Unit 3: Elasticity

Unit 3: Elasticity

Introduction to Elasticity

• Elasticity measures the responsiveness of buyers and sellers to changes in economic variables like prices and income.

• It adds precision to the supply-and-demand model by quantifying the impact of changes on equilibrium prices and quantities.

Price Elasticity of Demand ($e_p$)

• Measures how much the quantity demanded ($Q_d$) of a good changes in response to a change in its price ($P$).

• Formula: $e_p = \frac{\% \text{ change in quantity demanded}}{\% \text{ change in price}}$

• Midpoint Method for Calculation:
  $e<em>p = \frac{(Q</em>2 - Q<em>1) / [(Q</em>1 + Q<em>2) / 2]}{(P</em>2 - P<em>1) / [(P</em>1 + P_2) / 2]}$

• The absolute value is typically used since price elasticity of demand is usually negative due to the inverse relationship between price and quantity demanded.

• Classification:

  • Elastic: e_p > 1 (quantity demanded responds more than proportionately to price change).

  • Inelastic: e_p < 1 (quantity demanded responds less than proportionately to price change).

  • Unit Elastic: $e_p = 1$ (quantity demanded responds one-for-one with price change).

  • Perfectly Inelastic: $e<em>p = 0$ (vertical demand curve; no change in $Q</em>d$ regardless of $P$).

  • Perfectly Elastic: $e<em>p$ = infinite (horizontal demand curve; infinite $Q</em>d$ at a specific price, zero otherwise).

• Determinants:

  • Availability of close substitutes: More substitutes = more elastic demand.

  • Necessities vs. Luxuries: Necessities are more inelastic; luxuries are more elastic.

  • Definition of the market: Narrowly defined markets have more elastic demand.

  • Time horizon: Demand is more elastic over longer periods.

  • Cost relative to buyer's income: Goods representing a small portion of income have inelastic demand.

• Total Revenue and Price Elasticity of Demand:

  • Total Revenue ($TR$) = Price ($P$) $\times$ Quantity Sold ($Q$).

  • Inelastic demand: Price and total revenue move in the same direction (e.g., $P\uparrow$ $\implies$ $TR\uparrow$).

  • Elastic demand: Price and total revenue move in opposite directions (e.g., $P\uparrow$ $\implies$ $TR\downarrow$).

  • Unit elastic demand: Total revenue remains constant when price changes.

Income Elasticity of Demand

• Measures how much the quantity demanded of a good responds to a change in consumers' income.

• Formula: $\text{Income elasticity} = \frac{\% \text{ change in quantity demanded}}{\% \text{ change in income}}$

• Sign matters:

  • Normal goods: Positive income elasticity (demand increases with income).

    • Necessities: Small positive elasticity (<1).

    • Luxuries: Large positive elasticity (>1).

  • Inferior goods: Negative income elasticity (demand decreases with income).

Cross-Price Elasticity of Demand

• Refers to the responsiveness of demand for one good (X) to changes in the price of another good (Y).

• Formula: $\text{Cross-price elasticity} = \frac{\% \text{ change in quantity demanded of good X}}{\% \text{ change in price of good Y}}$

• Sign matters:

  • Complementary goods: Negative cross-price elasticity (e.g., $P<em>Y\uparrow$ $\implies$ $Q</em>X\downarrow$).

  • Substitute goods: Positive cross-price elasticity (e.g., $P<em>Y\uparrow$ $\implies$ $Q</em>X\uparrow$).

Price Elasticity of Supply

• Measures how much the quantity supplied ($Q_s$) of a good responds to a change in its price ($P$).

• Formula: $\text{Price elasticity of supply} = \frac{\% \text{ change in quantity supplied}}{\% \text{ change in price}}$

• Classification (similar to demand):

  • Elastic (>1), Inelastic (<1), Unit Elastic ($=1$), Perfectly Inelastic ($=0$), Perfectly Elastic (infinite).

• Determinants:

  • Time horizon: Supply is more elastic in the long run.

  • Number of firms: More firms = more elastic supply.

  • Availability of other factors: Limited factors reduce elasticity.

  • Ease of factor substitution: Greater ease = more elastic supply.

  • Flexibility of sellers: More flexibility = more elastic supply.

  • Level of production: Elasticity may vary at different production capacities.

Applications of Elasticity

• Farming: If demand for basic foodstuffs is inelastic, increased productivity (increased supply) can lead to lower prices and reduced total revenue for farmers.

• Drug Interdiction: If demand for drugs is inelastic, increased interdiction (reduced supply) can raise prices, increase total expenditure on drugs, and potentially increase drug-related crime.

• Taxation (Tax Incidence):

  • A tax creates a wedge between the price buyers pay and sellers receive, reducing equilibrium quantity.

  • The burden of a tax falls more heavily on the side of the market that is less elastic.

    • Inelastic demand: Buyers bear more of the tax burden.

    • Inelastic supply: Sellers bear more of the tax burden.

  • Tax incidence does not depend on whether the tax is levied on buyers or sellers.

