Understanding Price Elasticity of Demand

Theoretical Extremes: Perfectly Elastic and Inelastic

In theoretical models, we encounter two extreme ends of the spectrum:

• Perfectly Elastic Demand: A situation where any increase in price, no matter how small, causes the quantity demanded to drop to zero.
• Perfectly Inelastic Demand: A situation where the quantity demanded remains constant regardless of any change in price.

Exam Tip: Remember that elasticity is about proportions. A $1 change on a $2 item is a massive 50% change, while a $1 change on a $100 item is a tiny 1% change. Elasticity accounts for this difference.

Elasticity vs. Slope

A common point of confusion for students is the difference between the slope of a demand curve and its elasticity.

On a standard linear demand curve, the slope is constant—the "steepness" of the line does not change. However, the elasticity changes at every point along the curve. This happens because elasticity is calculated using percentage changes. As the starting price increases, a fixed dollar change represents a smaller percentage change.

For example, consider a $1 price increase:

• Moving from $1 to $2 is a 100% increase.
• Moving from $10 to $11 is only a 10% increase.

Consequently, demand tends to be more elastic at higher price points and more inelastic at lower price points.

Measuring Change: The Arc Elasticity Formula

Because elasticity changes depending on whether you are moving "up" or "down" the demand curve, economists use the arc elasticity measure to find the average responsiveness over a specific range. This avoids the issue of directionality when calculating changes between two points.

The formula for arc elasticity is: $\text{Arc Elasticity} = \frac{\frac{Q_2 - Q_1}{(Q_2 + Q_1)/2}}{\frac{P_2 - P_1}{(P_2 + P_1)/2}}$

Worked Example

Suppose that quantity demanded falls from 60 to 40 when the price rises from $3 to $5.

1. Calculate the change in quantity: $40 - 60 = -20$
2. Calculate the average quantity: $(40 + 60) / 2 = 50$
3. Calculate the change in price: $5 - 3 = 2$
4. Calculate the average price: $(5 + 3) / 2 = 4$

Plugging these into the formula: $\text{Arc Elasticity} = \frac{-20 / 50}{2 / 4} = \frac{-0.4}{0.5} = -0.8$

Since the absolute value (0.8) is less than 1, demand in this interval is inelastic.

Practical Applications

Total Revenue (TR) and Pricing Strategy

Total Revenue is calculated as $\text{Price} \times \text{Quantity}$. Understanding elasticity allows a firm to predict how a price change will affect its bottom line:

• If demand is elastic: A reduction in price will increase TR; an increase in price will decrease TR.
• If demand is inelastic: A reduction in price will decrease TR; an increase in price will increase TR.
• If demand is unit elastic: Total revenue remains unchanged regardless of price changes.

Price Discrimination

Businesses often use elasticity to practice price discrimination, which involves charging different customers different prices for the same product.

• Customers with inelastic demand (those willing to pay more) are charged higher prices.
• Customers with elastic demand (those more sensitive to price) are charged lower prices.

Determinants of Elasticity

Several factors influence how elastic a good's demand will be:

1. Availability of Substitutes: The more close substitutes available, the higher the elasticity.
2. Budget Share: If a good represents a large share of a consumer's budget, demand is more elastic.
3. Time Horizon: Demand tends to be more elastic over longer time periods.

Tax Incidence

Elasticity also determines who bears the burden of a tax.

• If supply is more elastic than demand, consumers bear a larger share of the tax burden.
• If demand is more elastic than supply, producers bear a larger share of the burden.