Economic Elasticities: Demand, Income, Cross-Price, and Supply

Elasticity: A Measure of Responsiveness

Elasticity is a fundamental concept in economics that quantifies the responsiveness of one economic variable to a change in another. It is often measured as the ratio of the percentage change in one variable to the percentage change in another variable, providing a unit-free measure.

Midpoint Formula for Elasticity

To calculate elasticity, especially between two points on a curve, the midpoint formula is often preferred. This method ensures that the elasticity value is the same whether you are moving from point A to point B or from point B to point A, by using the average of the initial and final values in the denominator.

Midpoint Calculation

When calculating percentage changes for elasticity, the standard formula is:
$\text{Percentage Change} = \frac{\text{Change}}{\text{Original Value}} \times 100\%$

However, using the midpoint formula, the 'original value' is instead replaced by the average of the two values in question. This is done to ensure consistency regardless of the direction of the change.

Midpoint Formula Equation

For quantity (Q) and price (P), the midpoint formula for percentage change is:
$\% \Delta Q = \frac{Q<em>2 - Q</em>1}{(Q<em>1 + Q</em>2)/2} \times 100\%$
$\% \Delta P = \frac{P<em>2 - P</em>1}{(P<em>1 + P</em>2)/2} \times 100\%$

Then, the elasticity using midpoints is calculated as:
$E = \frac{(Q<em>2 - Q</em>1)/((Q<em>1 + Q</em>2)/2)}{(P<em>2 - P</em>1)/((P<em>1 + P</em>2)/2)}$

Price Elasticity of Demand ($E_D$)

Definition

Price Elasticity of Demand ($E_D$) measures how much the quantity demanded of a good responds to a change in the price of that good. It indicates the degree of consumer responsiveness to price changes.

What it Measures

It measures the percentage change in the quantity demanded divided by the percentage change in price.

Equation

$E<em>D = \frac{\%\Delta Q</em>D}{\%\Delta P}$
Using the midpoint formula:
$E<em>D = \frac{(Q</em>2 - Q<em>1)/((Q</em>1 + Q<em>2)/2)}{(P</em>2 - P<em>1)/((P</em>1 + P_2)/2)}$
Note: By convention, price elasticity of demand is typically expressed as a positive number (ignoring the negative sign that arises because price and quantity demanded usually move in opposite directions).

Types of Elasticity

• Inelastic Demand: Occurs when the absolute value of $E<em>D$ is less than $1$ (|ED| < 1). This means that a percentage change in price leads to a smaller percentage change in quantity demanded. Consumers are not very responsive to price changes.
• Elastic Demand: Occurs when the absolute value of $E<em>D$ is greater than $1$ (|ED| > 1). This means that a percentage change in price leads to a larger percentage change in quantity demanded. Consumers are very responsive to price changes.
• Unit Elastic Demand: Occurs when the absolute value of $E<em>D$ is exactly $1$ ($|E</em>D| = 1$). This means that a percentage change in price leads to an equal percentage change in quantity demanded.
• Perfectly Inelastic Demand: Occurs when $E_D = 0$. Quantity demanded does not change at all, regardless of the price change.
• Perfectly Elastic Demand: Occurs when $E_D = \infty$. Any price increase causes quantity demanded to fall to zero, and even a tiny price decrease causes quantity demanded to become infinite.

Determinants of Price Elasticity of Demand

1. Existence of Substitutes: Goods with many close substitutes tend to have more elastic demand because consumers can easily switch to another product if the price increases. For example, if the price of Coca-Cola rises, consumers can easily switch to Pepsi.
2. Share of the Budget Spent on the Good: Goods that constitute a large portion of a consumer's budget tend to have more elastic demand. A $10\%$ increase in the price of a car (a large budget item) will likely have a greater impact on purchasing decisions than a $10\%$ increase in the price of a packet of gum (a small budget item).
3. Necessities or Luxuries: Necessities (e.g., basic food, medicine) tend to have more inelastic demand because consumers need them regardless of price. Luxuries (e.g., designer clothes, exotic vacations) tend to have more elastic demand because consumers can more easily forgo them if prices rise.
4. Broadness of Market Definition: The elasticity of demand depends on how broadly or narrowly a market is defined.
   • Broad Market: A broadly defined market, like