Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![### Average Cost Function Calculation
**Problem Statement:**
Find the average cost function if cost and revenue are given by:
\[ C(x) = 127 + 8.6x \]
and
\[ R(x) = 3x - 0.04x^2 \]
**Solution:**
The average cost function \( \overline{C}(x) \) is calculated as:
\[ \overline{C}(x) = \frac{C(x)}{x} \]
where \( C(x) \) is the total cost function.
Given that:
\[ C(x) = 127 + 8.6x \]
The average cost function is:
\[ \overline{C}(x) = \frac{127 + 8.6x}{x} \]
### Final Result:
The average cost function is:
\[ \overline{C}(x) = \frac{127 + 8.6x}{x} \]
For further learning, you can analyze how changes in \( x \), the number of units produced, affect the average cost function. This is a fundamental concept in cost analysis in economics and helps in determining the most efficient level of production.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1a0a3e2b-c166-4815-91b8-41dfa54aca6a%2F0dcbcb82-f489-4b55-b724-199fb4cdf8b7%2Fks8o3qb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Average Cost Function Calculation
**Problem Statement:**
Find the average cost function if cost and revenue are given by:
\[ C(x) = 127 + 8.6x \]
and
\[ R(x) = 3x - 0.04x^2 \]
**Solution:**
The average cost function \( \overline{C}(x) \) is calculated as:
\[ \overline{C}(x) = \frac{C(x)}{x} \]
where \( C(x) \) is the total cost function.
Given that:
\[ C(x) = 127 + 8.6x \]
The average cost function is:
\[ \overline{C}(x) = \frac{127 + 8.6x}{x} \]
### Final Result:
The average cost function is:
\[ \overline{C}(x) = \frac{127 + 8.6x}{x} \]
For further learning, you can analyze how changes in \( x \), the number of units produced, affect the average cost function. This is a fundamental concept in cost analysis in economics and helps in determining the most efficient level of production.
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