Week 3 Lecture: Equilibrium and Elasticity

Market Equilibrium and the Law of Supply and Demand

• Definition of Equilibrium: A situation in which supply and demand are in balance. At this point, there is no upward or downward pressure on the market price.

• Equilibrium Price:   - This is the price that sets the quantity demanded ($Q_d$) equal to the quantity supplied ($Q_s$).   - It is frequently referred to as the market-clearing price because everyone in the market has been satisfied: buyers have bought all they want to buy, and sellers have sold all they want to sell.   - Graphically, it is identified as the price at the point where the supply and demand curves intersect.

• Equilibrium Quantity:   - This represents both the quantity demanded and the quantity supplied at the equilibrium price.   - Graphically, it is the quantity coordinate at the intersection of the supply and demand curves.

• Markets Not in Equilibrium:   - Surplus (Excess Supply): Occurs when the market price is higher than the equilibrium price (P > P^).     - In this state, quantity supplied ($Q_s$) is larger than quantity demanded ($Q_d$).     - Suppliers face a buildup of unsold stock and respond by lowering prices to increase sales, moving the market back toward equilibrium.   - Shortage (Excess Demand): Occurs when the market price is lower than the equilibrium price (P < P^).     - In this state, quantity supplied ($Q_s$) is smaller than quantity demanded ($Q_d$).     - There are too many buyers chasing too few goods; suppliers respond by raising prices, moving the market back toward equilibrium.

• The Law of Supply and Demand: This principle states that the price of any good adjusts to bring the supply and demand for that good into balance.   - Note: This is distinct from the individual "Law of Supply" and "Law of Demand."   - Perfect competition ensures that the actions of buyers and sellers naturally move the price toward equilibrium.   - While markets may experience temporary surpluses or shortages (frictions), these are eventually eliminated by market forces.

Comparative Statics: Analyzing Changes in Equilibrium

• Terminology:   - Exogenous Event/Change: An external event that occurs outside of the model which causes a shift in the demand curve, the supply curve, or both.   - Endogenous Change: The subsequent change in the equilibrium price and quantity within the model resulting from the shift.   - Comparative Statics: The methodology used to analyze how an initial equilibrium compares to a new equilibrium following an exogenous event.

• The Three-Step Process for Analysis:   1. Decide whether the exogenous event shifts the supply curve, the demand curve, or both.   2. Decide in which direction the curve(s) shift (left for decrease, right for increase).   3. Use a supply-and-demand diagram to visualize how the shift changes the equilibrium price and quantity.

• Analysis of Single Shifts:   - Increase in Demand (e.g., Hot Summer affecting Ice Cream):     - The hot weather is an exogenous event that shifts the demand curve to the right ($D \rightarrow$).     - Result: A higher equilibrium price and a higher equilibrium quantity.   - Decrease in Supply (e.g., Bushfire affecting Ice Cream Factories):     - The fire is an exogenous event that shifts the supply curve to the left ($S \leftarrow$).     - Result: A higher equilibrium price and a lower equilibrium quantity.

• Simultaneous Shifts in Supply and Demand:   - If both a hot summer (demand increases) and a bushfire (supply decreases) occur, the equilibrium price will definitely increase. However, the change in equilibrium quantity is ambiguous and depends on the relative magnitude of the shifts.

• Comprehensive Summary of Equilibrium Changes:   - No Change in Demand + No Change in Supply: Price and Quantity remain the same.   - No Change in Demand + Increase in Supply: Price falls, Quantity rises.   - No Change in Demand + Decrease in Supply: Price rises, Quantity falls.   - Increase in Demand + No Change in Supply: Price rises, Quantity rises.   - Increase in Demand + Increase in Supply: Price is ambiguous, Quantity rises.   - Increase in Demand + Decrease in Supply: Price rises, Quantity is ambiguous.   - Decrease in Demand + No Change in Supply: Price falls, Quantity falls.   - Decrease in Demand + Increase in Supply: Price falls, Quantity is ambiguous.   - Decrease in Demand + Decrease in Supply: Price is ambiguous, Quantity falls.

Free Markets and the Rationing Function of Prices

• Free Market: A market environment where prices are allowed to adjust freely based on the forces of demand and supply without government intervention.

• Prices as a Mechanism: In a free market, prices serve as the primary mechanism for allocating scarce resources.

• The Rationing Function:   - The market mechanism ensures that any buyer willing and able to pay the equilibrium price can obtain the good.   - Simultaneously, any seller willing and able to produce the good at that price can sell it.

Price Elasticity of Demand (PED)

• Definition: A measure of how sensitive consumers are to a change in price. It quantifies the responsiveness of quantity demanded to a change in one of its determinants.

• Calculation: The price elasticity of demand is the percentage change in quantity demanded divided by the percentage change in price.   - $PED = \frac{\% \Delta Q_d}{\% \Delta P}$   - Because of the Law of Demand (inverse relationship), the result is typically negative; however, the minus sign is usually ignored, and the absolute value is used for interpretation.

