### Short Run Total Cost FunctionGiven below is the short run total cost function:\[ TC = 50 + 100Q - 4Q^2 + 2Q^3 \]**Tasks:**1. **Calculate TFC, AVC, AC, and MC** when the firm produces 5 units of output. 2. **Calculate the level of output at which AVC is minimum.**### Explanation of Terms:- **TFC (Total Fixed Cost):** The cost that does not change with the level of output.- **AVC (Average Variable Cost):** The variable cost per unit of output.- **AC (Average Cost):** The total cost per unit of output.- **MC (Marginal Cost):** The cost of producing one more unit of output.### Steps to Solve:1. **Substitute $ Q = 5 $ into the total cost function to find TC.**2. **Calculate TFC by identifying constant terms (independent of Q) in the total cost function.**3. **Determine AVC, AC, and MC using the cost functions derived for TC.**4. **Find the output level that minimizes AVC by setting the derivative of AVC with respect to Q to zero and solving for Q.**Use these steps to analyze cost behaviors and production efficiency.**Note:** Understanding cost functions is crucial in economics to predict how costs change with different levels of production and to make informed decisions.

Total cost is the sum total of cost including the variable and fixed cost, average cost is the, cost…

Given below is the short run total cost function: (2+1=3) TC = 50 + 100Q-4Q2 + 2Q3 Calculate TFC, AVC, AC and MC when the firm produces 5 units of output. Calculate the level of output at which AVC is minimum.

Given below is the short run total cost function: (2+1=3) TC = 50 + 100Q-4Q2 + 2Q3 Calculate TFC, AVC, AC and MC when the firm produces 5 units of output. Calculate the level of output at which AVC is minimum.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

### Short Run Total Cost Function

Given below is the short run total cost function:

\[ TC = 50 + 100Q - 4Q^2 + 2Q^3 \]

**Tasks:**

1. **Calculate TFC, AVC, AC, and MC** when the firm produces 5 units of output.

2. **Calculate the level of output at which AVC is minimum.**

### Explanation of Terms:

- **TFC (Total Fixed Cost):** The cost that does not change with the level of output.
- **AVC (Average Variable Cost):** The variable cost per unit of output.
- **AC (Average Cost):** The total cost per unit of output.
- **MC (Marginal Cost):** The cost of producing one more unit of output.

### Steps to Solve:

1. **Substitute $ Q = 5 $ into the total cost function to find TC.**
2. **Calculate TFC by identifying constant terms (independent of Q) in the total cost function.**
3. **Determine AVC, AC, and MC using the cost functions derived for TC.**
4. **Find the output level that minimizes AVC by setting the derivative of AVC with respect to Q to zero and solving for Q.**

Use these steps to analyze cost behaviors and production efficiency.

**Note:** Understanding cost functions is crucial in economics to predict how costs change with different levels of production and to make informed decisions.

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