Market Equilibrium Notes

Market Equilibrium

Definition of Market Equilibrium

Market equilibrium is a concept that represents a state of balance in a market, where the quantity demanded by consumers is equal to the quantity supplied by producers. In a broader sense, equilibrium can be viewed as a state of rest or balance where opposing forces equal each other. Specifically, in market terms, it can be defined as:

  • Equilibrium Quantity: The quantity at which demand equals supply.

  • Equilibrium Price: The price at which quantity demanded equals quantity supplied, also referred to as the market clearing price. At this point, there is neither excess supply nor excess demand in the market.

Graphical Representation of Market Equilibrium

Graphically, market equilibrium is represented by the intersection of the demand and supply curves on a price-quantity graph. The x-axis typically represents quantity, while the y-axis represents price. The point where the two curves intersect indicates the equilibrium price (P) and equilibrium quantity (Q).

Mathematical Derivation of Market Equilibrium

To find the equilibrium price and quantity mathematically, we set the demand function equal to the supply function. For example, if the demand function is given by Qd = a - bP and the supply function is Qs = c + dP, setting them equal yields:

a - bP = c + dP

By rearranging terms, we can solve for P (the equilibrium price):

P = \frac{a - c}{b + d}

To find the equilibrium quantity, substitute the equilibrium price back into either the demand or supply equation.

Shifts in Demand and Supply Curves

  • Shift in Demand Curve: When factors other than price change, such as consumer preferences or incomes, the demand curve shifts. An increase in demand shifts the curve to the right, leading to a higher equilibrium price and quantity. Conversely, a decrease shifts it to the left.

  • Shift in Supply Curve: Changes in production costs or technology can cause the supply curve to shift. A rightward shift indicates an increase in supply, resulting in a lower equilibrium price and higher quantity. A leftward shift implies a decrease in supply, causing the opposite effect.

Consumer Surplus and Producer Surplus

  • Consumer Surplus (CS): This represents the difference between what consumers are willing to pay for a good and what they actually pay. It's graphically depicted as the area under the demand curve and above the price level. Mathematically, it can be expressed as:

CS = \frac{1}{2} \times (base \times height)

  • Producer Surplus (PS): Producer surplus is the difference between what producers receive for a good and the minimum they are willing to accept. This is shown as the area above the supply curve and below the price level.

Example of Equilibrium Calculation

  1. Given the demand and supply functions:

    • Demand: Q_d = 700 - 50P

    • Supply: Q_s = -300 + 50P

  2. Setting the two equal for equilibrium:

    • 700 - 50P = -300 + 50P

    • Solving gives P = 10

  3. To find equilibrium quantity:

    • Substitute P back into either equation:

    • Q_d = 700 - 50(10) = 200

Thus, the equilibrium price is $10 and the equilibrium quantity is 200.

Disequilibrium in Markets

When a market is not in equilibrium, it can experience shortages and surpluses:

  • Shortage occurs when the quantity demanded exceeds the quantity supplied, typically at prices below the equilibrium price.

  • Surplus happens when the quantity supplied surpasses the quantity demanded, usually at prices above the equilibrium price.