Market Foundations: Demand, Supply, Equilibrium, and Comparative Statics

Market Foundations: Demand, Supply, Equilibrium, and Comparative Statics

Introduction

This chapter introduces the foundational concepts of market demand, market supply, market equilibrium, and comparative statics. These concepts are essential for understanding how markets function and how prices and quantities are determined in competitive environments.

Market Demand

Market Demand Function

The market demand function defines the relationship between the quantity demanded ($Q_D$) of a good and its determinants, including price and non-price factors such as consumer preferences and income.

• Mathematical Expression:

$Q_D = f(\text{Price}, \text{Non-price determinants})$

• Quantity Demanded ($Q_D$): The amount of a product that consumers are willing and able to purchase at a given price.

• As price changes, the quantity demanded also changes.

Price (P)	Quantity Demanded (QD)
$10	10 units
$20	5 units
$50	2 units

Law of Demand

• The law of demand states that there is a negative relationship between price and quantity demanded, holding non-price determinants constant.

• When price increases, quantity demanded decreases; when price decreases, quantity demanded increases.

• This relationship is depicted as a downward-sloping demand curve.

Demand Curve Equation Example: $P = 20 - 2Q$

Slope of demand curve: $\frac{dP}{dQ} = -2 < 0$

• The negative slope confirms the law of demand.

• In economics, the demand function is often written as $Q = f(P)$ (direct demand function) or $P = f(Q)$ (inverse demand function).

• The demand curve can also be interpreted as a willingness-to-pay curve, foundational for price analysis and consumer surplus.

Movement Along the Demand Curve

• A change in price leads to a movement along the demand curve (non-price determinants held constant).

• Upward movement (increase in price): $\uparrow P \rightarrow \downarrow Q$

• Downward movement (decrease in price): $\downarrow P \rightarrow \uparrow Q$

• Changes in non-price determinants (e.g., preferences, income) shift the entire demand curve.

Market Supply

Market Supply Function

The market supply function defines the relationship between the quantity supplied ($Q_S$) of a good and its determinants, including price and non-price factors such as production costs and the number of firms.

• Mathematical Expression:

$Q_S = f(\text{Price}, \text{Non-price determinants})$

• Quantity Supplied ($Q_S$): The amount of a product that firms are willing to produce and sell at a given price.

• As price changes, the quantity supplied also changes.

Price (P)	Quantity Supplied (QS)
$5	10 units
$20	20 units
$50	40 units

Law of Supply

• The law of supply states that there is a positive relationship between price and quantity supplied, holding non-price determinants constant.

• When price increases, quantity supplied increases; when price decreases, quantity supplied decreases.

• This relationship is depicted as an upward-sloping supply curve.

Supply Curve Equation Example: $P = 5 + Q$

Slope of supply curve: $\frac{dP}{dQ} = 1 > 0$

• The positive slope confirms the law of supply.

• In economics, the supply function is often written as $Q = f(P)$ (direct supply function) or $P = f(Q)$ (inverse supply function).

Movement Along the Supply Curve

• A change in price leads to a movement along the supply curve (non-price determinants held constant).

• Upward movement (increase in price): $\uparrow P \rightarrow \uparrow Q$

• Downward movement (decrease in price): $\downarrow P \rightarrow \downarrow Q$

• Changes in non-price determinants (e.g., input costs, technology) shift the entire supply curve.

Market Equilibrium

Definition and Determination

Market equilibrium occurs when the quantity demanded ($Q_D$) equals the quantity supplied ($Q_S$). The equilibrium price ($P^*$) and equilibrium quantity ($Q^*$) are determined by the intersection of the demand and supply curves.

• Equilibrium Condition: $Q_D(P^*) = Q_S(P^*)$

• At $P^*$, there is no excess supply (surplus) or excess demand (shortage).

• At equilibrium, there is no pressure for the price to change.

Price Adjustments

• If price is above equilibrium ($P > P^*$): Excess supply (surplus) exists, causing downward pressure on price.

• If price is below equilibrium ($P < P^*$): Excess demand (shortage) exists, causing upward pressure on price.

Example: Solving for Equilibrium

• Example 1:

  • Demand: $Q = 10 - 0.5P$

  • Supply: $Q = 5 + P$

  • Set $10 - 0.5P = 5 + P$

  • Solve for $P^*$ and $Q^*$.

• Example 2:

  • Demand: $P = 20 - 2Q$

  • Supply: $P = 5 + Q$

  • Set $20 - 2Q = 5 + Q$

  • Solve for $Q^*$ and $P^*$.

Comparative Statics

Definition and Application

Comparative statics analyzes how changes in non-price determinants (external factors) shift the demand or supply curve, leading to a new market equilibrium.

• Shifts in demand or supply change the equilibrium price and quantity.

• This method predicts how equilibrium adjusts when non-price determinants change.

Non-Price Determinants of Demand

Determinant	Effect on Demand	Relationship
Income (normal good)	Increase in income increases demand	Positive
Income (inferior good)	Increase in income decreases demand	Negative
Price of substitute goods	Increase in price of substitute increases demand	Positive
Price of complementary goods	Increase in price of complement decreases demand	Negative
Expected future price	Expected price increase raises current demand	Positive
Number of buyers	Increase in buyers increases demand	Positive

Non-Price Determinants of Supply

Determinant	Effect on Supply	Relationship
Input costs	Increase in costs decreases supply	Negative
Price of related goods (substitutes in production)	Increase in price of substitute decreases supply	Negative
Price of related goods (complements in production)	Increase in price of complement increases supply	Positive
Expected future price	Expected price increase decreases current supply	Negative
Number of firms	Increase in firms increases supply	Positive
Weather/other conditions	Good weather increases supply	Positive

Shifts and Market Equilibrium

• Increase in demand: Rightward shift of demand curve → higher equilibrium price and quantity.

• Decrease in demand: Leftward shift of demand curve → lower equilibrium price and quantity.

• Increase in supply: Rightward shift of supply curve → lower equilibrium price, higher equilibrium quantity.

• Decrease in supply: Leftward shift of supply curve → higher equilibrium price, lower equilibrium quantity.

Examples of Comparative Statics

• Example 3: If the price of Good A increases and A and B are substitutes in production, the supply curve for Good B shifts leftward (decreases).

• Example 4: If A and B are complements in consumption, an increase in the price of A decreases both the equilibrium price and quantity of B.

• Example 5: If A and B are complements in production, an increase in the price of A increases both the equilibrium price and quantity of B.

Case Study: Electric Vehicle (EV) Market

Demand Analysis

• Changes in consumer preferences toward sustainability increase demand for EVs.

• If consumers expect the price of EVs to rise, current demand increases.

• If the cost of EV charging falls, demand for EVs increases.

Supply Analysis

• Reduction in battery costs increases supply of EVs.

• If the price of gas-powered SUVs falls, supply of EVs by firms producing both may decrease (due to input reallocation).

Recap

• Quantity Demanded: Movement along the demand curve due to price change.

• Increase/Decrease in Demand: Rightward/leftward shift of the demand curve due to non-price determinants.

• Quantity Supplied: Movement along the supply curve due to price change.

• Increase/Decrease in Supply: Rightward/leftward shift of the supply curve due to non-price determinants.

• Market Equilibrium: $Q_D = Q_S$ at equilibrium price and quantity.

• Surplus: $Q_S > Q_D$ → price falls toward equilibrium.

• Shortage: $Q_D > Q_S$ → price rises toward equilibrium.

• Comparative Statics: Examines how shifts in demand or supply affect equilibrium outcomes.

Key Effects of Comparative Statics:

• Increase in demand → increase in price and quantity

• Decrease in demand → decrease in price and quantity

• Increase in supply → decrease in price, increase in quantity

• Decrease in supply → increase in price, decrease in quantity