Questions: A firm produces 400 units of output at a total cost of 1,000. If fixed costs are 200, average fixed cost is 10. average variable cost is 2. average total cost is 5. average total cost is 4.

A firm produces 400 units of output at a total cost of 1,000. If fixed costs are 200, average fixed cost is 10. average variable cost is 2. average total cost is 5. average total cost is 4.
Transcript text: A firm produces 400 units of output at a total cost of $\$ 1,000$. If fixed costs are \$200, average fixed cost is $\$ 10$. average variable cost is $\$ 2$. average total cost is $\$ 5$. average total cost is $\$ 4$.
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Solution

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To solve this problem, we need to analyze the cost structure of the firm based on the information provided.

  1. Fixed Costs (FC): The problem states that fixed costs are \$200.

  2. Total Cost (TC): The total cost for producing 400 units is \$1,000.

  3. Average Fixed Cost (AFC): This is calculated as the fixed costs divided by the quantity of output. Given that AFC is \$10, we can verify this: \[ AFC = \frac{FC}{Q} = \frac{200}{400} = \$0.50 \] This calculation shows that the given average fixed cost of \$10 is incorrect.

  4. Average Variable Cost (AVC): This is calculated as the total variable cost divided by the quantity of output. We can find the total variable cost (TVC) by subtracting fixed costs from total costs: \[ TVC = TC - FC = 1000 - 200 = \$800 \] Then, calculate AVC: \[ AVC = \frac{TVC}{Q} = \frac{800}{400} = \$2 \] The given average variable cost of \$2 is correct.

  5. Average Total Cost (ATC): This is calculated as the total cost divided by the quantity of output: \[ ATC = \frac{TC}{Q} = \frac{1000}{400} = \$2.50 \] The given average total costs of \$5 and \$4 are both incorrect.

Summary:

  • The correct average fixed cost is \$0.50, not \$10.
  • The average variable cost is correctly given as \$2.
  • The correct average total cost is \$2.50, not \$5 or \$4.
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