You are a painter, and the price of a gallon of paint increases from $3.00 a gallon from 3.50 a gallon. your usage of paint drops from 35 gallons a month to 20 gallons a month. perform the following:
1. compute the price elasticity of demand for paint and show your calculations.
2. decide whether the demand for paint is elastic, unitary elastic, or inelastic.
3. explain your reasoning and interpret results?
You are a painter, and the price of a gallon of paint increases from $3.00 a gallon from 3.50 a gallon. your usage of paint drops from 35 gallons a month to 20 gallons a month. perform the following:
To compute the price elasticity of demand for paint, you will need to use the formula:
Price Elasticity of Demand = ((Q2 - Q1) / ((Q2 + Q1) / 2)) / ((P2 - P1) / ((P2 + P1) / 2))
Where:
Q1 = Initial quantity of paint (35 gallons)
Q2 = Final quantity of paint (20 gallons)
P1 = Initial price of paint ($3.00/gallon)
P2 = Final price of paint ($3.50/gallon)
Let's calculate the price elasticity of demand step by step:
Step 1: Calculate the change in quantity (Q2 - Q1):
Change in quantity = 20 - 35 = -15
Step 2: Calculate the average quantity [(Q2 + Q1) / 2]:
Average quantity = (20 + 35) / 2 = 27.5
Step 3: Calculate the change in price (P2 - P1):
Change in price = 3.50 - 3.00 = 0.50
Step 4: Calculate the average price [(P2 + P1) / 2]:
Average price = (3.50 + 3.00) / 2 = 3.25
Step 5: Now substitute the values into the price elasticity of demand formula:
Price Elasticity of Demand = ((-15) / 27.5) / (0.50 / 3.25)
Simplifying further:
Price Elasticity of Demand = (-0.5455) / (0.1538)
Price Elasticity of Demand = -3.5485
To answer the second part of the question, let's interpret the result:
Since the price elasticity of demand is greater than 1 (specifically, it is -3.5485), we can conclude 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, the increase in price from $3.00 to $3.50 resulted in a decrease in demand from 35 gallons to 20 gallons, indicating sensitivity to price changes.