There are a number of different ways to measure the costs of production, and some costs are related in interesting ways. Let's look at the way in which average cost and marginal cost are related.

To start off, let's quickly define the two. Average cost, also called average total cost, is the total cost divided by quantity produced. Marginal cost is the incremental cost of the last unit produced.

### Introduction to Average and Marginal Cost

### A Helpful Analogy for the Average and Marginal Cost Relationship

The relationship between average cost and marginal cost can be easily explained via a simple analogy. Rather than think about costs, let's think about grades on a series of exams for a second.

Let's assume that your current average grade in a course is a score of 85. If you were to get a score of 80 on your next exam, this score would pull your average down, and your new average score would be something less than 85. Put another way, your average score would be decreasing.

If, instead, you were to get a score of 90 on your next exam, this score would pull your average up, and your new average score would be something greater than 85. Put another way, your average score would be increasing.

Lastly, if you were to get a score of exactly 85 on your next exam, your average score would not change and would remain at 85.

Returning to the context of production costs, think of average cost for a particular production quantity as the current average grade and marginal cost at that quantity as the grade on the next exam.

Granted, one typically thinks of marginal cost at a given quantity as the incremental cost associated with the last unit produced, but marginal cost at a given quantity can also be interpreted as the incremental cost of the next unit. This distinction becomes irrelevant when calculating marginal cost using very small changes in quantity produced.

Therefore, following the grade analogy, average cost will be decreasing in quantity produced when marginal cost is less than average cost and average cost will be increasing in quantity when marginal cost is greater than average cost. Furthermore, average cost will be neither decreasing nor increasing when marginal cost at a given quantity is equal to average cost at that quantity.

### The Shape of the Marginal Cost Curve

The production processes of most businesses eventually result in diminishing marginal product of labor and diminishing marginal product of capital, which means that most businesses reach a point of production where each additional unit of labor or capital isn't as useful as the one that came before.

Once diminishing marginal products are reached, the marginal cost of producing each additional unit will be greater than the marginal cost of the previous unit. In other words, the marginal cost curve for most production processes will eventually slope upwards, as shown above.

### The Shape of the Average Cost Curves

Because average cost includes fixed cost whereas marginal cost does not, it is generally the case that average cost is greater than marginal cost at small quantities of production.

This implies that average cost generally takes on a U-type shape, since average cost will be decreasing in quantity as long as marginal cost is less than average cost and then will start increasing in quantity when marginal cost becomes greater than average cost.

This relationship also implies that average cost and marginal cost intersect at the minimum of the average cost curve. This is because average cost and marginal cost come together when average cost has done all of its decreasing but hasn't started increasing yet.

### The Relationship Between Marginal Cost and Average Variable Cost

A similar relationship holds between marginal cost and average variable cost. When marginal cost is less than average variable cost, average variable cost is decreasing. And, when marginal cost is greater than average variable cost, average variable cost is increasing.

In some cases, this also means that average variable cost takes on a U-shape, though this is not guaranteed since neither average variable cost nor marginal cost contain a fixed cost component.

### Average Cost for a Natural Monopoly

Because marginal cost for a natural monopoly doesn't increase in quantity as it eventually does for most firms, average cost takes on a different trajectory for natural monopolies than for other firms.

Specifically, the fixed costs involved with a natural monopoly imply that average cost is greater than marginal cost for small quantities of production. And, the fact that marginal cost for a natural monopoly doesn't increase in quantity implies that average cost will be greater than marginal cost at all production quantities.

This means that, rather than being U-shaped, average cost for a natural monopoly is always declining in quantity, as shown above.