Market Equilibrium - Chapter 5

Road Map / Objectives

• Explain how a market reaches its equilibrium price and quantity
• Discuss the effects of price ceilings and price floors
• Show how shifts in supply and demand affect a market’s equilibrium
• Solve problems involving market equilibrium

Equilibrium Point

• Equilibrium occurs at the intersection of the demand and supply curves.
• The equilibrium price and quantity are the point where the two curves intersect.
• Notation:
  • $P_E$ = equilibrium price
  • $Q_E$ = equilibrium quantity
  • $Q_D(P)$ = quantity demanded at price $P$
  • $Q_S(P)$ = quantity supplied at price $P$
• Equilibrium condition: when the two curves intersect, we have
  • $Q<em>D(P</em>E) = Q<em>S(P</em>E) = Q_E$
• Implication: at this point, there is no inherent pressure for the price to change (assuming other conditions hold).

Shortages and Surpluses

• When a market is not in equilibrium, shortages and surpluses occur for consumers and producers.
• Definitions:
  • Shortage occurs when the quantity demanded exceeds the quantity supplied: $Q<em>D(P) > Q</em>S(P)$
  • Surplus occurs when the quantity supplied exceeds the quantity demanded: $Q<em>S(P) > Q</em>D(P)$
• Notation recap:
  • Equilibrium price and quantity: $P<em>E, Q</em>E$ with $Q<em>D(P</em>E) = Q<em>S(P</em>E) = Q_E$
• At non-equilibrium prices, prices adjust to move the market toward equilibrium; shortages put upward pressure on price, surpluses put downward pressure on price.

Market Schedule Example: Sub Sandwich Market

• Given data (price per sandwich, quantity demanded, quantity supplied):
  

  Price	Quantity Demanded	Quantity Supplied
  $3	36	8
  $6	30	16
  $9	24	24
  $12	18	32
  $15	12	40
  $18	0	48

• Analysis:
• At $P = 9$, $Q<em>D = Q</em>S = 24$ → Equilibrium price $P<em>E = 9$, equilibrium quantity $Q</em>E = 24$
• Prices below equilibrium (e.g., $P = 3$, $P = 6$): $Q<em>D > Q</em>S$ → Shortage
• Prices above equilibrium (e.g., $P = 12, 15, 18$): $Q<em>S > Q</em>D$ → Surplus
• Summary of outcomes for this schedule:
  • Shortage at $P = 3, 6$
  • Equilibrium at $P = 9$ with $Q = 24$
  • Surplus at $P = 12, 15, 18$

Price Controls

• Binding price controls can lead to shortages or surpluses depending on whether they lie below or above the equilibrium price.
• Price ceiling:
  • An artificial upper limit on the price of a good or service
  • If binding (set below equilibrium), tends to create a shortage
• Price floor:
  • An artificial lower bound on the price of a good or service
  • If binding (set above equilibrium), tends to create a surplus
• The general principle: binding price controls disrupt the natural price mechanism and can misallocate resources.
• Practical implications and examples:
  • Price ceilings are often discussed in housing markets (rent control).
  • Price floors are commonly discussed in agricultural markets (minimum prices).
• Connection to equilibrium concepts:
  • When a price control is in effect, the market price may be forced away from the equilibrium price $P_E$, resulting in either a shortage (ceiling) or surplus (floor) until other market factors adjust.

Key Formulas and Concepts (summary)

• Equilibrium condition: $Q<em>D(P</em>E) = Q<em>S(P</em>E) = Q_E$
• Shortage condition: $Q<em>D(P) > Q</em>S(P)$
• Surplus condition: $Q<em>S(P) > Q</em>D(P)$
• Notation recap:
  • $P_E$ = equilibrium price
  • $Q_E$ = equilibrium quantity
  • $Q_D(P)$ = quantity demanded at price $P$
  • $Q_S(P)$ = quantity supplied at price $P$
• Price controls: binding when set relative to $P_E$ can create shortages (ceiling) or surpluses (floor)