Each firm's variable cost is 12q². The equation for each firm's average total cost is (50 + 12q²) / q. The average total cost is at its minimum when the quantity each firm produces equals 10.
Each firm's variable cost can be calculated by subtracting the fixed cost from the total cost. In this case, the fixed cost is the constant term in the total cost equation, which is 50. So, each firm's variable cost is 12q2.
The equation for each firm's average total cost can be obtained by dividing the total cost by the quantity produced. Therefore, the equation for average total cost is (50 + 12q2) / q.
The average total cost is at its minimum when the marginal cost is equal to the average total cost. From the table provided, we can see that the marginal cost is 10 at quantity 10. Therefore, the average total cost is also 10 at that quantity.