Sure! Let's go through each part step by step. --- ## Given Data | Price (P) | Quantity series I | Quantity series II | |-----------|------------------|-------------------| | $3 | 30 | 150 | | $6 | 60 | 120 | | $9 | 90 | 90 | | $12 | 120 | 60 | | $15 | 150 | 30 | --- ## a. Identify Demand and Supply Series - **Quantity series I**: As price increases, quantity increases → **Supply** - **Quantity series II**: As price increases, quantity decreases → **Demand** **Answer:** - **Quantity series I:** Quantity Supplied - **Quantity series II:** Quantity Demanded --- ## b. Identify the Linear Demand Function A linear demand function has the form: \[ Q_d = a - bP \] Let's use two points from Quantity series II (Demand): - At \( P = 3, Q = 150 \) - At \( P = 15, Q = 30 \) **Find slope (b):** \[ b = \frac{Q_2 - Q_1}{P_2 - P_1} = \frac{30 - 150}{15 - 3} = \frac{-120}{12} = -10 \] **Solve for a using one point (e.g., \( P = 3, Q = 150 \)):** \[ Q = a - bP \\ 150 = a - (-10) \times 3 \\ 150 = a + 30 \\ a = 120 \] **So, the demand function is:** \[ \boxed{Q_d = 180 - 10P} \] --- ## c. Identify the Linear Supply Function A linear supply function has the form: \[ Q_s = c + dP \] Let's use two points from Quantity series I (Supply): - At \( P = 3, Q = 30 \) - At \( P = 15, Q = 150 \) **Find slope (d):** \[ d = \frac{150 - 30}{15 - 3} = \frac{120}{12} = 10 \] **Solve for c using one point (e.g., \( P = 3, Q = 30 \)):** \[ 30 = c + 10 \times 3 \\ 30 = c + 30 \\ c = \] **So, the supply function is:** \[ \boxed{Q_s = 10P} \] --- ## d. Predict Quantity Supplied and Demanded at \( P = \$10 \) **Demand:** \[ Q_d = 180 - 10P = 180 - 10 \times 10 = 80 \] **Supply:** \[ Q_s = 10 \times 10 = 100 \] --- ## e. Find the Market Equilibrium Price and Quantity At equilibrium, \( Q_d = Q_s \): \[ 180 - 10P = 10P \\ 180 = 20P \\ P^* = 9 \] **Plug \( P^* \) back to get \( Q^* \):** \[ Q^* = 10 \times 9 = 90 \] **Equilibrium:** \[ \boxed{P^* = 9, \quad Q^* = 90} \] --- ## f. Sketch the Demand and Supply Functions Here's what the graph should look like: - **Horizontal axis (x):** Quantity (Q) - **Vertical axis (y):** Price (P) - **Demand curve:** Starts high at \( Q = 150 \) when \( P = 3 \), goes down to \( Q = 30 \) at \( P = 15 \) - **Supply curve:** Starts low at \( Q = 30 \) when \( P = 3 \), goes up to \( Q = 150 \) at \( P = 15 \) - **Equilibrium point:** \( (Q^*, P^*) = (90, 9) \) ``` | | / (Supply) | / | / |-----------/---------------- | / | / | / (Demand) | +--------+----------------- Q ``` - Label the intersection as **Equilibrium (Q=90, P=9)**. --- Let me know if you need further clarification or want the graph plotted!

# Summary of Demand and Supply Analysis ## Given Data | Price (P) | Quantity Supplied (Series I) | Quantity Demanded (Series II) | |-----------|-------------------------------|--------------------------------| | $3 | 30 | 150 | | $6 | 60 | 120 | | $9 | 90 | 90 | | $12 | 120 | 60 | | $15 | 150 | 30 | ## a. Demand and Supply Series Identification - **Quantity Supplied (Series I)**: Increases with price. - **Quantity Demanded (Series II)**: Decreases with price. ## b. Linear Demand Function Form: \[ Q_d = a - bP \] ### Calculation - Points: \( (3, 150) \) and \( (15, 30) \) - Slope (\( b \)): \[ b = \frac{30 - 150}{15 - 3} = -10 \] - Intercept (\( a \)): \[ 150 = a + 30 \implies a = 120 \] **Demand Function:** \[ \boxed{Q_d = 180 - 10P} \] ## c. Linear Supply Function Form: \[ Q_s = c + dP \] ### Calculation - Points: \( (3, 30) \) and \( (15, 150) \) - Slope (\( d \)): \[ d = \frac{150 - 30}{15 - 3} = 10 \] - Intercept (\( c \)): \[ 30 = c + 30 \implies c = 0 \] **Supply Function:** \[ \boxed{Q_s = 10P} \] ## d. Quantity Supplied and Demanded at \( P = 10 \) - **Demand:** \[ Q_d = 180 - 10 \times 10 = 80 \] - **Supply:** \[ Q_s = 10 \times 10 = 100 \] ## e. Market Equilibrium Price and Quantity Set \( Q_d = Q_s \): \[ 180 - 10P = 10P \implies 180 = 20P \implies P^* = 9 \] - **Quantity at Equilibrium:** \[ Q^* = 10 \times 9 = 90 \] **Equilibrium:** \[ \boxed{P^* = 9, \quad Q^* = 90} \] ## f. Graphical Representation - **Axes:** - Horizontal: Quantity (Q) - Vertical: Price (P) - **Demand Curve:** Starts high at \( (150, 3) \) and ends at \( (30, 15) \). - **Supply Curve:** Starts low at \( (30, 3) \) and ends at \( (150, 15) \). - **Equilibrium Point:** \( (90, 9) \). ### Graph Sketch ``` | | / (Supply) | / | / |-----------/---------------- | / | / | / (Demand) | +--------+----------------- Q ``` - Mark the intersection as **Equilibrium (Q=90, P=9)**. --- Let me know if you need additional details or explanations!