To analyze the demand function you've provided, \( Q_d = 150 - 50p \), we can look at various aspects of this linear demand equation:

### 1. Understanding the Equation
The demand function \( Q_d = 150 - 50p \) represents the relationship between quantity demanded (\( Q_d \)) and price (\( p \)):
- **Intercept (150)**: When the price \( p \) is zero, the quantity demanded (\( Q_d \)) is 150 units.
- **Slope (-50)**: For each unit increase in price (\( p \)), the quantity demanded (\( Q_d \)) decreases by 50 units.

### 2. Calculating Specific Values
We can calculate the quantity demanded for any given price by substituting values of \( p \) into the equation.

For example:
1. **If \( p = 1 \):**
   \[
   Q_d = 150 - 50 \times 1 = 150 - 50 = 100
   \]
2. **If \( p = 2 \):**
   \[
   Q_d = 150 - 50 \times 2 = 150 - 100 = 50
   \]
3. **If \( p = 3 \):**
   \[
   Q_d = 150 - 50 \times 3 = 150 - 150 = 0
   \]

This result shows that the demand falls to zero when the price reaches 3. Therefore, **the maximum price at which this good can be sold is 3** (the demand would be zero beyond this price).

### 3. Demand Curve Characteristics
Since the slope is negative, this is a downward-sloping linear demand curve, indicating an inverse relationship between price and quantity demanded.

Would you like more details or have questions about this analysis? Here are some related questions for further exploration:

1. How would the demand function change if the intercept or slope were altered?
2. What happens to the quantity demanded if there is a fixed increase in price, say by 1 unit?
3. Can we calculate the price elasticity of demand at specific points on this demand curve?
4. How do we interpret this demand function if we add constraints, like a minimum price?
5. What would the revenue function be for this demand equation?

**Tip:** In linear demand equations, the slope indicates how sensitive quantity demanded is to price changes; a steeper slope shows greater sensitivity.

Explore a detailed analysis of the linear demand function Qd = 150 - 50p, covering concepts in algebra and economics. Learn to interpret the intercept and slope, calculate specific quantity values based on price, and understand demand curve characteristics, including the price at which demand falls to zero. Ideal for students in Grades 10-12.

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