The Elasticity of Demand and Supply - Economics 1101: Principles of Microeconomics

The Elasticity of Demand and Supply

The Elasticity of Demand

• Price Elasticity of Demand ($E_d$)

  • Definition: A measure of the responsiveness of quantity demanded to a change in the price of that good.

  • It quantifies buyers' sensitivity to a price change.

  • It represents the percentage by which quantity demanded will change if the price of the good changes by $1\%$.

  • Formula: $E_d = \frac{\% \text{Change in Quantity Demanded (Qd)}}{\% \text{Change in Price (P)}}$

  • Magnitude: When computing, the absolute value is crucial for interpreting elasticity, as the Law of Demand typically results in a negative value.

Computing Price Elasticity of Demand: Midpoint Method (ARC Elasticity)

• This method is used to calculate elasticity between two points $(Q<em>1, P</em>1)$ and $(Q<em>2, P</em>2)$ to avoid different elasticity values depending on the direction of the price change.

• Percentage Change in Quantity Demanded: $\frac{Q<em>2 - Q</em>1}{(Q<em>2 + Q</em>1) / 2} \times 100\%$

• Percentage Change in Price: $\frac{P<em>2 - P</em>1}{(P<em>2 + P</em>1) / 2} \times 100\%$

Elasticity Problem Example

• Scenario: The price of a good rises from $\$8$ to $\$12$, and the quantity demanded falls from $110$ to $90$ units.

• Given: $P<em>1 = \$8$, $P</em>2 = \$12$, $Q<em>1 = 110$, $Q</em>2 = 90$

• Step 1: Calculate Percentage Change in Quantity Demanded

  • $\% \Delta Q_d = \frac{90 - 110}{(90 + 110) / 2} = \frac{-20}{200 / 2} = \frac{-20}{100} = -0.20 \text{ or } -20\%$

• Step 2: Calculate Percentage Change in Price

  • $\% \Delta P = \frac{12 - 8}{(12 + 8) / 2} = \frac{4}{20 / 2} = \frac{4}{10} = 0.40 \text{ or } 40\%$

• Step 3: Calculate Price Elasticity of Demand

  • $E_d = \frac{-20\%}{40\%} = -0.5$

• Interpretation: Taking the absolute value, $E_d = 0.5$. This indicates inelastic demand.

Classification of Demand Elasticity

• Demand is Elastic: Price elasticity of demand Ed > 1 . (Example: if price increases by $1\%$ and Qd decreases by $2\%$, then $E</em>d = 2$)

• Demand is Inelastic: Price elasticity of demand Ed < 1 . (Example: if price increases by $1\%$ and Qd decreases by $0.50\%$, then $E</em>d = 0.50$)

• Demand has Unit Elasticity: Price elasticity of demand $E<em>d = 1$. (Example: if price increases by $1\%$ and Qd decreases by $1\%$, then $E</em>d = 1$)

• Demand is Perfectly Inelastic: Price elasticity of demand $E_d = 0$. The demand curve is vertical, meaning quantity demanded does not change, regardless of price changes. Consumers buy a fixed quantity.

• Demand is Perfectly Elastic: Price elasticity of demand $E_d = \infty$. The demand curve is horizontal, meaning consumers will buy any amount at a specific price, but none at a higher price, and unlimited amounts at a lower price. A tiny change in price leads to an enormous change in demand.

Determinants of Price Elasticity of Demand

• Availability of Close Substitutes

  • Goods with close substitutes tend to have more elastic demand (e.g., butter vs. margarine).

• Necessities versus Luxuries

  • Necessities: Tend to have inelastic demand (e.g., medicine, basic food).

  • Luxuries: Tend to have elastic demand (e.g., sports cars, yachts).

• Definition of the Market

  • Narrowly defined markets: Have more elastic demand (e.g., blue running shoes are more elastic than shoes in general).

  • Broadly defined markets: Have more inelastic demand (e.g., food is more inelastic than apples).

• Time Horizon

  • Demand is generally more elastic over longer time horizons as consumers have more time to adapt to price changes or find substitutes.

Variety of Demand Curves and Elasticity

• The flatter the demand curve, the greater the price elasticity of demand.

• For a linear demand curve, the slope is constant, but elasticity varies along the curve.

  • Near the top (high price, small quantity), the elasticity is large (elastic).

  • As we move down the curve (low price, high quantity), the elasticity becomes smaller (inelastic).

The Elasticity of Demand and Total Revenue (TR)

• Total Revenue (TR): The amount paid by buyers and received by sellers of a good. It is calculated as Price (P) multiplied by Quantity Sold (Q), i.e., $TR = P \times Q$.

• Impact of Price Changes on Total Revenue based on Elasticity

  • Inelastic Demand ( E_d < 1 )

    • If Price (P) increases, Total Revenue (TR) also increases.

    • If Price (P) decreases, Total Revenue (TR) also decreases.

    • (P and TR move in the same direction).

  • Elastic Demand ( E_d > 1 )

    • If Price (P) increases, Total Revenue (TR) decreases.

    • If Price (P) decreases, Total Revenue (TR) increases.

    • (P and TR move in opposite directions).

  • Unit Elastic Demand ($E_d = 1$)

    • Total Revenue (TR) remains constant when the price changes.

The Income Elasticity of Demand

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

• Formula: $E_y = \frac{\% \text{Change in Quantity Demanded}}{\% \text{Change in Income}}$

  • The midpoint formula can also be applied.

• Interpretation by Value

  • Normal Goods: Have a positive income elasticity ( E_y > 0 ).

    • Necessities: Have smaller positive income elasticities (typically between $0$ and $1$).

