Picture how graphs the Using given values of TU=2Q, 2×1=2  2×2=4  2×3=6           2×4=8           2×5=10 graph TU and MU. identify the stages of utility MU should have + zero and - values.

To graph the Total Utility (TU) and Marginal Utility (MU) based on the given values, we'll follow these steps:

### 1. **Calculate and Graph Total Utility (TU):**
   The Total Utility (TU) is given as \( TU = 2Q \), where \( Q \) is the quantity.

   Given values:
   \[
   \begin{aligned}
   Q = 1 & : TU = 2 \times 1 = 2 \\
   Q = 2 & : TU = 2 \times 2 = 4 \\
   Q = 3 & : TU = 2 \times 3 = 6 \\
   Q = 4 & : TU = 2 \times 4 = 8 \\
   Q = 5 & : TU = 2 \times 5 = 10 \\
   \end{aligned}
   \]

   These values give you the following coordinates for the TU curve:
   - (1, 2)
   - (2, 4)
   - (3, 6)
   - (4, 8)
   - (5, 10)

   These points will form a straight line since TU is a linear function of \( Q \).

### 2. **Calculate and Graph Marginal Utility (MU):**
   Marginal Utility (MU) is the change in Total Utility as the quantity increases by one unit.

   \[
   \begin{aligned}
   MU(Q=1) & = TU(2) - TU(1) = 4 - 2 = 2 \\
   MU(Q=2) & = TU(3) - TU(2) = 6 - 4 = 2 \\
   MU(Q=3) & = TU(4) - TU(3) = 8 - 6 = 2 \\
   MU(Q=4) & = TU(5) - TU(4) = 10 - 8 = 2 \\
   \end{aligned}
   \]

   For this linear case, MU is constant at 2 for all values of \( Q \).

### 3. **Identify Stages of Utility:**
   - **Positive Marginal Utility**: Since MU is constant at 2 for all \( Q \), it is positive throughout. This indicates that each additional unit of \( Q \) increases total utility.
   - **Zero Marginal Utility**: If MU were to reach 0, this would indicate that the total utility has reached its maximum and further increases in \( Q \) do not increase TU.
   - **Negative Marginal Utility**: If MU were negative, it would indicate that additional units of \( Q \) reduce the total utility.

   Since \( MU = 2 \) is constant and positive, the graph only reflects the positive phase of utility, with no zero or negative values in this particular case.

### Graph:
- **TU Curve**: A straight, upward-sloping line starting from (1,2) and ending at (5,10).
- **MU Curve**: A horizontal line at \( MU = 2 \) across the values of \( Q \).

Let me know if you need a visual graph or more details!

### Questions:
1. How does Marginal Utility change when Total Utility is a non-linear function?
2. What happens to the graph of Marginal Utility when Total Utility reaches its maximum?
3. Can Marginal Utility ever be negative, and what does it signify in real-life scenarios?
4. How would the TU and MU curves look if \( TU = Q^2 \) instead of \( TU = 2Q \)?
5. What does the slope of the TU curve represent in the context of utility?

**Tip:** Marginal Utility is the derivative of the Total Utility function concerning quantity, showing how utility changes with an additional unit of consumption.

Learn how to graph Total Utility (TU) and Marginal Utility (MU) using the given function TU = 2Q. Explore the stages of utility, including positive MU throughout. Suitable for advanced high school students studying utility theory.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation