Market Equilibrium: Demand and Supply Equation Examples

Market Equilibrium

Introduction to Market Equilibrium

Market equilibrium is a fundamental concept in macroeconomics, describing the point at which the quantity demanded by consumers equals the quantity supplied by producers. This balance determines the market price and quantity of goods exchanged. The following examples illustrate how to set up and solve equilibrium equations using linear demand and supply functions.

Key Terms and Definitions

• Quantity Demanded (Qd): The amount of a good consumers are willing and able to purchase at a given price.

• Quantity Supplied (Qs): The amount of a good producers are willing and able to sell at a given price.

• Equilibrium Price (Pe): The price at which Qd equals Qs.

• Equilibrium Quantity (Qe): The quantity exchanged at the equilibrium price.

General Method for Finding Equilibrium

1. Set the demand equation equal to the supply equation: $Q_d = Q_s$

2. Solve for the equilibrium price $P_e$.

3. Substitute $P_e$ back into either equation to find the equilibrium quantity $Q_e$.

Examples of Demand and Supply Equations

Below are ten examples of linear demand and supply equations. Each pair can be used to find the market equilibrium.

Example	Demand Equation ($Q_d$)	Supply Equation ($Q_s$)
1	$Q_d = 100 - 2P$	$Q_s = 20 + 3P$
2	$Q_d = 80 - 2P$	$Q_s = 10 + P$
3	$Q_d = 120 - 4P$	$Q_s = 40 + 2P$
4	$Q_d = 90 - 3P$	$Q_s = 15 + 2P$
5	$Q_d = 150 - 5P$	$Q_s = 30 + 3P$
6	$Q_d = 70 - 2P$	$Q_s = 5 + P$
7	$Q_d = 110 - 6P$	$Q_s = 20 + 4P$
8	$Q_d = 60 - P$	$Q_s = 10 + 2P$
9	$Q_d = 90 - 0.5P$	$Q_s = 20 - 0.3P$
10	$Q_d = 100 - 0.6P$	$Q_s = 20 - 0.3P$

Worked Example

Let us solve Example 1 for equilibrium price and quantity:

• Step 1: Set $Q_d = Q_s$:

• $100 - 2P = 20 + 3P$

• Step 2: Solve for $P$:

• $100 - 20 = 3P + 2P$

• $80 = 5P$

• $P_e = 16$

• Step 3: Substitute $P_e$ into either equation to find $Q_e$:

• $Q_d = 100 - 2(16) = 68$

• Thus, Equilibrium Price is $16$, and Equilibrium Quantity is $68$.

Applications and Importance

• Understanding equilibrium helps predict market outcomes and the effects of policy interventions.

• Shifts in demand or supply curves (due to external factors) will change the equilibrium price and quantity.

• Linear equations are commonly used for introductory analysis; more complex models may use nonlinear functions.

Summary Table: Steps to Find Market Equilibrium

Step	Description	Equation
1	Set $Q_d = Q_s$	$a - bP = c + dP$
2	Solve for $P_e$	$P_e = \frac{a - c}{b + d}$
3	Find $Q_e$	Substitute $P_e$ into either equation

Additional info: These examples are foundational for understanding how markets function and how equilibrium is determined in basic macroeconomic models.