Introduction:
Average cost and marginal cost are important concepts in economics that help businesses determine their production decisions. Average cost is the total cost divided by the number of units produced, while marginal cost is the additional cost incurred by producing one additional unit. When marginal cost is equal to average cost, it implies that the average cost is constant. This can be explained using a numerical example.

Numerical Example:
Let's consider a hypothetical company that produces widgets. The total cost of producing different quantities of widgets is given below:

- Quantity (Q) = 1: Total Cost (TC) = $10
- Quantity (Q) = 2: Total Cost (TC) = $15
- Quantity (Q) = 3: Total Cost (TC) = $18
- Quantity (Q) = 4: Total Cost (TC) = $20
- Quantity (Q) = 5: Total Cost (TC) = $22

Calculating Marginal Cost:
To calculate marginal cost, we need to determine the change in total cost when one additional unit is produced. We can do this by subtracting the total cost of the previous quantity from the total cost of the current quantity.

- Marginal Cost (MC) = TC(Q) - TC(Q-1)

For example, the marginal cost of producing the second widget would be:

MC(Q=2) = TC(Q=2) - TC(Q=1)
= $15 - $10
= $5

Similarly, we can calculate the marginal cost for all the other quantities.

Calculating Average Cost:
Average cost is obtained by dividing the total cost by the quantity produced.

- Average Cost (AC) = TC(Q) / Q

For example, the average cost of producing the second widget would be:

AC(Q=2) = TC(Q=2) / Q
= $15 / 2
= $7.5

Similarly, we can calculate the average cost for all the other quantities.

Comparing Marginal Cost and Average Cost:
To determine if average cost is constant when marginal cost is equal to it, we need to compare the values of marginal cost and average cost at each quantity.

- Q = 1: MC(Q=1) = $10, AC(Q=1) = $10
- Q = 2: MC(Q=2) = $5, AC(Q=2) = $7.5
- Q = 3: MC(Q=3) = $3, AC(Q=3) = $6
- Q = 4: MC(Q=4) = $2, AC(Q=4) = $5
- Q = 5: MC(Q=5) = $2, AC(Q=5) = $4.4

Conclusion:
From the above comparison, we can see that when marginal cost is equal to average cost, the average cost remains constant. In our example, this occurs at a quantity of 5 widgets, where both marginal cost and average cost are $2. This implies that the additional cost of producing one more widget is equal to the average cost of all the widgets produced so far. When marginal cost is equal to average cost, it suggests that the firm is operating at its efficient scale, where it achieves optimal cost minimization.