Costs and Profit-Maximizing Output?

Because Profit = Total revenue - Total cost, which can be written as: Profit = (P*Q) - (TC).

Divide by Q (output) to obtain an expression for the average profit:

Avg profit =(P) -(AVC).

If the firm is breaking even, then it is making zero economic profit, so equate the previous expression to zero:

0 = (P) - (AVC), which means that: P=AVC.

In other words, if the firm is breaking even it means that it is making enough revenues to just cover its costs, so it is making zero economic profit. This will happen when price is equal to average cost, not necessarily minimun avg cost.