Unit 3: Elasticity

Introduction to Elasticity

Elasticity is a fundamental economic concept that measures how responsive buyers and sellers are to changes in economic variables, such as prices and income. It provides a more precise understanding of the supply-and-demand model by quantifying the impact of these changes on equilibrium prices and quantities.

Price Elasticity of Demand ($e_p$)

Price Elasticity of Demand ($e_p$) quantifies the extent to which the quantity demanded ($Q_d$) of a good alters in response to a change in its price ($P$). The formula for its calculation is $e_p = \frac{\% \text{ change in quantity demanded}}{\% \text{ change in price}}$. For practical computation, especially when dealing with two points, the midpoint method is often employed: $e_p = \frac{(Q<em>2 - Q</em>1) / [(Q<em>1 + Q</em>2) / 2]}{(P<em>2 - P</em>1) / [(P<em>1 + P</em>2) / 2]}$. Typically, the absolute value of $e_p$ is considered because the inverse relationship between price and quantity demanded results in a negative value. Goods are classified based on their price elasticity: demand is considered elastic if e_p > 1, meaning quantity demanded responds more than proportionately to a price change. It is inelastic if e_p < 1, indicating a less proportionate response. Unit elastic demand occurs when $e_p = 1$, signifying a proportionate change. In extreme cases, demand can be perfectly inelastic ($e_p = 0$), where quantity demanded remains constant regardless of price, or perfectly elastic ($e_p = \infty$), where even a minuscule price change leads to an infinite change in quantity demanded.

Income Elasticity of Demand

Income Elasticity of Demand measures the responsiveness of the quantity demanded of a good to changes in consumers' income. The formula used is $\text{Income elasticity} = \frac{\% \text{ change in quantity demanded}}{\% \text{ change in income}}$. The sign of this elasticity is crucial for classification. Normal goods exhibit a positive income elasticity, as demand for them increases with income. Within normal goods, necessities have a small positive elasticity (<1), while luxuries show a large positive elasticity (>1). Conversely, inferior goods have a negative income elasticity, meaning their demand decreases as consumer income rises.

Cross-Price Elasticity of Demand

Cross-Price Elasticity of Demand assesses how the demand for one good (X) changes in response to alterations in the price of another good (Y). Its formula is given by $\text{Cross-price elasticity} = \frac{\% \text{ change in quantity demanded of good X}}{\% \text{ change in price of good Y}}$. The sign of the cross-price elasticity indicates the relationship between the two goods. Complementary goods have a negative cross-price elasticity; for example, if the price of good Y increases ($P<em>Y\uparrow$), the quantity demanded of good X decreases ($Q</em>X\downarrow$). In contrast, substitute goods display a positive cross-price elasticity, meaning an increase in the price of good Y ($P<em>Y\uparrow$) leads to an increase in the quantity demanded of good X ($Q</em>X\uparrow$).

Price Elasticity of Supply

Price Elasticity of Supply measures how significantly the quantity supplied ($Q_s$) of a good reacts to a change in its price ($P$). It is calculated using the formula: $\text{Price elasticity of supply} = \frac{\% \text{ change in quantity supplied}}{\% \text{ change in price}}$. Similar to demand elasticity, supply can be elastic (>1), meaning quantity supplied responds more than proportionately to price changes; inelastic (<1), indicating a less proportionate response; or unit elastic ($=1$), where the response is proportionate. Supply can also be perfectly inelastic ($=0$), if quantity supplied does not change at all with price, or perfectly elastic ($=\infty$), if sellers will supply any quantity at a particular price but nothing at a slightly lower price. Several factors determine the price elasticity of supply, including the time horizon, where supply is generally more elastic in the long run; the number of firms in the market, with more firms leading to more elastic supply; the availability of other factors of production, as limited availability reduces elasticity; the ease of factor substitution, where greater ease allows for more elastic supply; the flexibility of sellers in adjusting production; and the level of production, as elasticity can change depending on how close firms are to their full capacity.

Applications of Elasticity

Elasticity has several important applications in economics. In farming, for instance, if the demand for basic foodstuffs is inelastic, an increase in agricultural productivity (which boosts supply) can result in significantly lower prices and, consequently, a decrease in the total revenue earned by farmers. Another application is in drug interdiction. If the demand for illegal drugs is inelastic, intensified interdiction efforts (which reduce supply) tend to drive up drug prices. This increase in prices can lead to higher total expenditure on drugs by consumers and potentially an increase in drug-related crime, as addicts seek more funds to finance their habit. Finally, taxation, specifically tax incidence, is heavily influenced by elasticity. A tax creates a "wedge" between the price buyers pay and the price sellers receive, thereby reducing the equilibrium quantity traded. The ultimate burden of this tax is not necessarily on the party it is levied upon but falls more heavily on the side of the market that is less elastic. Specifically, if demand is inelastic, buyers will bear a larger portion of the tax burden, as they are less responsive to price changes. Conversely, if supply is inelastic, sellers will bear more of the tax burden. It is important to note that tax incidence is determined by the relative elasticities of supply and demand, regardless of whether the tax is formally levied on buyers or sellers.