Final answer:
The profit of the firm is $200. The marginal cost is -$192. The average variable cost is $6. The efficient scale of the firm is exactly 100 units.
Step-by-step explanation:
A profit-maximizing firm in a competitive market will produce a quantity of output where marginal cost is equal to the market price, since this is where profits are highest. In this case, the firm is producing 100 units of output. The firm has an average revenue of $10, which is also the market price. The firm has an average total cost of $8. To calculate profit, we subtract the average total cost from the average revenue and multiply the result by the quantity of output:
Profit = (Average revenue - Average total cost) * Quantity of output
Profit = ($10 - $8) * 100 = $200
The marginal cost is the additional cost of producing one more unit of output. It can be calculated by finding the change in total cost when the quantity of output is increased by one unit:
MC = Change in Total cost / Change in Quantity of output
In this case, since the firm is producing 100 units of output, the marginal cost is equal to total cost minus fixed cost:
MC = Average total cost - Fixed cost
MC = $8 - $200 = -$192
The average variable cost is the variable cost per unit of output, which can be calculated by subtracting the average fixed cost from the average total cost:
AVC = Average total cost - Average fixed cost
AVC = $8 - (Fixed cost / Quantity of output)
AVC = $8 - ($200 / 100) = $8 - $2 = $6
The firm's efficient scale is the quantity of output where average total cost is at its minimum. In this case, the firm's average total cost is $8, which is at its minimum when producing 100 units of output. Therefore, the efficient scale of the firm is exactly 100 units.