Complete the problem by using the accompanying figure, which shows a supply function and a demand function. (Assume price is measured in dollars.)

The q p-coordinate plane is given. There 4 points and 2 lines on the graph.
Point A is at (0, 400), point B is at (0, 250), point C is at (300, 250), and point D is at (0, 100).
The first line begins at p = 100 on the positive p-axis at point D, goes up and right, passes through the point C crossing the second line, and exits the window in the first quadrant.
The second line begins at p = 400 on the positive p-axis at point A, goes down and right, passes through the point C crossing the first line, and exits the window in the first quadrant.
(a) Label each function as "demand" or "supply."
function 1
---Select---
function 2
---Select---

(b) Which of the labeled points is the equilibrium point?
point A
point B
point C
point D

Determine the price and quantity at which market equilibrium occurs.
price    	$
quantity
units

Let's break down the given problem step-by-step:

### Part (a) - Identifying the demand and supply functions:

You are given two lines:
1. **Line 1:** Begins at point $ D(0, 100) $ and passes through $ C(300, 250) $.
2. **Line 2:** Begins at point $ A(0, 400) $ and passes through $ C(300, 250) $.

- The **supply function** typically has a positive slope, indicating that as the quantity $ q $ increases, the price $ p $ also increases. This reflects the fact that suppliers are willing to supply more at higher prices.
- The **demand function** usually has a negative slope, meaning that as the price $ p $ decreases, the quantity $ q $ demanded increases. This is because consumers are willing to buy more at lower prices.

Based on this:
- **Function 1** (which starts at $ D(0, 100) $ and passes through $ C(300, 250) $) has a **positive slope**, so it is the **supply function**.
- **Function 2** (which starts at $ A(0, 400) $ and passes through $ C(300, 250) $) has a **negative slope**, so it is the **demand function**.

So:
- **Function 1 is the supply function.**
- **Function 2 is the demand function.**

### Part (b) - Identifying the equilibrium point:

The **equilibrium point** is where the supply and demand curves intersect. This represents the price and quantity where the amount suppliers are willing to supply equals the amount consumers are willing to purchase.

From the given description, the two curves intersect at **Point C** $(300, 250)$.

- **Point C is the equilibrium point.**

### Part (c) - Determining the price and quantity at equilibrium:

At the equilibrium point $ C(300, 250) $:
- The price is the $ p $-coordinate, which is **$250**.
- The quantity is the $ q $-coordinate, which is **300 units**.

### Final Answer:

- **(a)**
  - Function 1: Supply
  - Function 2: Demand
- **(b)**
  - The equilibrium point is **Point C**.
- **Price at equilibrium:** **$250**
- **Quantity at equilibrium:** **300 units**

Would you like more details or have any further questions?

---

Here are 5 related questions to expand on this concept:
1. How do you derive the equations for the supply and demand curves from the graph?
2. What happens to equilibrium if the supply curve shifts due to external factors?
3. How would you calculate consumer surplus using this graph?
4. What does it mean for the market if the price is set above or below the equilibrium price?
5. How can you use algebra to solve for equilibrium algebraically instead of graphically?

**Tip:** In economics, equilibrium represents an efficient market where there is no shortage or surplus. Understanding how shifts in supply or demand affect this point is crucial for analyzing market dynamics.

Complete the problem by using the accompanying figure, which shows a supply function and a demand function. (Assume price is measured in dollars.)

The q p-coordinate plane is given. There are 4 points and 2 lines on the graph.
Point A is at (0, 400), point B is at (0, 250), point C is at (300, 250), and point D is at (0, 100).
The first line begins at p = 100 on the positive p-axis at point D, goes up and right, passes through the point C crossing the second line, and exits the window in the first quadrant.
The second line begins at p = 400 on the positive p-axis at point A, goes down and right, passes through the point C crossing the first line, and exits the window in the first quadrant.
(a) Label each function as 'demand' or 'supply.'
(b) Which of the labeled points is the equilibrium point?
Determine the price and quantity at which market equilibrium occurs.

Explore how to solve a supply and demand problem by identifying the equilibrium point using a graphical representation. Learn how to distinguish between the supply and demand functions, and find the price and quantity at market equilibrium. Suitable for Grades 10-12 economics students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation