Elasticity Summary: Videos & Practice Problems

Understanding price elasticity of demand and supply is crucial for analyzing market behavior. The formula for price elasticity is given by ${\%}^2\left(\mathrm{Qd}\right)/{\%}^2\left(P\right)$. An elasticity greater than 1 indicates elastic demand, while less than 1 indicates inelastic demand. Additionally, income elasticity and cross-price elasticity help determine normal goods and substitutes. Understanding these concepts aids in maximizing revenue and recognizing market equilibrium.

Elasticity Summary

Understanding price elasticities of demand and supply is crucial for analyzing how changes in price affect the quantity demanded or supplied. The formula for calculating price elasticity of demand (PED) is given by:

$$ \text{PED} = \frac{\text{Percentage Change in Quantity Demanded}}{\text{Percentage Change in Price}} $$

Similarly, price elasticity of supply (PES) uses the same structure:

$$ \text{PES} = \frac{\text{Percentage Change in Quantity Supplied}}{\text{Percentage Change in Price}} $$

Both PED and PES yield positive values when using absolute values, which means that if the elasticity is greater than 1, the demand or supply is considered elastic. This indicates that consumers or producers are responsive to price changes. Conversely, if the elasticity is less than 1, it is inelastic, meaning that quantity demanded or supplied changes less than proportionately to price changes.

In addition to price elasticity, there are other important concepts such as income elasticity of demand and cross-price elasticity of demand. The formula for income elasticity of demand (YED) is:

$$ \text{YED} = \frac{\text{Percentage Change in Quantity Demanded}}{\text{Percentage Change in Income}} $$

For cross-price elasticity of demand (XED), the formula is:

$$ \text{XED} = \frac{\text{Percentage Change in Quantity Demanded of Good X}}{\text{Percentage Change in Price of Good Y}} $$

When analyzing YED and XED, the sign of the elasticity is significant. A positive YED indicates a normal good, while a negative YED suggests an inferior good. For XED, a positive value indicates that the goods are substitutes, while a negative value indicates that they are complements.

When using the midpoint method for calculating these elasticities, it is essential to check the signs of the quantities and prices involved after performing the calculations. This ensures accurate interpretation of the results.

Furthermore, the relationship between price elasticity and total revenue is vital. For a straight-line demand curve, the point where total revenue is maximized is known as unit elasticity. To the left of this point, demand is elastic, and to the right, it is inelastic. If the price increases and total revenue also increases, demand is inelastic, while if total revenue decreases, demand is elastic.

By consolidating these concepts, students can effectively prepare for assessments and apply their understanding of elasticity in real-world scenarios.

A linear, downward-sloping demand curve is

• A. Inelastic
• B. Unit Elastic
• C. Elastic
• D. Inelastic at some points, and elastic at others

Answer: (D)

An increase in the supply of a good will increase the total revenue producers receive if:

• A. The demand curve is inelastic
• B. The demand curve is elastic
• C. The supply curve is inelastic
• D. The supply curve is elastic

Answer: (B)

A life-saving machine without any close substitutes will tend to have:

• A. A small price elasticity of demand
• B. A large price elasticity of demand
• C. A small price elasticity of supply
• D. A large price elasticity of supply

Answer: (A)

Here’s what students ask on this topic:

What is the formula for calculating price elasticity of demand?

The formula for calculating price elasticity of demand (PED) is given by:

$\frac{\%∆Q{d}_{}}{\%∆P}$

Where $\%∆Q{d}_{}$ is the percentage change in quantity demanded and $\%∆P$ is the percentage change in price. This formula helps determine how sensitive the quantity demanded of a good is to a change in its price.

How do you interpret the value of price elasticity of demand?

The value of price elasticity of demand (PED) indicates how responsive the quantity demanded is to a change in price. If PED > 1, demand is elastic, meaning consumers are highly responsive to price changes. If PED < 1, demand is inelastic, meaning consumers are less responsive to price changes. If PED = 1, demand is unit elastic, meaning the percentage change in quantity demanded is equal to the percentage change in price.

What is the difference between price elasticity of demand and price elasticity of supply?

Price elasticity of demand (PED) measures how much the quantity demanded of a good responds to a change in its price, while price elasticity of supply (PES) measures how much the quantity supplied of a good responds to a change in its price. Both use similar formulas, but PED focuses on consumer behavior, and PES focuses on producer behavior.

How do you calculate income elasticity of demand?

Income elasticity of demand (YED) is calculated using the formula:

$\frac{\%∆Q{d}_{}}{\%∆I}$

Where $\%∆Q{d}_{}$ is the percentage change in quantity demanded and $\%∆I$ is the percentage change in income. This helps determine whether a good is a normal good (positive YED) or an inferior good (negative YED).

What is cross-price elasticity of demand and how is it calculated?

Cross-price elasticity of demand (XED) measures how the quantity demanded of one good responds to a change in the price of another good. It is calculated using the formula:

$\frac{\%∆Q{d}_X}{\%∆P{Y}_{}}$

Where $\%∆Q{d}_X$ is the percentage change in quantity demanded of good X and $\%∆P{Y}_{}$ is the percentage change in price of good Y. A positive XED indicates substitute goods, while a negative XED indicates complementary goods.