Let's analyze the given data and determine the demand and supply at different prices for Ewa and Tom's window cleaning business. --- ## Step 1: Understand the data| Price (£) | Demand (units) | Supply (units) | |------------|----------------|----------------| | 10 | 100 | 20 | | 20 | 80 | 60 | | 30 | 60 | 40 | | 40 | 40 | 80 | | 50 | 20 | 100 | --- ## Step 2: Find the **equilibrium price** and **quantity** **Equilibrium** occurs when **demand = supply**. - At Price = £10: Demand = 100, Supply = 20 → Not equal. - At Price = £20: Demand = 80, Supply = 60 → Not equal. - At Price = £30: Demand = 60, Supply = 40 → Not equal. - At Price = £40: Demand = 40, Supply = 80 → Not equal. - At Price = £50: Demand = 20, Supply = 100 → Not equal. **Observation:** - Demand decreases as price increases. - Supply increases as price increases. The demand and supply are closest at prices **£30** and **£40**: - At £30: Demand (60) > Supply (40) → Excess demand. - At40: Demand (40) < Supply (80) → Excess supply. **Therefore, the equilibrium price lies between £ and £40**. --- ## Step 3: Interpolating to find the approximate equilibrium Assuming linear demand supply between these points: ### Demand between £30 and £40: - Demand drops from 60 to 40 over £10 increase in price: \[ \textDemand slope} = \frac{40 - 60}{40 - 30} = \frac{-20}{10} = -2 \text{ units per £} \] Demand at price \( P \) (between 30 and 40): \[ D(P) = 60 + (-2)(P - 30) \] - At \( P = 35 \): \[ D(35) = 60 + (-2)(35 - 30) = 60 - 10 = 50 \] ### Supply between £30 and £40: - Supply increases from 40 to 80 over £10: \[ \text{Supply slope} = \frac{80 - 40}{40 - 30} = \frac{40}{10} = 4 \text{ units per £} \] - Supply at price \( P \): \[ S(P) = 40 + 4(P - 30) \] - At \( P = 35 \): \[ S(35) = 40 + 4(5) = 40 + 20 = 60 \] ### Find the price where demand equals supply: Set \( D(P) = S(P) \): \[ 50 = 40 + 4(P - 30) \] \[ 50 = 40 + 4P - 120 \] \[ 50 = 4P - 80 \] \[ 4P = 130 \] \[ P = \frac{130}{4} = 32.5 \] --- ## **Final Answer:** ### **Equilibrium Price:** **£32.50** ### **Equilibrium Quantity:** - Demand at \( P = 32.50 \): \[ D(32.50) = 60 + (-2)(32.50 - 30) = 60 - 5 = 55 \] - Supply at \( P = 32.50 \): \[ S(32.50) = 40 + 4(2.5) = 40 + 10 = 50 \] Since demand (55) slightly exceeds supply (50), the equilibrium quantity is approximately **50 units**. --- ## **Summary:** - **Equilibrium Price:** **£32.50** - **Equilibrium Quantity:** **50 units** This is the point where demand and supply are approximately equal based on linear interpolation between data points.

# Equilibrium Price and Quantity ## Definition - **Equilibrium Price:** The price at which quantity demanded equals quantity supplied. - **Equilibrium Quantity:** The amount of goods sold at the equilibrium price. ## Economic Context - This concept falls under **microeconomics**, focusing on individual markets and consumer behavior. ## Step-by-Step Explanation ### Step 1: Analyze Data - Identify demand and supply at various prices to understand market behavior. ### Step 2: Find Equilibrium - Determine where demand equals supply, indicating market stability. ### Step 3: Interpolate - Use interpolation to estimate equilibrium between data points for greater accuracy. ### Final Answer - **Equilibrium Price:** £32.50 - **Equilibrium Quantity:** Approximately 50 units.