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^) and quantity (Q^). This allows for prediction of price and quantity.
  • Finding Equilibrium Quantitatively: Given equations for demand (QD = f(P)) and supply (QS = g(P)), the equilibrium price (P^) is found by setting QD = QS. Once P^ 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} = rac{ 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: rac{Q1 - Q0}{(Q1 + Q0) / 2} imes 100 (where Q0 is initial quantity, Q1 is final quantity).
    • Percentage Change in Price: rac{P1 - P0}{(P1 + P0) / 2} imes 100 (where P0 is initial price, P1 is final price).
    • Price Elasticity of Demand (Midpoint Formula): PED = rac{ rac{Q1 - Q0}{(Q1 + Q0) / 2}}{ rac{P1 - P0}{(P1 + P0) / 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 = rac{ ext{Change in Quantity}}{ ext{Change in Price}} imes rac{ ext{Price}}{ ext{Quantity}} or PED = rac{ ext{dQ}}{ ext{dP}} imes rac{P}{Q}
  • Example: If multiple demand curves share a common price-quantity point (P0, Q0), the rac{P}{Q} ratio is the same for all. The difference in elasticity among these curves will then be determined solely by their slopes ( rac{ ext{dQ}}{ ext{dP}})). A greater absolute slope (steeper curve) at that point implies lower elasticity.