# Price Elasticity of Demand Calculator

Created by Tibor Pal, PhD candidate and Bogna Szyk
Reviewed by Jack Bowater
Based on research by
Krugman, P.; Wells, R. Economics, Fifth Edition (2017)
Last updated: May 10, 2022

The price elasticity of demand calculator is a tool for everyone who is trying to establish the perfect price for their products. Thanks to this calculator, you will be able to decide whether you should charge more for your product (and sell a smaller quantity) or decrease the price but increase the demand.

This calculator uses the midpoint formula for the elasticity of demand. Once you have calculated its value, you can head straight to the optimum price calculator to deduce what price is the best for your product.

Read on to learn how to calculate the price elasticity of demand with the midpoint method!

You may also try other elasticity related tools, such as:

## What is the price elasticity of demand?

Imagine that you run an home electronics shop. Every month, you sell 200 TV sets for $800 each. You begin to wonder what will happen if you decrease the price of a TV set to$700. Will you get more customers, and if you do, will you get enough of them to increase your revenue despite the price cut?

What you are actually thinking about is the price elasticity of demand. It describes the behavior of customers once the price has been changed.

If elasticity is high, a price decrease will cause an overly proportional increase in demand, making it profitable to decrease the price. Such a situation is usually associated with luxury products, such as electronics or cars.

If elasticity is low, a price decrease will cause a slight increase in demand. In such a case, the demand increase will be unsatisfactory from the point of view of the revenue. Essential products, such as car fuel or medicines, display this behavior.

Price elasticity of demand has nothing to do with different packaging types – it won't tell you whether it's more profitable to sell a 0.5-liter bottle of water for $0.50 or a 1.5-liter bottle for$1.25. For this type of problem, head to our price and quantity calculator.

## Midpoint formula for elasticity of demand

The elasticity of demand is evaluated with the use of the midpoint formula:

$\small \text{PED} = \frac{(Q_1 - Q_0)/[(Q_1 + Q_0)/2]}{(P_1 - P_0)/[(P_1 + P_0) /2]}$

where:

• $P_0$ – Initial price of the product;
• $P_1$ – Final price of the product;
• $Q_0$ – Initial demand;
• $Q_1$ – Demand after the price change; and
• $\rm{PED}$ – Price elasticity of demand.

The price elasticity of demand is almost always negative. It means that the relationship between price and demand is inversely proportional – the higher the price, the lower the demand, and vice versa.

You can also use this midpoint method calculator to find any of the values in the equation ($P_0$, $P_1$, $Q_0$, or $Q_1$). Simply input all of the remaining variables, and the result will be calculated automatically.

## How to calculate price elasticity of demand

Let's analyze the example of an electronic store together.

1. Begin by noting down the initial price of the product. In our case, one TV set costs $800. 2. Determine the initial demand. In the case of an electronic store, the demand was equal to 200 per month. 3. Decide on the new price. In our case, the price is equal to$700.

4. Measure the quantity sold for a new price. LEt's assume you managed to sell 250 TV sets for this lowered price.

5. Use the midpoint formula for the elasticity of demand:

\footnotesize \ \ \ \begin{align*} \text{PED} &= \frac{(Q_1 - Q_0)/[(Q_1 + Q_0)/2]}{(P_1 - P_0)/[(P_1 + P_0) /2]}\\\\ &= \frac{(250 - 200)/[(250 + 200)/2]}{(700 - 800)/[(700 + 800) /2]}\\\\ &= \frac{50/225}{-100/750}\\\\ &= \frac{0.22\dot{2}}{-1.33\dot{3}}\\\\ &= -1.67 \end{align*}
1. You can perform the calculations manually or use the price elasticity of demand calculator to do all of the work for you!

## Revenue increase and PED

You can calculate the revenue in both the initial and final state using the equation:

$\small R = P \times Q$

Hence, the revenue increase (usually expressed as a percentage) can be found as:

\small \begin{align*} \Delta R &= R_1 - R_0\\ &= P_1 \times Q_1 - P_0 \times Q_0 \end{align*}

A negative revenue increase means that the revenue is actually dropping.

The price elasticity of demand is directly related to the revenue increase. The following rules apply:

• PED is perfectly inelastic (PED = 0). In this case, a price change does not affect demand. This is the case of goods necessary for survival – people will still buy them, whatever the price. Hence, if the price is lowered, the total revenue will drop drastically.

• PED is inelastic (-1 < PED < 0). In this case, a decrease in prices causes an increase in demand but a drop in overall revenue (revenue increase is negative).

• PED is unitary elastic (PED = -1). In such a case, price decrease is directly proportional to demand increase, and the overall revenue doesn't change.

• PED is elastic (-∞ < PED < -1). This is the case when a price decrease causes a substantial increase in demand and an increase in overall revenue.

• PED is perfectly elastic (PED = -∞). In this case, any increase in price will immediately cause the demand to drop to zero. These are fixed-value goods that usually have their price determined by the law. For example, a one-dollar bill is a fixed-value item; selling this bill for $1.01 will cause the demand to drop to zero. The revenue increase equals -100% (all revenue is lost). ## FAQ ### What does the price elasticity of demand measure? Price elasticity of demand measures how much the demand for a good changes with its price. If the demand changes with price, the demand is elastic, while if it doesn’t change, it is inelastic. Luxury goods and necessary goods are an example of each of these, respectively. ### What are the major determinants of price elasticity of demand? The major determinants of price elasticity are: • The number of substitutes to the product on the market. • The timeframe being considered and how it affects demand. • The price of the product relative to people’s income. • Whether the product is a luxury or a necessity. • How big the market is being considered. ### How does elasticity affect a company's pricing policy? As a general rule, businesses will charge as much for a product as possible without affecting demand. If the cost of producing a product rises, the business's profits will fall. To offset this, the business will raise the price of an inelastic good, as its demand is less sensitive to price than an elastic good, and so will not decrease that much. ### What is cross price elasticity? Cross price elasticity is a measure of how the demand for one good changes following a change in the price of another related good. Products in competitive demand will see the demand for one product increase if the price of the rival increases, while products in joint demand will see the demand for one increase if the price of the other decreases. The cross-price elasticity is said to be positive and negative, respectively. ### How is the price elasticity of demand measured? To measure the price elasticity of demand, you would record the price at which you sold a product and how much of the product you sold at one time, then change the price and measure how much of the product was sold again, over the same period of time. You can then use the midpoint formula to find the price elasticity of demand. ### How do you calculate the price elasticity of demand from the demand function? 1. Get the demand function and the price at which you want to find the elasticity. 2. Differentiate the demand function with respect to the price. 3. Multiply the differentiated function by the price. 4. Plug the price into the demand equation to get Q. 5. Divide the result of step 3 by the result from step 4. 6. The result is the percentage price elasticity of demand at your chosen price. ### How is total revenue related to the price elasticity of demand? For two products that initially cost the same, the total revenue for the inelastic product will be higher if the prices are increased. This is because the demand for elastic products is more affected by their price, so people will stop buying them if an increase occurs, lowering total revenue. Inelastic products are not affected in the same way so total revenue will increase. Tibor Pal, PhD candidate and Bogna Szyk Initial price$
Initial quantity
Final price
$Final quantity Price elasticity of demand Elasticity Revenue Initial revenue$
Final revenue
\$
Revenue increase
%
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