## Lessons From Alternative Measures of Cost

### Learning Objectives

• Explain profit margin

Breaking down total costs into fixed cost, marginal cost, average total cost, and average variable cost is useful because each statistic offers its own insights for the firm. Whatever the firm’s quantity of production, total revenue must exceed total costs if it is to earn a profit.

Fixed costs are often sunk costs that, once incurred, cannot be recouped. In thinking about what to do next, sunk costs should typically be ignored, since this spending has already been made and cannot be changed. However, variable costs can be changed, so they convey information about the firm’s ability to cut costs in the present and the extent to which costs will increase if production rises.

## Profit Margin

Businesses often talk about their profit margin (or average profit). Profit margin tells a firm for any level of output are they making money or losing money. Profit is defined as revenues minus costs.

$\text{total profit}=\text{total revenue}-\text{total cost}$

### Finding Average Profit

Starting with the equation for total profit above, if we divide both sides of the total profit equation by quantity, we get average profit:

$\text{average profit}=\frac{\text{total profit}}{\text{quantity produced}}=\frac{\text{total revenue-total cost}}{\text{quantity produced}}$

If we separate the two parts of the right hand side we get:

$\text{average profit}=\frac{\text{total revenue}}{\text{quantity produced}}-\frac{\text{total cost}}{\text{quantity produced}}$

Or, in other words:

$\displaystyle\text{average profit}=\text{average revenue}-\text{average cost}$

But, average revenue is just another name for price, as shown below:

$\displaystyle\text{average revenue}=\frac{\text{price}\times\text{quantity produced}}{\text{quantity produced}}$

$\displaystyle\text{average revenue}=\text{price}$

Substituting this back into the equation for average profit above, we get:

$\text{average profit}=\text{price}-\text{average cost}$

Average profit is the firm’s profit margin. What this means is that if, at a given level of output, the market price is above average cost, average profit and thus total profit, will be positive; in other words, the firm is making money. We’ll be able to show this graphically beginning in the next module, but for now, let’s look at it numerically. If, for a given level of output, price is below average cost, then profits will be negative, and the firm is losing money.

Suppose a firm is producing 100 units of output at a price of $5 each. Suppose the firm’s average cost is$3 per unit of output.  Since the $5 price is greater than the$3 average cost, we can immediately tell that the firm’s profit margin is $2 for each of the 100 units of output produced and sold. Thus, the firm’s total profit is$2 per unit times 100 units = $200. Alternatively, we could compute the total revenue as price times quantity =$5 per unit x 100 units = $500. Similarly, we could compute the total cost as average cost times quantity =$3 per unit x 100 units = $300. Thus, the firm’s total profit is total revenue minus total cost =$500 minus $300 =$200, which you’ll note is the same answer we got by using the profit margin.

## Cost Pattern Variety

The pattern of costs varies among industries and even among firms in the same industry. Some businesses have high fixed costs, but low marginal costs. Consider, for example, an Internet company that provides medical advice to customers. Such a company might be paid by consumers directly, or perhaps hospitals or healthcare practices might subscribe on behalf of their patients.

Setting up the website, collecting the information, writing the content, and buying or leasing the computer space to handle the web traffic are all fixed costs that must be undertaken before the site can work. However, when the website is up and running, it can provide a high quantity of service with relatively low variable costs, like the cost of monitoring the system and updating the information.

In this case, the total cost curve might start at a high level, because of the high fixed costs, but then might appear close to flat, up to a large quantity of output, reflecting the low variable costs of operation. If the website is popular, however, a large rise in the number of visitors will overwhelm the website, and increasing output further could require a purchase of additional computer space.

For other firms, fixed costs may be relatively low. For example, consider firms that rake leaves in the fall or shovel snow off sidewalks and driveways in the winter. For fixed costs, such firms may need little more than a car to transport workers to homes of customers and some rakes and shovels. Still other firms may find that diminishing marginal returns set in quite sharply. If a manufacturing plant tried to run 24 hours a day, seven days a week, little time remains for routine maintenance of the equipment, and marginal costs can increase dramatically as the firm struggles to repair and replace overworked equipment.

Every firm can gain insight into its task of earning profits by dividing its total costs into fixed and variable costs, and then using these calculations as a basis for average total cost, average variable cost, and marginal cost. However, making a final decision about the profit-maximizing quantity to produce and the price to charge will require combining these perspectives on cost with an analysis of sales and revenue, which in turn requires looking at the market structure in which the firm finds itself. Before we turn to the analysis of market structure in other modules, we will analyze the firm’s cost structure from a long-run perspective.

### gLossary

profit margin:
at a given level of output, the difference between price and average cost; also known as average profit
sunk costs:
fixed costs that, once incurred, cannot be recouped

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