• Mid-point Formula Example (Slide 24):   - Milk: Price increases from $1\,dm^3$ to $3\,dm^3$ ($+100\%$ change via midpoint). Demand decreases from $7\,dm^3$ to $3\,dm^3$ ($-80\%$ change via midpoint).     - $PED = \frac{-80\%}{100\%} = -0.8$ (which is rounded/interpreted as $0.8$).   - Cereals: Price increases from $1\,kg$ to $3\,kg$ ($+100\%$ change). Demand decreases from $3\,kg$ to $1\,kg$ ($-100\%$ change).     - $PED = \frac{-100\%}{100\%} = -1$.   - Conclusion: The demand for cereals is more price elastic than the demand for milk because its absolute value is higher.

• Classification of Elasticity:   - Elastic (PED > 1): Buyers respond strongly. The percentage change in quantity is larger than the percentage change in price.   - Inelastic (PED < 1): Buyers do not respond strongly. The percentage change in quantity is smaller than the percentage change in price.   - Unitary Elastic ($PED = 1$): The percentage change in quantity equals the percentage change in price.   - Perfectly Inelastic ($PED = 0$): The demand curve is vertical; quantity demanded remains the same regardless of price.   - Perfectly Elastic ($PED = \infty$): The demand curve is horizontal; at a specific price, consumers buy any quantity, but above that price, demand drops to zero.

• Determinants of PED:   - Availability of Close Substitutes: Elasticity is higher when substitutes are available (e.g., specific brands of ice cream).   - Necessities vs. Luxuries: Elasticity is higher for luxuries (sports cars) and lower for necessities (electricity).   - Scope of the Market: Narrowly defined markets (e.g., apples) have more elastic demand than broadly defined markets (e.g., food).   - Time Horizon: Demand is more elastic over longer time periods as consumers have more time to adjust behavior (e.g., petrol consumption).

• Geometry and Slope: As a rule of thumb, the flatter the demand curve, the greater the price elasticity; the steeper the curve, the lower the elasticity. Elasticity varies along a linear demand curve: it is higher at high prices/low quantities and lower at low prices/high quantities.

Total Revenue (TR) and Elasticity

• Formula: $TR = P \times Q$. This represents the amount received by sellers and paid by buyers.

• Relationship with Elasticity:   - Inelastic Demand: Price and Total Revenue move in the same direction. If price increases, TR increases because the decrease in quantity is proportionally smaller than the price rise.   - Elastic Demand: Price and Total Revenue move in opposite directions. If price increases, TR decreases because the decrease in quantity is proportionally larger than the price rise.   - Unitary Elasticity: A change in price results in a proportional change in quantity, leaving TR unaffected.

• Application: Illegal Drugs and Crime:   - Demand for illegal drugs is typically inelastic.   - Policy 1: Law Enforcement (Supply Reduction): Decreasing supply raises the price. Since demand is inelastic, the price rise is larger than the quantity fall, causing total expenditure to increase, potentially increasing drug-related crime to fund the higher costs.   - Policy 2: Education/Treatment (Demand Reduction): Decreasing demand lowers both price and quantity. This leads to a decrease in total expenditure, likely reducing drug-related crime.

Other Types of Elasticity

• Income Elasticity of Demand: Measures responsiveness of $Q_d$ to a change in consumer income.   - $\text{Income Elasticity} = \frac{\% \Delta Q_d}{\% \Delta \text{Income}}$   - Normal Goods: Positive elasticity (> 0). Includes necessities (inelastic, < 1) and luxuries (elastic, > 1).   - Inferior Goods: Negative elasticity (< 0).

• Cross-Price Elasticity of Demand: Measures responsiveness of $Q_d$ of one good to the price change of another good.   - $\text{Cross-Price Elasticity} = \frac{\% \Delta Q_{d1}}{\% \Delta P_2}$   - Substitutes: Positive elasticity.   - Complements: Negative elasticity.

• Price Elasticity of Supply (PES): Measures responsiveness of $Q_s$ to a change in price.   - $PES = \frac{\% \Delta Q_s}{\% \Delta P}$   - Determined by the flexibility of suppliers to change production and the time period (supply is more elastic over the long run).   - Inelastic supply examples: Picasso paintings, beachfront land.   - Elastic supply examples: Manufactured goods like books or cars.

Questions & Discussion

• Pingo Session 5718 - Problem 1: In 2022, Australia experienced floods damaging farmland, and the prices of diesel and fertilizer rose due to the war in Ukraine. How do these events affect the lettuce market?   - Answer: These are supply-side shocks. Both the damage to farmland (resource destruction) and the increase in input costs (diesel/fertilizer) shift the market supply curve to the left ($S \leftarrow$). (Option C selected).

• Pingo Session 5718 - Problem 2: According to the S&D model, what is the resulting change in equilibrium for the lettuce market based on the previous events?   - Answer: A leftward shift in supply leads to an increase in equilibrium price and a decrease in equilibrium quantity ($P \uparrow$ and $Q \downarrow$). (Option A selected).

• Lecture Review Question 1: What is a competitive market equilibrium?   - Answer: The situation where quantity demanded equals quantity supplied. While markets can be knocked out of equilibrium by exogenous events, the forces of Supply and Demand naturally lead the market back to a new equilibrium.

• Lecture Review Question 2: What is the price elasticity of D&S?   - Answer: A measure of sensitivity calculated as the percentage change in quantity divided by the percentage change in price.

• Lecture Review Question 3: When are D&S defined as being inelastic?   - Answer: When the elasticity value is less than 1. This is graphically represented by steep curves.