ECON 101 - Week 9 - Market Equilibrium

Market Equilibrium

Definition

  • Market equilibrium is the condition where the quantity demanded by consumers equals the quantity supplied by producers.

  • This results in a stable market price and quantity.

  • It's the point where the demand curve and the supply curve intersect.

  • Mathematically, it is the point where Q<em>d=Q</em>sQ<em>d = Q</em>s.

Shortage and Surplus

  • Shortage: Occurs when the quantity demanded is greater than the quantity supplied at a given price.

    • Too many buyers, not enough goods.

  • Surplus: Occurs when the quantity supplied is greater than the quantity demanded at a given price.

    • Too much product, not enough buyers.

Finding Market Equilibrium Using Mathematical Functions

  • Example: Given demand function Q<em>d=80−4PQ<em>d = 80 - 4P and supply function Q</em>s=−10+5PQ</em>s = -10 + 5P.

  • Equilibrium Condition: Set quantity demanded equal to quantity supplied: Q<em>d=Q</em>sQ<em>d = Q</em>s.

  • Substitute the given functions: 80−4P=−10+5P80 - 4P = -10 + 5P.

  • Rearrange the equation to isolate PP: 80+10=5P+4P80 + 10 = 5P + 4P.

  • Simplify: 90=9P90 = 9P.

  • Solve for PP: 909=P\frac{90}{9} = P.

  • Equilibrium price: P=10P = 10.

  • Verification: Substitute P=10P = 10 into both demand and supply functions.

    • Qd=80−4(10)=80−40=40Q_d = 80 - 4(10) = 80 - 40 = 40.

    • Qs=−10+5(10)=−10+50=40Q_s = -10 + 5(10) = -10 + 50 = 40.

  • Since Q<em>d=Q</em>s=40Q<em>d = Q</em>s = 40, the equilibrium price is indeed P<em>e=10P<em>e = 10 and the equilibrium quantity is Q</em>e=40Q</em>e = 40 units.

Finding Market Equilibrium Using a Schedule

  • A table can be used to find the market equilibrium by comparing the quantity demanded and quantity supplied at different prices.

  • Example:

    • Price 0: Quantity Demanded (Qd) = 80, Quantity Supplied (Qs) = -10.

      • Qs - Qd = -10 - 80= -90, Market Condition: Shortage.

    • Price 5: Quantity Demanded (Qd) = 60, Quantity Supplied (Qs) = 15.

      • Qs - Qd = 15 - 60= -45, Market Condition: Shortage.

    • Price 10: Quantity Demanded (Qd) = 40, Quantity Supplied (Qs) = 40.

      • Qs - Qd = 40 - 40= 0, Market Condition: Equilibrium.

    • Price 15: Quantity Demanded (Qd) = 20, Quantity Supplied (Qs) = 65.

      • Qs - Qd = 65 - 20= 45, Market Condition: Surplus.

    • Price 20: Quantity Demanded (Qd) = 0, Quantity Supplied (Qs) = 90.

      • Qs -Qd = 90 - 0= 90, Market Condition: Surplus.

  • Key Insight:

    • At price 10 and quantity 40, the market is in equilibrium.