# What is the Midpoint Formula?

by C. Taylor; Updated September 26, 2017The midpoint formula modifies the original price elasticity calculation to determine how various factors influence the price of a product. This formula typically assesses the relationship between price and product demand, but it can also illustrate the influence of supply. In the former case, actual purchase quantities are used to measure the level of demand.

### Price Elasticity of Demand

The price elasticity of demand formula describes how changes in price affect demand for a product. By comparing the quantity purchased at two price points, the formula derives a coefficient that illustrates the elasticity of demand. However, the original formula produces different results depending on which prices you enter as the original and updated price. This inconsistency renders the formula virtually useless, so it was necessary to modify it. The result was the midpoint formula, which consistently produces the same results regardless of how you enter each price.

### Midpoint Formula

The midpoint formula calculates the price elasticity of demand by dividing the percentage change in purchase quantity by the percentage change in price. The percentage changes are found by subtracting the original and updated values and then dividing the result by their average. If a negative value results, simply discard the negative sign, so you're using the absolute value.

### Example Calculation

Say you originally sold 40 units of a product for $20, but you could only sell 30 units after increasing the price to $25. First, subtract 30 from 40 to discover you're selling 10 fewer units at the increased price. Next, add the two quantities and divide by 2 to calculate the average. Divide the difference by the average to calculate the 0.29 percent change in quantity in decimal format. You could multiply by 100 to convert that figure to an actual percentage, but the percentages eventually cancel out, so you don't need this extra step. Repeat the same calculation for the change in price to get 0.22. Finally, divide 0.29 by .022 to calculate the elasticity coefficient of 1.32 using the midpoint formula.

### Interpreting the Results

If the elasticity coefficient equals 1, then the percentage change of price and demand are equivalent, which means raising or lowering the price has no effect on revenue. An elasticity coefficient greater than 1 means demand is elastic, so changes in price create a greater change in demand. In this case, increasing the product price has a negative effect on revenues, which is the situation discovered in the example calculation. Conversely, an elasticity coefficient less than 1 means demand is inelastic, so changes in price produce a smaller change in demand. In such cases, you should increase the product price to maximize revenue.

### Influences on Elasticity

Various factors cause demand for a product to be elastic. If substitutes exist, such as generic brands versus name brands, customers have more choices and are less willing to pay a premium. Demand also becomes more elastic when prices consume a larger percentage of the customer's income or the product is a luxury item rather than a necessity. Time also influences demand, such that limited time availability tends to reduce elasticity.

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