Elasticities of Demand and Supply

UNIT 3: ELASTICITIES OF DEMAND AND SUPPLY

Definition of Elasticity

Elasticity measures the responsiveness of quantity demanded (or supplied) to a change in price, income, etc.

Price Elasticity of Demand

The formula for price elasticity of demand can be expressed as:
$E_d = rac{ ext{Percentage change in quantity demanded}}{ ext{Percentage change in price}}$
This means that because demand curves slope downwards, the percentage changes in quantity and price have opposite signs, and their ratio is negative. The minus sign at the front merely converts the elasticity to a positive number, since elasticity is defined in absolute terms.

Range and Meaning of Elasticity

• Elasticity values can range between zero and infinity:
    - Inelastic Demand (E_d < 1): A given percentage change in price results in a smaller percentage change in quantity demanded.
    - Elastic Demand (E_d > 1): A given percentage change in price results in a larger percentage change in quantity demanded.
    - Perfectly Inelastic Demand (E_d = 0): A given percentage change in price leads to no change in quantity demanded; this is illustrated by a vertical demand curve.
    - Unit Elastic Demand (E_d = 1): A given percentage change in price results in an equal percentage change in quantity demanded.
    - Perfectly Elastic Demand (E_d = ext{infinity}): Any increase in price (no matter how small) leads to zero demand; represented by a horizontal demand curve where consumers are willing to buy any quantity only at that price.

Description of Elasticity Across the Demand Curve

• At the top of the demand curve:
    - The percentage change in quantity is large (because the quantity level is low), while the percentage change in price is small (since the price level is high).
    - Thus, demand is relatively elastic at this position.

• At the bottom of the demand curve:
    - The same change in quantity demanded is now a smaller percentage change (with a high quantity), whereas the change in price represents a large percentage change (with a low price).
    - Hence, demand appears to be relatively inelastic at this position.

Elasticity Along a Linear Demand Curve

Elasticity continuously diminishes along a linear demand curve. At high prices (top of the curve), demand is highly elastic; conversely, at low prices (bottom of the curve), it becomes highly inelastic. The shifting from elastic to inelastic demand occurs at the point where demand is unit elastic.

Calculation of Price Elasticity (Mid-point Formula)

To measure the elasticity of demand in an interval from a price of $4 to a price of $5, the percentage change in price is calculated:

• If increasing from $4 to $5, price increases by 25%.

• Conversely, if moving from $5 down to $4, price decreases by 20%.

• Arc elasticity avoids ambiguity by using the midpoint of the interval to calculate elasticity mathematically:
  $E_d = rac{(Q_2 - Q_1) / ((Q_1 + Q_2)/2)}{(P_2 - P_1) / ((P_1 + P_2)/2)}$

Example Calculation

Assuming quantity demanded decreases from 60 to 40 when the price rises from $3 to $5:

• This situation results in:
  $E_d = rac{(40 - 60) / ((60 + 40)/2)}{(5 - 3) / ((3 + 5)/2)}$
  Thus, in this interval, demand is inelastic since E_d < 1.

Elasticity and Total Revenue

Total revenue can be calculated as:
$ext{Total Revenue} = ext{Price} imes ext{Quantity}$

• When observing a downward-sloping demand curve and considering how total revenue changes with price adjustments:
    - If price falls:
      - Elastic Demand: Total revenue increases.
      - Unit Elastic Demand: Total revenue remains unchanged.
      - Inelastic Demand: Total revenue decreases.
    - If price rises:
      - Elastic Demand: Total revenue decreases.
      - Unit Elastic Demand: Total revenue remains unchanged.
      - Inelastic Demand: Total revenue increases.

Summary Table of Revenue Change with Price Elasticity

Total Revenue In Relation to Demand Elasticity

• Total revenue will increase with quantity, while total revenue decreases when quantity increases in the inelastic demand curve region. Revenue reaches its maximum at the point where demand is unit elastic.

Cross-price Elasticity of Demand

Cross-price elasticity measures the percentage change in the quantity demanded of good X relative to the percentage change in the price of good Y, all else being equal. The formula for calculating cross-price elasticity is:
$ext{Cross-price elasticity} = rac{ ext{Percentage change in quantity demanded of good X}}{ ext{Percentage change in price of good Y}}$

• Cross-price elasticity can yield negative or positive results:
    - If ext{E}{xy} > 0, goods are substitutes (an increase in the price of Y results in a rise in the quantity demanded of X).   - If ext{E}{xy} < 0, goods are complements.
    - The greater the absolute value of $ext{E}_{xy}$, the stronger the substitutability or complementarity between the goods.

Income Elasticity of Demand

Income elasticity measures the percentage change in quantity demanded concerning the percentage change in consumers' income, ceteris paribus.

• It can take positive or negative values:
    - A positive income elasticity indicates a normal good (quantity demanded rises with an increase in income).
    - A negative income elasticity indicates an inferior good (quantity demanded falls as income increases).

• Income elasticity interprets as follows:
    - If 0 < ext{E}_I < 1: Goods are necessities; quantity demanded rises by a smaller percentage than income.   - If ext{E}_I > 1: Goods are luxuries; quantity demanded rises by a larger percentage than income.

Summary Table of Income Elasticity

• As income grows, consumers spend a larger share on luxury goods, ensuring that a 10% increase in income leads to more than a 10% increase in spending on luxury goods. Conversely, a lesser share of income is devoted to necessities as income rises. All luxury goods are classified as normal goods, while inferior goods correspond to necessities. Normal goods may be either categorized as necessities or luxuries.

UNIT 4: Price Elasticity of Supply

The price elasticity of supply can be described as follows: A perfectly inelastic supply curve is illustrated as vertical, indicating a price elasticity of supply equal to zero.

Characteristics of Supply Curves

• For certain prices, the supply curve can become perfectly inelastic, especially for goods where only a limited quantity is available (e.g., highly perishable commodities that must be sold quickly). A practical example includes a fisherman with no storage facilities, who must sell his catch by the end of the day at whatever price is available.

• Conversely, a perfectly elastic supply curve appears horizontal. This is common in markets with numerous buyers and sellers, where individual buyers or sellers cannot influence the market price (they are price-takers).

Short Run vs Long Run in Supply Elasticity

• The short run is referred to as the time period during which capital is fixed, meaning only one factor is variable.

• In the long run, all inputs are flexible, and firms can adjust their capital. Supply elasticity is typically greater in the long run than in the short run. For example:
    - In the short run, a demand surge for personal computers might lead to increased employment, overtime hours, and added shifts in computer manufacturing plants.
    - In the long run, however, higher prices can stimulate a much larger output expansion as new factories are established.