Paint increase from $3.00 a gallon to $3.50 a gallon. The paint drops from 35 gallons a month to 20 gallons a month. Compute the price elasticity of demand for paint and show the calculations
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.
1. At $3 per gallon, you consumption is 35 gallons for expenditure of $105 per month. At $3.50 per gallon, your consumption drops to 20 gallons for expenditure of $75 per month. In that price range, the demand is relatively elastic. Calculation of Price Elasticity of Demand:
Q2 - Q1
-----------------------
( Q1 + Q2 ) / 2
-------------------------------
P2 - P1
-----------------------
( P1 + P2 ) / 2
20 gal - 35 gal / (35 + 20)/2 = -15 / 27.5 = -.5455
$3.50 - $3 / ($3 + $3.50)/2 = $.50 / $3.25 = .1538
-.5455 / .1538 = 3.5468 = 3.55
2. 3.55 > 1; demand is elastic
Edit: When demand is elastic, increasing the price decreases total revenue. When demand is inelastic, increasing the price increases total revenue. When demand is unitary elastic, changes in price don't effect total revenue.
Example of unitary elastic: Concert tickets can be priced $50, $75, $100, or $125. Research demonstrates that at $50, 3000 tickets will be sold. At $75, 2000 tickets will be sold. At $100, 1500 tickets will be sold. At $125, 1200 tickets will be sold.
Total revenue at each price/ticket sales level:
$50 x 3000 = $150,000
$75 x 2000 = $150,000
$100 x 1500 = $150,000
$125 x 1200 = $150,000
To compute the price elasticity of demand for paint, we need to 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:
Percentage Change in Quantity Demanded = ((New Quantity Demanded - Initial Quantity Demanded) / Initial Quantity Demanded) * 100
Initial Quantity Demanded = 35 gallons
New Quantity Demanded = 20 gallons
Percentage change in quantity demanded = ((20 - 35) / 35) * 100 = (-15 / 35) * 100 = -42.85%
Next, let's calculate the percentage change in price:
Percentage Change in Price = ((New Price - Initial Price) / Initial Price) * 100
Initial Price = $3.00
New Price = $3.50
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 formula:
Price Elasticity of Demand = (-42.85% / 16.67%)
Using a calculator, we can divide -42.85% by 16.67% to get the price elasticity of demand.
Price Elasticity of Demand ≈ -2.571
Therefore, the price elasticity of demand for paint is approximately -2.571.