Free tool
Enter two prices and the two quantities demanded. You get the midpoint (arc) elasticity, whether demand is elastic, inelastic or unitary, and what happened to total revenue.
Built for MicroeconomicsSwap the old and new points and the answer does not change. That is the point of the midpoint method.
Enter two prices and two quantities.
Elasticity is a setup problem more than a math problem. Encodr turns the midpoint formula and the total revenue rule into typed cards on a spaced schedule, so you can do them without looking.
Get started freeEach percentage change uses the average of the two values as its base:
% change = (new - old) / ((new + old) / 2) x 100. Then
price elasticity of demand = % change in quantity / % change in price.
The raw number is negative because price and quantity demanded move in opposite directions, so you report the absolute value.
Greater than 1 is elastic, exactly 1 is unitary and less than 1 is inelastic. Elasticity has no units and is not the slope of the demand curve. Compute with unrounded percentages and round only the elasticity, to 2 decimal places. Total revenue is price times quantity: with elastic demand a price cut raises it, and with inelastic demand a price cut lowers it.
Worked example: a price falls from $70 to $60 and quantity demanded rises from 2,800 to 3,000. Quantity changes by 200 / 2,900 = 6.90% and price by -10 / 65 = -15.38%, so elasticity = 6.90 / 15.38 = 0.45, which is inelastic. Revenue falls from $196,000 to $180,000, as the rule predicts. The full walkthrough, including why the midpoint formula exists, is in price elasticity of demand explained, and the whole course is in the free Microeconomics deck.
This tool is for price elasticity of demand. Income and cross-price elasticity use the same arithmetic but you keep the sign, so the absolute value shown here would hide the answer.
Price elasticity of demand explained: the midpoint formula, elastic vs inelastic, the total revenue rule and why elasticity is not slope, with every step shown.
What's in a Principles of Microeconomics course: all 20 units, from supply and demand and elasticity to costs, market structures, externalities and trade.
How to study for microeconomics: drill curve shifts, work cost tables and elasticity by hand, separate look-alike terms, and space reviews across the semester.
The fixed-cost, price, and variable-cost math behind every intro accounting and entrepreneurship break-even problem.
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