elasticity of Demand = (-42.86% / 16.67%) ≈ -2.57
The price elasticity of demand for paint is approximately -2.57.
Interpreting the results:
Since the price elasticity of demand is greater than 1 (in absolute value), it means that the demand for paint is elastic. This means that a change in price has a relatively larger impact on the quantity demanded. In this case, we can see that the increase in price from $3.00 to $3.50 resulted in a significant decrease in quantity demanded from 35 gallons to 20 gallons.