Elasticity in Microeconomics
Elasticity
Introduction to Elasticity
Definition: Elasticity measures the sensitivity of one variable to changes in another variable. It is commonly used in economics to assess the responsiveness of quantity demanded or supplied to price changes.
Overview of Lecture Topics
The lecture is based on Chapter 3 of Perloff's "Microeconomics" and will cover:
How the shapes of supply and demand curves influence economic shocks.
The sensitivity of quantity demanded in relation to price (price elasticity of demand).
The sensitivity of quantity supplied to price changes (price elasticity of supply).
Optional discussions on the effects of a sales tax.
How Shapes of Supply and Demand Curves Matter
The shape of supply and demand curves plays a crucial role in determining the impact of economic shocks on equilibrium price and quantity.
Example: The supply of avocados is influenced by two factors:
The price of avocados.
The price of fertilizer, which is a major input in avocado production.
Effect of Supply Shocks on Demand Curves
When the price of fertilizer increases, the avocado supply curve shifts leftward from S1 to S2.
The change in equilibrium price and quantity of avocados as a result of this supply shock depends on the characteristics of the demand curve.
Sensitivity of Quantity Demanded to Price
Price Elasticity of Demand
Definition: Price elasticity of demand (B5) is defined as the percentage change in quantity demanded in response to a given percentage change in price. It is assessed at a particular point on the demand curve.
Understanding the elasticity of demand is important for predicting the effects of price shocks in supply and demand models.
Formula for Price Elasticity of Demand
Formally expressed as:
B5 = rac{ ext{Percentage change in Quantity Demanded}}{ ext{Percentage change in Price}} = rac{ rac{ riangle Q}{Q}}{ rac{ riangle P}{P}} = rac{ riangle Q}{ riangle P} imes rac{P}{Q}Where:
B5: Price elasticity of demand
riangle Q: Change in Quantity Demanded
riangle P: Change in Price
Example of Price Elasticity of Demand
If a 1% increase in price leads to a 3% decrease in quantity demanded, the price elasticity of demand is:
B5 = - rac{3 ext{%}}{1 ext{%}} = -3The negative sign indicates an inverse relationship between price and quantity demanded, confirming the law of demand.
Categories of Price Elasticity of Demand
Relative Elasticity: |E| > 1 (demand is elastic)
Relative Inelasticity: 0 < |E| < 1 (demand is inelastic)
Unitary Elasticity: |E| = 1 (demand is unitary elastic)
Perfect Elasticity: |E| = ∞ (demand is perfectly elastic)
Perfect Inelasticity: |E| = 0 (demand is perfectly inelastic)
Variations in Elasticity Along Demand Curves
The elasticity of demand varies at different points along most demand curves, particularly downwards sloping linear demand curves.
Elasticities are constant along horizontal (perfectly elastic) and vertical (perfectly inelastic) demand curves.
Horizontal Demand Curve
In a perfectly elastic demand scenario (horizontal curve), consumers are prepared to purchase any quantity at a given price (p*).
A slight increase beyond p* leads demand to fall to zero, indicating extreme sensitivity to price changes.
Vertical Demand Curve
In a perfectly inelastic demand scenario (vertical curve), quantity demanded remains unchanged regardless of price changes, common for essential goods.
Application Example: Diabetes Treatment
The demand curve for insulin illustrates perfect inelasticity (vertical) below price p* and becomes perfectly elastic at p*, reflecting a maximum affordability limit for patients.
Demand Elasticity and Revenue Implications
Changes in equilibrium price influenced by demand elasticity affect total revenue:
With Elastic Demand: An increase in price results in a decrease in total revenue.
With Inelastic Demand: An increase in price causes total revenue to rise.
Visual Representation of Revenue Effects
Graphical representations help illustrate how equilibrium prices impact revenue under different elasticity scenarios.
Demand Elasticities Over Time
Elasticities may differ in the short run versus the long run:
For most goods, long-run elasticities tend to be larger due to greater substitution capabilities.
Certain goods, particularly easily storable or durable items, may exhibit the opposite trend.
Examples of Price Elasticities
Common elasticities observed in various goods:
Coffee: Short run -0.2, long run -0.33
Kitchen appliances: -0.63
Restaurant meals: -2.27
U.S. airline travel: -1.98
U.S. oil demand: Short run -0.06, long run -0.45
Income Elasticity of Demand
Definition
Income Elasticity: Measures how quantity demanded changes in response to income changes, defined as:
B5_{Y} = rac{ riangle Q/Q}{ riangle Y/Y}Example: If a 1% increase in income results in a 3% increase in quantity demanded, the income elasticity is:
B5_{Y} = rac{3 ext{%}}{1 ext{%}} = 3
(indicating a normal good).
Income Elasticity Cases
Positive income elasticity indicates normal goods (within the range 0 ≤ B5 ≤ 1).
Zero income elasticity suggests necessity goods.
Negative income significance characterizes inferior goods (when income increases, demand decreases).
Example of Income Elasticity
Example: Survey results indicate the income elasticity for children in a family is negative but close to zero, showing low sensitivity to changes in household income.
Cross-Price Elasticity of Demand
Definition
Cross-Price Elasticity: Defined as:
B5{X} = rac{ riangle Q/Q}{ riangle P{o}/P_{o}}Indicates how the quantity demanded of one good changes in response to the price change of another good.
Examples of Cross-Price Elasticity
Positive cross-price elasticity suggests substitutive relationships. For instance, an increase in the price of an iPhone leading to higher demand for Samsung phones.
Negative cross-price elasticity indicates complementary goods, such as an increase in petroleum price leading to decreased demand for cars.
Unrelated goods have a cross-price elasticity of zero.
Elasticity of Supply
Definition
Elasticity of Supply: Indicates how quantity supplied responds to price changes, formally represented as:
B7 = rac{ riangle Q/Q}{ riangle P/P}
Example on Elasticity of Supply
For a specific instance:
If a 1% increase in price of corn results in a 2% increase in quantity supplied, then:
B7 = rac{2 ext{%}}{1 ext{%}} = 2
Variations in Supply Elasticity
Advantages of supply elasticity change over time, affected by the capacity of firms to adapt to production adjustments, typically being greater in the long run than in the short run.
Optional Section: Effects of a Sales Tax
Fundamental Questions About Sales Tax
Effects on equilibrium price, quantity, and tax revenue.
The dependency of equilibrium price and quantity on tax collection methods.
The extent to which taxes are passed to consumers.
Comparative effects of ad valorem and specific taxes on prices, quantities, and revenues.
Types of Sales Taxes
Ad Valorem Tax: Tax is a percentage of the sale price (e.g., a % for every dollar spent).
Specific Tax (Unit Tax): Fixed monetary amount collected per unit sold.
Solved Problems and Examples
Demonstrated mathematical solutions for sales tax effects to equilibrium prices and quantities, investigating incidences across consumers and producers.
Conclusion
Elasticities of demand and supply serve as pivotal tools for understanding market dynamics, consumer behavior, and producer responses to price changes. This foundational knowledge will guide economic predictions and policy formulation.