# Price Elasticity of Demand

Price elasticity of demand, or demand elasticity, is a measure of how much the quantity demanded changes in response to price changes. In other words, it gauges consumers' sensitivity to price fluctuations. Specifically, it shows how much less consumers are willing to buy when the price increases or, conversely, how much more they consume when the price decreases. It is expressed as a percentage that indicates the proportional change in the quantity demanded resulting from a 1% change in price.

## How is Price Elasticity of Demand Calculated?

It is calculated as the percentage change in quantity demanded divided by the percentage change in price:

\[ \text{Price Elasticity of Demand} = \frac{\text{Percentage Change in Quantity Demanded}}{\text{Percentage Change in Price}} \]

Since the percentage change in a variable is the change in the variable (final value minus initial value), divided by the initial value, the price elasticity of demand can be written as follows:

\[ \text{Price Elasticity of Demand} = \frac{\left( \frac{\text{Final Quantity} - \text{Initial Quantity}}{\text{Initial Quantity}} \right)}{\left( \frac{\text{Final Price} - \text{Initial Price}}{\text{Initial Price}} \right)} \]

Where:

- \(\text{Final Quantity}\) is the quantity demanded after the price change.
- \(\text{Initial Quantity}\) is the quantity demanded before the price change.
- \(\text{Final Price}\) is the new price after the change.
- \(\text{Initial Price}\) is the original price before the change.

\[ E_d = \frac{\Delta Q / Q_i}{\Delta P / P_i} \]

Where:

- \(\Delta Q = \text{Final Quantity} - \text{Initial Quantity}\) is the absolute change in quantity demanded.
- \(\Delta P = \text{Final Price} - \text{Initial Price}\) is the absolute change in price.
- \(Q_i\) is the initial quantity.
- \(P_i\) is the initial price.

Next, we can simplify the formula by dividing the two fractions:

\[ E_d = \frac{\Delta Q}{Q_i} \div \frac{\Delta P}{P_i} \]

This is equivalent to multiplying the numerator by the inverse of the denominator:

\[ E_d = \frac{\Delta Q}{Q_i} \cdot \frac{P_i}{\Delta P} \]

Finally, generalizing for any quantity \( Q \) and price \( P \), we arrive at the final formula:

\[ E_d = \frac{\Delta Q}{\Delta P} \cdot \frac{P}{Q} \]

Where \( \frac{\Delta Q}{\Delta P} \) is the slope of the demand curve, and \( \frac{P}{Q} \) adjusts the relative change in terms of prices and quantities.

## Example of Calculating Price Elasticity of Demand

Suppose we have the following two points on a demand curve:

- Point 1: \( (P_1 = 10, Q_1 = 100) \)
- Point 2: \( (P_2 = 8, Q_2 = 120) \)

We want to calculate the price elasticity of demand between these two points.

First, calculate the absolute change in quantity demanded (\( \Delta Q \)) and the absolute change in price (\( \Delta P \)):

\[ \Delta Q = Q_2 - Q_1 = 120 - 100 = 20 \]

\[ \Delta P = P_2 - P_1 = 8 - 10 = -2 \]

Next, apply these values to the price elasticity formula:

\[ E_d = \frac{\Delta Q}{\Delta P} \cdot \frac{P_1}{Q_1} \]

Substituting the values obtained:

\[ E_d = \frac{20}{-2} \cdot \frac{10}{100} = -10 \cdot 0.1 = -1 \]

**Interpretation:**

The price elasticity of demand is \( E_d = -1 \), meaning that the demand is unitary elastic at this point on the curve. This indicates that a percentage change in price results in an equal but opposite percentage change in quantity demanded.

Since the quantity demanded of a good typically moves in the opposite direction of its price, the percentage change in quantity has the opposite sign to the percentage change in price. Therefore, price elasticity of demand is often expressed as a negative number, although sometimes it is given as an absolute value.

It is also worth noting that this formula is a simplified formula that assumes small changes in price and quantities; therefore, in most cases, other methods for calculating elasticity, such as the midpoint method, are more accurate.

## Determinants of Demand Elasticity

There is no universal rule or single determinant of the elasticity of a demand curve, as demand is influenced by economic, psychological, and social forces that shape consumer preferences. However, several factors particularly affect elasticity:

Goods with close substitutes tend to have higher elasticity because consumers can easily replace one good with another. The existence of a close substitute means that price increases lead to reduced purchases of the good in favor of the substitute. Conversely, when there are no close substitutes, demand tends to be more inelastic.Necessary goods tend to have lower elasticity compared to luxury goods. Consumers find it easier to forgo or replace a luxury item than a necessity in response to price changes.

Demand tends to be more elastic in the long run because consumers have more time to adjust their consumption to price changes.The definition of the market also affects elasticity. Narrowly defined markets tend to have more elastic demand than broadly defined markets. For example, the demand for fruit is likely to be less elastic than the demand for apples, as it is easier to find close substitutes for apples, such as pears, than for all fruits.

### Elastic, Inelastic, and Unitary Demand

When the price elasticity of demand is greater than one, the demand is elastic, meaning that the quantity demanded responds more than proportionally to price changes. A 1% change in price leads to a greater than 1% change in quantity demanded.

When the price elasticity of demand is less than one, the demand is inelastic, meaning that quantity demanded responds less than proportionally to price changes. When the elasticity of demand equals one, the demand is unitary elastic, meaning the percentage change in quantity demanded is exactly equal to the percentage change in price. To summarize:

**Demand elasticity** is classified as follows:

**Perfectly inelastic:**\(E_d = 0\) - The quantity demanded does not change in response to price changes. The demand curve is vertical.**Inelastic:**\(0 < E_d < 1\) - Quantity demanded changes less than proportionally to price changes. A price increase causes a smaller reduction in quantity demanded.**Unitary elasticity:**\(E_d = 1\) - Quantity demanded changes in the same proportion as the price change. A price increase leads to an exactly proportional decrease in quantity demanded.**Elastic:**\(E_d > 1\) - Quantity demanded changes more than proportionally to price changes. A price increase causes a larger reduction in quantity demanded.**Perfectly elastic:**\(E_d = \infty\) - Quantity demanded changes infinitely in response to a small price change. The demand curve is horizontal.