    • Luxuries: Have large positive income elasticities (typically greater than $1$).

  • Inferior Goods: Have a negative income elasticity ( E_y < 0 ). As income rises, the quantity demanded of these goods falls.

Cross-Price Elasticity of Demand

• Definition: Measures how much the quantity demanded of one good responds to a change in the price of another good.

• Formula: $E_{xy} = \frac{\% \text{Change in Quantity Demanded of Good X}}{\% \text{Change in Price of Good Y}}$

• Interpretation by Value

  • Substitutes: If the cross-price elasticity between two products (A and B) is positive ( E_{xy} > 0 ), they are substitutes. An increase in the price of one good leads to an increase in the demand for the other.

  • Complements: If the cross-price elasticity is negative ( E_{xy} < 0 ), they are complements. An increase in the price of one good leads to a decrease in the demand for the other.

  • Unrelated Goods: If the cross-price elasticity is zero ($E_{xy} = 0$), the goods are not related.

The Elasticity of Supply

• Price Elasticity of Supply ($E_s$)

  • Definition: Measures how much the quantity supplied of a good responds to a change in the price of that good.

  • It depends on the flexibility of sellers to change the amount of the good they produce.

  • Formula: $E_s = \frac{\% \text{Change in Quantity Supplied}}{\% \text{Change in Price}}$

  • Always Positive: For a typical upward-sloping supply curve, price and quantity supplied move in the same direction, so the elasticity of supply is always positive.

  • The midpoint method can be used for calculation between two points $(Q<em>1, P</em>1)$ and $(Q<em>2, P</em>2)$.

Determinant of Price Elasticity of Supply

• Time Period

  • Supply is generally more elastic in the long run because producers have more time to adjust their production capacity, acquire new resources, or enter/exit the market.

  • Supply is generally less elastic (more inelastic) in the short run due to fixed capacities and limited immediate adjustments.

Classification of Supply Elasticity

• Supply is Elastic: Price elasticity of supply E_s > 1 . Quantity supplied responds substantially to price changes.

• Supply is Inelastic: Price elasticity of supply E_s < 1 . Quantity supplied responds only slightly to price changes.

• Supply is Unit Elastic: Price elasticity of supply $E_s = 1$.

• Supply is Perfectly Inelastic: Price elasticity of supply $E_s = 0$. The supply curve is vertical; quantity supplied is fixed regardless of price changes.

• Supply is Perfectly Elastic: Price elasticity of supply $E_s = \infty$. The supply curve is horizontal; producers will supply any quantity at a specific price, but none below that price.

Variety of Supply Curves and Elasticity

• The flatter the supply curve, the greater the price elasticity of supply.

• For a typical supply curve, elasticity can vary:

  • At points with low price and low quantity: Supply tends to be elastic because firms have unused production capacity and can easily increase output.

  • At points with high price and high quantity: Supply tends to be inelastic as firms approach their maximum production capacity, making it harder to increase output further.

Applications of Elasticity

1. Can Good News for Farming Be Bad News for Farmers?

• This is a paradox in public policy, often leading to policies that induce farmers not to plant crops.

• Example: A bountiful harvest (good news for farming) shifts the supply curve of agricultural products to the right. If the demand for these products is inelastic (which is often the case for basic food items), the large increase in quantity supplied combined with inelastic demand will lead to a significant drop in price, causing total revenue for farmers to decrease. So, what seems like good news (more crops) can result in lower income for farmers.

2. Why Did OPEC Fail to Keep the Price of Oil High?

• OPEC members attempted to increase oil prices through supply reductions in $1973 - 1974$ and $1979 - 1981$.

• Short-Run Impact: In the short run, both the supply and demand for oil are relatively inelastic.

  • A decrease in supply (shift left of $S<em>1$ to $S</em>2$) leads to a large increase in price and only a small decrease in quantity.

• Long-Run Impact: In the long run, both the supply and demand for oil are relatively elastic.

  • Consumers find more fuel-efficient cars, alternative energy sources, and change consumption habits (elastic demand).

  • Non-OPEC producers increase exploration and production (elastic supply).

  • Therefore, in the long run, the same decrease in supply leads to a smaller increase in price and a larger decrease in quantity traded.

  • OPEC's strategy was unsustainable in the long run due to the increased elasticity of demand and supply.

3. Does Drug Interdiction Increase or Decrease Drug-Related Crime?

• This application examines the effectiveness of two policies: drug interdiction and drug education.

• Policy: Drug Interdiction (e.g., increased federal agents against drugs)

  • Effect: Reduces the supply of illegal drugs (supply curve shifts left from $S<em>1$ to $S</em>2$).

  • Result: Higher price (from $P<em>1$ to $P</em>2$) and lower quantity (from $Q<em>1$ to $Q</em>2$).

  • Impact on Crime: Demand for illegal drugs is often highly inelastic (addiction makes users relatively insensitive to price changes).

    • When demand is inelastic, a higher price due to reduced supply leads to higher total revenue for drug dealers (as discussed in Section 2).

    • This higher total revenue means drug users have to spend more money, potentially leading to an increase in drug-related crime to finance their habit.

• Policy: Drug Education

  • Effect: Reduces the demand for illegal drugs (demand curve shifts left from $D<em>1$ to $D</em>2$).

  • Result: Lower quantity (from $Q<em>1$ to $Q</em>2$) and lower price (from $P<em>1$ to $P</em>2$).

  • Impact on Crime: When drug demand is reduced, both the price and quantity of drugs decrease. This leads to lower total revenue for drug dealers, and less need for users to commit crimes to fund their habit, thus potentially reducing drug-related crime.