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Price elasticity of demand
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# Price Elasticity of Demand Calculator

By Bogna Haponiuk

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 will 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!

## What is the price elasticity of demand?

Imagine that you run a shop with electronics. 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 change?

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 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 0.5-liter bottle of water for \$0.50 or 1.5-liter bottle for \$1.25. For this type of problems, head to our price and quantity calculator.

## Midpoint formula for elasticity of demand

Elasticity of demand is evaluated with the use of the midpoint formula:

`PED = [ (Q₁ - Q₀) / (Q₁ + Q₀) ] / [ (P₁ - P₀) / (P₁ + P₀) ]`

where:

• P₀ is the initial price of the product;
• P₁ is the final price of the product;
• Q₀ is the initial demand;
• Q₁ is the demand after the price change;
• PED is the price elasticity of demand.

Price elasticity of demand is almost always negative. It means that the relation 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 (P₀, P₁, Q₀ or Q₁). 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 with 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:

`PED = [ (Q₁ - Q₀) / (Q₁ + Q₀) ] / [ (P₁ - P₀) / (P₁ + P₀) ]`

`PED = [ (250 - 200) / (250 + 200) ] / [ (700 - 800) / (700 + 800) ]`

`PED = [ 50 / 450 ] / [ -100 / 1500 ]`

`PED = (50 * 1500) / (-100 * 450)`

`PED = 75,000 / -45,000 = -1.67`

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 initial and final state, using the equation

`R = P * Q`

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

`ΔR = R₁ - R₀ = P₁ * Q₁ - P₀ * Q₀`.

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

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

• PED is perfectly inelastic (PED = 0). In this case, change of price has no effect on 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 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 is equal to -100% (all revenue is lost).

Bogna Haponiuk

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