https://file.aiquickdraw.com/mathbot/file/1729128273681z1ee8qrv.jpg

The image shows a cost function problem related to economics, specifically focusing on total cost (TC) analysis. The cost function given is:

\[
TC = 20Q + 45
\]

Where:
- \( TC \) is the total cost,
- \( Q \) is the quantity of output.

The question asks to determine the following:
a) FC (Fixed Cost),
b) VC (Variable Cost),
c) AVC (Average Variable Cost),
d) AC (Average Cost).

### Solutions:

1. **Fixed Cost (FC):**
   The fixed cost is the constant term in the total cost function. In this case, \( FC = 45 \), because it does not depend on \( Q \).

2. **Variable Cost (VC):**
   The variable cost is the part of the total cost that depends on the output quantity \( Q \). In this case, \( VC = 20Q \).

3. **Average Variable Cost (AVC):**
   The average variable cost is the variable cost per unit of output, calculated by dividing the variable cost by \( Q \):
   \[
   AVC = \frac{VC}{Q} = \frac{20Q}{Q} = 20
   \]

4. **Average Cost (AC):**
   The average cost is the total cost per unit of output, calculated by dividing the total cost by \( Q \):
   \[
   AC = \frac{TC}{Q} = \frac{20Q + 45}{Q} = 20 + \frac{45}{Q}
   \]

Thus, the average cost depends on the quantity \( Q \), and it decreases as \( Q \) increases due to the fixed cost \( \frac{45}{Q} \).

Would you like more detailed explanations on any part of this? Here are 5 follow-up questions for deeper exploration:

1. How does increasing output \( Q \) affect the average cost \( AC \)?
2. What is the economic interpretation of fixed and variable costs in this function?
3. How does the average variable cost relate to the marginal cost in this case?
4. How would the total cost function change if the fixed cost were higher?
5. What happens to the average cost as output \( Q \) approaches infinity?

**Tip:** Remember that fixed costs remain constant regardless of output, while variable costs change with the quantity produced.

The cost function is TC = 20Q + 45. Determine the following:
a) Fixed Cost (FC)
b) Variable Cost (VC)
c) Average Variable Cost (AVC)
d) Average Cost (AC)

Learn how to analyze a cost function with the equation TC = 20Q + 45. This step-by-step solution covers key economic concepts, including Fixed Cost (FC), Variable Cost (VC), Average Variable Cost (AVC), and Average Cost (AC). Ideal for high school economics or business 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