Ifis the total cost of producing a quantityof some product, the average cost is the total cost divided by the quantity,

and the marginal cost is the increase in the total cost as a result of producing one more of the product.

In practice, the marginal cost is taken to be the slope of the cost function at

A typical cost finction is shown below.

The total cost increases quite quickly at first, as fixed costs – costs regardless of the level of production – must be met. At a certain point, economies of scale become significant, and as production increases further, capacity constraints become significant, leading to a rapid increase in the cost function as more investment must be made to increase production further.

Of special interest to manufacturers is the point at which the average cost is miniminized. On the diagram below the average cost is the slope of the line from the origin to the point

The slope, and so the average cost, is a minimum when average cost equals marginal cost, as shown below.

We can find the output that minimises the average cost using the equation

Example: A factory has a cost functionFindthat minimises the average cost.

We solve

hence