If a firm wished to minimize its cost of production, then what output level should it produce?

If a firm wants to minimize its cost, it should produce a quantity where its average total cost (ATC) is at its minimum. That can be found by graphing the ATC and seeing where it is lowest. It can also be found by calculating the ATC in a table and seeing which quantity level has the lowest ATC. This quantity is also called "productive efficiency" since it is the quantity where the products are the cheapest.

You can also find the productive efficient quantity given a total cost function. Marginal cost (MC) is the rate of change in the total cost function. To find ATC given the total cost function, just divide it by quantity. Then just set MC equal to ATC and solve for quantity and you will also find the cheapest per unit quantity. This works because when the MC is lower than ATC, it pulls the average lower and when MC is above ATC, it pulls the ATC higher. So at the minimum of ATC, it will equal MC.