Describe the meaning of the slope of the demand function, in the context of the price and demand for widgets

The slope of the demand function represents the rate at which the quantity demanded changes in response to a change in price. In the context of the price and demand for widgets, the slope indicates how sensitive the quantity demanded is to price changes.

### Interpretation of the Slope:

In the demand function $ Q = -120P + 6600 $, the slope is $-120$. Here's what this means:

1. **Rate of Change**: For every 1 dollar increase in the price of a widget, the quantity demanded decreases by 120 widgets. Conversely, for every 1 dollar decrease in the price, the quantity demanded increases by 120 widgets.
2. **Price Sensitivity**: The slope's negative sign indicates an inverse relationship between price and quantity demanded, which is typical in demand functions. As the price increases, demand decreases, and vice versa.
3. **Magnitude**: The absolute value of the slope ($120$) measures the magnitude of this sensitivity. A larger absolute value would imply greater sensitivity (i.e., demand changes significantly with price changes), while a smaller absolute value would imply lesser sensitivity.

### Example:

- If the price is increased from $20 to $21:
  - The decrease in demand would be $120 \times (21 - 20) = 120$ widgets.
  - Thus, the new quantity demanded would be $4200 - 120 = 4080$ widgets.

- If the price is decreased from $25 to $24:
  - The increase in demand would be $120 \times (25 - 24) = 120$ widgets.
  - Thus, the new quantity demanded would be $3600 + 120 = 3720$ widgets.

### Conclusion:

The slope of $-120$ in the demand function $ Q = -120P + 6600 $ quantifies how the quantity demanded for widgets responds to changes in price. It indicates that for every dollar increase in price, the demand decreases by 120 widgets, highlighting the inverse relationship between price and demand.

Would you like more details or have any questions?

Here are some additional questions you might find interesting:
1. How would a more elastic demand function affect the slope?
2. What factors could cause the demand function to shift?
3. How would the demand function be used to maximize revenue?
4. What are the implications of a linear demand function in real-world scenarios?
5. How can you calculate the equilibrium price and quantity from this demand function?

**Tip:** When analyzing demand functions, it's essential to consider external factors such as consumer preferences, market competition, and economic conditions that might influence the relationship between price and demand.

Explore the meaning of the slope of the demand function in economics with detailed examples and interpretations. Learn how changes in price affect the quantity demanded of widgets using the demand function formula Q = -120P + 6600.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation