Market Equilibrium, Shifts, and Elasticity

Market Equilibrium: Supply and Demand

• Basic Market Setup: A simple operating market consists of firms producing and selling goods and consumers purchasing them, with no other economic agents.
• Supply Curve: Upward sloping, reflecting that firms are willing to supply more at higher prices.
• Demand Curve: Downward sloping, indicating consumers demand less at higher prices.
• Equilibrium: The point where supply and demand intersect, determining the market-clearing price ($P^<em>$) and quantity ($Q^</em>$). This allows for prediction of price and quantity.
• Finding Equilibrium Quantitatively: Given equations for demand $(Q<em>D = f(P))$ and supply $(Q</em>S = g(P))$, the equilibrium price $(P^<em>)$ is found by setting $Q<em>D = Q</em>S$. Once $P^</em>$ is found, substitute it into either the demand or supply equation to find the equilibrium quantity $(Q^*)$.

Shifts in Supply and Demand

• Exogenous Changes: Changes originating outside the basic supply and demand model can shift the curves, leading to a new equilibrium.
• Demand Shifters (Factors changing consumer behavior at any given price):
  • Consumer Preferences: A change in taste towards or away from a good.
  • Consumer Income:
    • Normal Goods: An increase in income shifts demand to the right (consumers buy more). Most goods fall into this category.
    • Inferior Goods: An increase in income shifts demand to the left (consumers buy less, opting for higher-quality alternatives).
  • Price of Related Goods:
    • Substitutes: If the price of a substitute good increases, demand for the original good shifts to the right (e.g., if coffee prices rise, demand for tea increases).
    • Complements: If the price of a complementary good increases, demand for the original good shifts to the left (e.g., if printer ink prices rise, demand for printers might decrease).
  • Expectations: Future price or income expectations.
  • Number of Buyers: An increase in the number of consumers shifts demand to the right.
• Supply Shifters (Factors changing producer behavior at any given price):
  • Input Prices: Changes in the cost of resources used in production.
  • Technology: Advances in production technology.
  • Expectations: Future price expectations for the product.
  • Number of Sellers: An increase in the number of firms in the market.
  • Government Policies: Taxes, subsidies, regulations.
• Impact of Shifts on Equilibrium: Determining the new equilibrium price and quantity:
  • Demand Shifts: If demand shifts, the market moves along the existing supply curve.
    • Demand shifts Right (increases): Price increases, and quantity increases (moving in the same direction).
    • Demand shifts Left (decreases): Price decreases, and quantity decreases (moving in the same direction).
  • Supply Shifts: If supply shifts, the market moves along the existing demand curve.
    • Supply shifts Right (increases): Price decreases, and quantity increases (moving in opposite directions).
    • Supply shifts Left (decreases): Price increases, and quantity decreases (moving in opposite directions).

Understanding Elasticity: General Concepts

• Marginal: A common term in economics indicating a rate of change. It always involves two variables.
  • Definition: The rate at which one variable changes with respect to another.
  • Examples:
    • Marginal Cost: The rate at which total cost changes as output quantity changes.
    • Marginal Profit: The rate at which profit changes as output changes.
    • Marginal Revenue: The rate at which revenue changes as quantity changes.
    • Marginal Benefit: The rate at which consumer benefits change as quantity changes.
  • Mathematical Representation: In calculus, it's a derivative; graphically, it's a slope.
• Elasticity: An advanced sensitivity measure related to marginal changes.
  • Definition: A ratio of percentage changes between two variables, rather than absolute rates of change.
  • Purpose: To measure sensitivity in a unit-free way. This allows for comparison across different goods or markets regardless of the units of measurement (e.g., dollars, pounds, liters).
  • General Formula: $ext{Elasticity} = \frac{ ext{Percentage Change in Variable 1}}{ ext{Percentage Change in Variable 2}}$

Types of Elasticity

• Price Elasticity of Demand (PED): Measures how sensitive the quantity demanded is to changes in price.
• Income Elasticity of Demand: Measures how sensitive the quantity demanded is to changes in consumers' income.
• Price Elasticity of Supply: Measures how sensitive the quantity supplied is to changes in price.

Calculating Elasticity: Midpoint Method

• Challenge with Percentage Change: The standard percentage change formula $(( ext{Final Value} - ext{Initial Value}) / ext{Initial Value} imes 100))$ gives different results depending on the direction of change (e.g., price increase vs. price decrease).
• Midpoint Method Solution: To ensure the elasticity measure is consistent regardless of the direction of change, the midpoint (average) of the initial and final values is used as the reference point in the denominator.
  • Percentage Change in Quantity: $\frac{Q<em>1 - Q</em>0}{(Q<em>1 + Q</em>0) / 2} imes 100$ (where $Q<em>0$ is initial quantity, $Q</em>1$ is final quantity).
  • Percentage Change in Price: $\frac{P<em>1 - P</em>0}{(P<em>1 + P</em>0) / 2} imes 100$ (where $P<em>0$ is initial price, $P</em>1$ is final price).
  • Price Elasticity of Demand (Midpoint Formula): $PED = \frac{\frac{Q<em>1 - Q</em>0}{(Q<em>1 + Q</em>0) / 2}}{\frac{P<em>1 - P</em>0}{(P<em>1 + P</em>0) / 2}}$
• Interpretation: This method calculates the elasticity at the midpoint between two given points on a demand curve, acting as an approximation. As the distance between the two points shrinks, this becomes an increasingly accurate measure of point elasticity.

Interpreting Price Elasticity of Demand (PED)

• Sign: Price elasticity of demand is typically a negative number because price and quantity demanded move in opposite directions (due to the law of demand).
• Absolute Value: It is common to discuss PED in terms of its absolute value to focus on the magnitude of responsiveness, making it a positive number.
• Categories of Elasticity (using absolute value):
  • Unit Elastic ($| ext{PED}| = 1$): The percentage change in quantity demanded is exactly equal to the percentage change in price. For example, a 10% increase in price leads to a 10% decrease in quantity demanded.
  • Elastic ($| ext{PED}| > 1$): Quantity demanded is very sensitive to price changes. A small percentage change in price leads to a larger percentage change in quantity demanded. For example, a 5% increase in price leads to a 15% decrease in quantity demanded.
  • Inelastic ($| ext{PED}| < 1$): Quantity demanded is relatively insensitive to price changes. A large percentage change in price leads to a smaller percentage change in quantity demanded. For example, a 10% increase in price leads to only a 3% decrease in quantity demanded.

Slope vs. Elasticity

• Distinction: The slope of the demand curve is not the same as its elasticity, although they are related.
• Relationship:
  • A steeper demand function generally tends to be less elastic (or more inelastic).
  • A flatter demand function generally tends to be more elastic.
• Point Elasticity Formula (using slope): For a specific point ($P, Q$) on the demand curve, the PED can be calculated as: $PED = \frac{ ext{Change in Quantity}}{ ext{Change in Price}} imes \frac{ ext{Price}}{ ext{Quantity}}$ or $PED = \frac{ ext{dQ}}{ ext{dP}} imes \frac{P}{Q}$
• Example: If multiple demand curves share a common price-quantity point ($P<em>0, Q</em>0$), the $\frac{P}{Q}$ ratio is the same for all. The difference in elasticity among these curves will then be determined solely by their slopes $( \frac{ ext{dQ}}{ ext{dP}}))$. A greater absolute slope (steeper curve) at that point implies lower elasticity.