Equilibrium

Equilibrium

Definition of Equilibrium

• Equilibrium: A market situation where quantity supplied equals quantity demanded.

• This occurs when the supply and demand curves intersect.

• Equilibrium Price: The price at which quantity supplied balances quantity demanded. It is also known as the market-clearing price.

• Equilibrium Quantity: The quantity supplied and quantity demanded at the equilibrium price.

Finding Equilibrium: Examples

Graphical Example (Ice Cream Cones)

• The equilibrium is found at the intersection of the supply and demand curves.

• Example: If the equilibrium price is $2.00$, then $7$ ice-cream cones are supplied and $7$ ice-cream cones are demanded.

Market Outcomes at Non-Equilibrium Prices (Example 1)

• Scenario 1: Market Price is $80$ (Above Equilibrium)

  • The market is not at equilibrium.

  • If quantity demanded ($Q<em>d$) is $600$ and quantity supplied ($Q</em>s$) is $1200$

  • There is a surplus of $600$ units. This is calculated as $Q<em>s - Q</em>d = 1200 - 600 = 600$.

• Scenario 2: Market Price is $40$ (Below Equilibrium)

  • The market is not at equilibrium.

  • If quantity demanded ($Q<em>d$) is $1000$ and quantity supplied ($Q</em>s$) is $400$

  • There is a shortage of $600$ units. This is calculated as $Q<em>d - Q</em>s = 1000 - 400 = 600$.

Mathematical Example (Example 2)

• Given Equations:

  • Demand: $P = 140 - 0.1Q_d$ (Equation 1)

  • Supply: $P = 20 + 0.05Q_s$ (Equation 2)

• Calculation of Equilibrium Price and Quantity:

  • At equilibrium, $Q<em>d = Q</em>s = Q$ and the price $P$ is the same for both.

  • Set the two price equations equal to each other:
    $20 + 0.05Q = 140 - 0.1Q$

  • Combine terms with $Q$:
    $0.05Q + 0.1Q = 140 - 20$
    $0.15Q = 120$

  • Solve for $Q$:
    $Q = rac{120}{0.15} = 800$

  • Substitute $Q = 800$ into either equation to find $P$:

    • Using Equation 2: $P = 20 + 0.05(800) = 20 + 40 = 60$

    • Using Equation 1: $P = 140 - 0.1(800) = 140 - 80 = 60$

  • Therefore, the equilibrium price ($P^<em>$) is $60$ and the equilibrium quantity ($Q^</em>$) is $800$.

• Market Outcomes at Non-Equilibrium Prices:

  • Scenario 1: Market Price is $80$

    • Calculate $Q<em>d$ at $P=80$ using Equation 1: $80 = 140 - 0.1Q</em>d$
      $0.1Q<em>d = 140 - 80$ $0.1Q</em>d = 60$
      $Q_d = 600$

    • Calculate $Q<em>s$ at $P=80$ using Equation 2: $80 = 20 + 0.05Q</em>s$
      $0.05Q<em>s = 80 - 20$ $0.05Q</em>s = 60$
      $Q_s = rac{60}{0.05} = 1200$

    • Outcome: Surplus of $600$ units ($Q<em>s - Q</em>d = 1200 - 600 = 600$).

  • Scenario 2: Market Price is $40$

    • Calculate $Q<em>d$ at $P=40$ using Equation 1: $40 = 140 - 0.1Q</em>d$
      $0.1Q<em>d = 140 - 40$ $0.1Q</em>d = 100$
      $Q_d = 1000$

    • Calculate $Q<em>s$ at $P=40$ using Equation 2: $40 = 20 + 0.05Q</em>s$
      $0.05Q<em>s = 40 - 20$ $0.05Q</em>s = 20$
      $Q_s = rac{20}{0.05} = 400$

    • Outcome: Shortage of $600$ units ($Q<em>d - Q</em>s = 1000 - 400 = 600$).

