Elasticity

As the price of sweetened beverages increases, the quantity demanded typically decreases.
To measure how much quantity changes in response to price, we focus on elasticity, which is defined as the measure of how much one economic variable responds to changes in another based on percentage changes.

The price elasticity of demand measures the responsiveness of the quantity demanded when price changes.
The formula for price elasticity of demand is:
\text{Price Elasticity of Demand} = \frac{\text{Percentage Change in Quantity Demanded}}{\text{Percentage Change in Price}}
The slope of the demand curve is related to the price elasticity of demand but is not the same. Because price and quantity change in opposite directions on the demand curve, the price elasticity of demand is expressed as a negative number.
We often refer to “more negative” elasticities as “larger” or “higher.”

Elastic Demand: When price elasticity of demand is larger in absolute value than 1 (i.e., elastic demand means that a price change leads to a proportionally larger change in quantity demanded).
Inelastic Demand: When price elasticity of demand is less than 1 in absolute value (implying quantity demanded changes little as price changes).
Unit Elastic Demand: When price elasticity of demand equals -1 (indicating that a percentage change in price results in an equivalent percentage change in quantity).

Consider the impact of cutting the price of a beverage from $1.50 to $1.35:
- Scenario A: Quantity sold increases from 1,000 to 1,200 (elastic demand).
- Scenario B: Quantity sold increases from 1,000 to only 1,050 (inelastic demand).

Calculating percentage changes can lead to confusion due to their non-symmetrical nature when moving between two points.
Example: From point A to B, quantity changes from 1,000 to 1,200 (20% change), but going back from B to A reflects a 16.7% decrease.
Thus, to standardize measurement, the midpoint formula for percentage changes is employed:
\text{Percentage Change} = \frac{Q2 - Q1}{(Q2 + Q1) / 2}

The price elasticity of demand using the midpoint formula is:
\text{Price Elasticity of Demand} = \frac{(Q2 - Q1) / ((Q2 + Q1) / 2)}{(P2 - P1) / ((P2 + P1) / 2)}

Situation: Price of Coca-Cola dropped from $1.50 to $1.30, increasing sales from 2,000 to 2,500 gallons per day.
- Average Quantity: \frac{2,000 + 2,500}{2} = 2,250
- Average Price: \frac{1.50 + 1.30}{2} = 1.40
Percentage Change Calculations:
- Percentage change in quantity demanded: \frac{2500 - 2000}{2250} \times 100 = 22.22\%
- Percentage change in price: \frac{1.30 - 1.50}{1.40} \times 100 = -14.29\%
Price Elasticity Calculation:
\text{Price Elasticity of Demand} = \frac{22.22\%}{-14.29\%} = -1.56
Since this value is greater than 1 in absolute terms, demand is price elastic.
If quantity had only increased to 2,100 while price remained the same, the price elasticity calculation would result in a value less than 1 (inelastic demand).

Elasticity comparisons can be made:
- A vertical demand curve signifies perfectly inelastic demand where quantity demanded does not change with price changes (elasticity = 0).
- A horizontal demand curve signifies perfectly elastic demand where quantity demanded is infinitely responsive to price changes (elasticity = ).
- A case of unit elastic demand occurs when a percentage price change leads to an equivalent percentage quantity change.

Total Revenue (TR) is calculated as the product of the price per unit and the quantity sold:
ext{Total Revenue} = ext{Price} \times ext{Quantity}
The pricing strategy should consider how price elasticity will impact total revenue:
- For inelastic demand: Lowering price leads to a decrease in total revenue.
- For elastic demand: Lowering price results in an increase in total revenue.

If demand is inelastic, decreasing price lowers revenue as few customers are gained relative to the revenue lost.
If demand is elastic, decreasing price raises revenue due to substantially increased customer acquisition.

Graphs may illustrate the effect of price cuts on revenue transitions, affirming elasticity types (e.g., elastic vs inelastic demand)

Cross-Price Elasticity of Demand: Measures the responsiveness of the quantity demanded of one good as the price of another good changes.
- Cross-price elasticity can be positive—indicating substitute goods, negative—indicating complementary goods, or zero—indicating unrelated goods.
Income Elasticity of Demand: The measure of responsiveness of quantity demanded to changes in income equations: \text{Income Elasticity of Demand} = \frac{\text{Percentage Change in Quantity Demanded}}{\text{Percentage Change in Income}}
- Normal goods reflect positive income elasticity, whereas inferior goods reflect negative.

Price Elasticity of Supply measures responsiveness of quantity supplied to change in price given by:
\text{Price Elasticity of Supply} = \frac{\text{Percentage Change in Quantity Supplied}}{\text{Percentage Change in Price}}
Determinants include firm capacity to change production levels with price increases over varying time scales.

Tables summarizing the values for price elasticities for demand, supply, and income.
Includes visual representations with classifications for goods based on elasticities.

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