When the average revenue is equal to the average total cost, it follows that the total revenue is also equal to the total cost.

The average total cost is calculated as:

• ATC=TCQATC=TCQ

Thus, the total cost can be expressed as:

• TC=ATC∗QTC=ATC∗Q

And the average revenue is calculated as:

• AR=TRQAR=TRQ

Thus, the total revenue can be expressed as:

• TR=AR∗QTR=AR∗Q

Profit is calculated as:

• ∏=TR−TC∏=TR−TC

Therefore:

• ∏=AR∗Q−ATC∗Q∏=AR∗Q−ATC∗Q

• ∏=AR∗Q−ATC∗Q∏=AR∗Q−ATC∗Q

If the averae revenue is equal to the average total cost, then the profit is equal to zero.

• 0=AR∗Q−ATC∗Q0=AR∗Q−ATC∗Q

At zero profit, the total cost must be equal to the total revenue.

• AR∗Q=ATC∗QAR∗Q=ATC∗Q

• TR=TCTR=TC

The Average Revenue and Average Total Cost:

The average revenue is the revenue that is earned per unit of output that is sold. It is calculated by dividing the total revenue by the total output sold. The average total cost is the cost incurred per unit of output sold. It is calculated by dividing the total cost by the total output produced.