Factors that Shift Demand and Supply

Factors that Shift Demand (Causes for a change in demand)

• Number of buyers

• Income of consumers

• Consumer preferences and/or taste

• Prices of related goods (substitutes and complements)

• Expected future prices

Factors that Shift Supply (Causes for a change in supply)

• Number of sellers

• Input prices (cost of production)

• Technology (improvements or limitations)

• Prices of related goods in production

• Expected future prices

Analyzing Changes in Equilibrium: Three Steps

1. Decide which curve shifts: Determine if the change affects the supply curve, demand curve, or both.

2. Decide the direction of the shift: Determine if the curve shifts to the right (increase) or to the left (decrease).

3. Use the supply-and-demand diagram: Analyze how the shift changes the equilibrium price and quantity.

Example: Change in Market Equilibrium Due to a Shift in Demand (Hot Weather)

• Event: One summer, very hot weather occurs.

• Effect on Ice Cream Market: Hot weather acts as a change in consumer tastes.

• Shift: The demand curve for ice cream shifts to the right (increase in demand).

• Outcome: This results in a higher equilibrium price and a higher equilibrium quantity for ice cream.

  • Illustration: Demand curve shifts from $D<em>1$ to $D</em>2$. Equilibrium price rises from $2.00$ to $2.50$. Equilibrium quantity rises from $7$ to $10$ cones.

Shifts vs. Movements Along Curves

• Shift in the supply curve: Represents a change in supply (caused by non-price factors).

• Movement along a fixed supply curve: Represents a change in the quantity supplied (caused by a change in the good's own price).

• Shift in the demand curve: Represents a change in demand (caused by non-price factors).

• Movement along a fixed demand curve: Represents a change in the quantity demanded (caused by a change in the good's own price).

Example: Change in Market Equilibrium Due to a Shift in Supply (Hurricane and Sugarcane)

• Event: One summer, a hurricane destroys part of the sugarcane crop, leading to a higher price of sugar.

• Effect on Ice Cream Market: A higher price of sugar (an input) affects the supply curve.

• Shift: The supply curve for ice cream shifts to the left (decrease in supply).

• Outcome: This results in a higher equilibrium price and a lower equilibrium quantity for ice cream.

  • Illustration: Supply curve shifts from $S<em>1$ to $S</em>2$. Equilibrium price rises from $2.00$ to $2.50$. Equilibrium quantity falls from $7$ to $4$ cones.

Practice Questions & Scenarios

Surplus and Shortage Basics

• If a product is in surplus supply, its price is above the equilibrium level.

• A shortage of $160$ units would be encountered if the price was $0.50 (assuming the provided graph showed a discrepancy of $160$ at that price point, specifically where quantity demanded exceeds quantity supplied by $160$).

Impact of Supply and Demand Changes

• An increase in demand with no change in supply will result in an increase in sales (equilibrium quantity).

Factors Affecting Supply of Automobile Tires

• Technological advance in production methods: Will increase the supply of tires (supply curve shifts right).

• Decline in the number of firms in the tire industry: Will decrease the supply of tires (supply curve shifts left).

• Increase in the price of rubber (input): Will decrease the supply of tires (supply curve shifts left).

• Expectation that future equilibrium price of auto tires will be lower: Will increase current supply of tires (sellers want to sell now before prices fall, supply curve shifts right).

• Decline in the price of large tires for semi-trucks (no change in auto tire price): This implies sellers might shift production towards more profitable auto tires, potentially increasing the supply of auto tires (supply curve shifts right).

• Levying of a per-unit tax on each auto tire sold: Will decrease the supply of tires (increases cost of production, supply curve shifts left).

• Granting of a $50$-cent-per-unit subsidy for each auto tire produced: Will increase the supply of tires (reduces effective cost of production, supply curve shifts right).

Real-world Example: Foot-and-Mouth Disease Outbreak (2017)

• Event: Outbreak of foot-and-mouth disease led to burning millions of cattle carcasses.

• Impact on Supply of Cattle Hides: The destruction of cattle drastically reduced the supply of cattle hides (a key input for leather).

• Impact on Hide Prices: With reduced supply and unchanged demand, the price of hides increased.

• Impact on Supply of Leather Goods: Since hides became more expensive (an increased input cost for leather production), the cost of producing leather goods increased. This led to a reduction in the supply of leather goods.

• Impact on Price of Leather Goods: With reduced supply of leather goods and unchanged demand, the price of leather goods increased.