Price Elasticity Calculator
Quickly compute price elasticity with accurate formulas. See amortization schedules, growth projections, and side-by-side comparisons.
Formula
PED = (% Change in Quantity) / (% Change in Price) using midpoint method
Price elasticity of demand is the ratio of the percentage change in quantity demanded to the percentage change in price. The midpoint method uses the average of old and new values as the base for percentage calculations, ensuring consistent results regardless of the direction of change.
Worked Examples
Example 1: Coffee Shop Price Increase
Problem: A coffee shop raises latte prices from $5.00 to $5.50, and daily sales drop from 200 to 180 lattes. Calculate the price elasticity.
Solution: Using midpoint method:\n% Change in Price = (5.50 - 5.00) / ((5.50 + 5.00) / 2) x 100 = 0.50 / 5.25 x 100 = 9.52%\n% Change in Quantity = (180 - 200) / ((180 + 200) / 2) x 100 = -20 / 190 x 100 = -10.53%\nPED = -10.53% / 9.52% = -1.106\n|PED| = 1.106 (Elastic)\nOld Revenue: $5.00 x 200 = $1,000\nNew Revenue: $5.50 x 180 = $990
Result: PED = -1.106 (Elastic) | Revenue decreased by $10 | Consider lowering price
Example 2: Gasoline Price Spike
Problem: Gasoline prices rise from $3.50 to $4.20 per gallon. A household reduces consumption from 50 to 47 gallons per month.
Solution: Using midpoint method:\n% Change in Price = (4.20 - 3.50) / ((4.20 + 3.50) / 2) x 100 = 0.70 / 3.85 x 100 = 18.18%\n% Change in Quantity = (47 - 50) / ((47 + 50) / 2) x 100 = -3 / 48.5 x 100 = -6.19%\nPED = -6.19% / 18.18% = -0.340\n|PED| = 0.340 (Inelastic)\nOld Revenue: $3.50 x 50 = $175\nNew Revenue: $4.20 x 47 = $197.40
Result: PED = -0.340 (Inelastic) | Revenue increased by $22.40 | Typical for necessities
Frequently Asked Questions
What is price elasticity of demand and why is it important?
Price elasticity of demand (PED) measures how responsive the quantity demanded of a good is to a change in its price. It is calculated as the percentage change in quantity demanded divided by the percentage change in price. A PED greater than 1 (elastic) means consumers are highly sensitive to price changes, while a PED less than 1 (inelastic) means demand barely changes with price. This concept is crucial for businesses setting pricing strategies, for governments predicting tax revenue impacts, and for economists analyzing market behavior. Understanding elasticity helps companies maximize revenue by knowing whether to raise or lower prices for specific products.
How does price elasticity affect total revenue?
The relationship between elasticity and revenue is fundamental to pricing strategy. When demand is elastic (PED greater than 1), a price increase reduces total revenue because the large drop in quantity more than offsets the higher price, while a price decrease increases revenue. When demand is inelastic (PED less than 1), raising prices increases total revenue because quantity barely changes, and lowering prices decreases revenue. At unit elasticity (PED equals 1), total revenue is maximized and any price change in either direction reduces revenue. This is why pharmaceutical companies can charge high prices for life-saving drugs with inelastic demand, while competitive consumer goods markets often see aggressive price competition.
What is the difference between price elasticity, income elasticity, and cross elasticity?
Price elasticity of demand measures quantity responsiveness to price changes of the same good. Income elasticity of demand measures how quantity demanded changes when consumer income changes: normal goods have positive income elasticity while inferior goods like instant noodles have negative income elasticity. Luxury goods have income elasticity greater than 1. Cross-price elasticity measures how the quantity demanded of one good changes when the price of a related good changes. Substitute goods like Coca-Cola and Pepsi have positive cross elasticity, while complementary goods like cars and gasoline have negative cross elasticity. Together, these three elasticity measures provide a comprehensive picture of demand behavior in markets.
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