## Calculating Profits and Losses

### Learning Objectives

• Describe a firm’s profit margin
• Use the average cost curve to calculate and analyze a firm’s profits and losses
• Identify and explain the firm’s break-even point

## Profits and Losses with the Average Cost Curve

Does maximizing profit (producing where MR = MC) imply an actual economic profit? The answer depends on firm’s profit margin (or average profit), which is the relationship between price and average total cost. If the price that a firm charges is higher than its average cost of production for that quantity produced, then the firm’s profit margin is positive and it is earning economic profits. Conversely, if the price that a firm charges is lower than its average cost of production, the firm’s profit margin is negative and it is suffering an economic loss. You might think that, in this situation, the farmer may want to shut down immediately. Remember, however, that the firm has already paid for fixed costs, such as equipment, so it may make sense to continue to produce and incur a loss. Figure 1 illustrates three situations: (a) where at the profit maximizing quantity of output (where P = MC), price is greater than average cost, (b) where at the profit maximizing quantity of output (where P = MC), price equals average cost, and (c) where at the profit maximizing quantity of output (where P = MC), price is less than average cost. Figure 1. Price and Average Cost at the Raspberry Farm. In (a), price intersects marginal cost above the average cost curve. Since price is greater than average cost, the firm is making a profit. In (b), price intersects marginal cost at the minimum point of the average cost curve. Since price is equal to average cost, the firm is breaking even. In (c), price intersects marginal cost below the average cost curve. Since price is less than average cost, the firm is making a loss.

First consider a situation where the price is equal to $5 for a pack of frozen raspberries. The rule for a profit-maximizing perfectly competitive firm is to produce the level of output where Price= MR = MC, so the raspberry farmer will produce a quantity of approximately 85, which is labeled as E’ in Figure 1(a). The firm’s average cost of production is labeled C’. Thus, the firm’s profit margin is the distance between E’ and C’, and it is positive. The firm is making money, but how much? Remember that the area of a rectangle is equal to its base multiplied by its height. The farm’s total revenue at this price will be shown by the rectangle from the origin over to a quantity of 85 packs (the base) up to point E’ (the height), over to the price of$5, and back to the origin. The average cost of producing 85 packs is shown by point C’ or about $3.50. Total costs will be the quantity of 85 times the average cost of$3.50, which is shown by the area of the rectangle from the origin to a quantity of 90, up to point C, over to the vertical axis and down to the origin. The difference between total revenues and total costs is profits. Thus, profits will be the blue shaded rectangle on top.

We calculate this as:

$\begin{array}{lll}\text{profit}& =& \text{total revenue}-\text{total cost}\\& =& \left(85\right)\left(\5.00\right)-\left(85\right)\left(\3.50\right)\\& =& \170\end{array}$

Or, we can calculate it as:

$\begin{array}{lll}\text{profit}& =& \text{(price}-\text{average cost)}\times \text{quantity}\\ & =& \left(\5.00-\3.50\right) \times 85\\ & =& \170\end{array}$

### Watch It

Watch this video for more practice solving for the profit-maximizing point and finding total revenue using a table.

### Try It

Play the simulation below multiple times to practice applying these concepts and to see how different choices lead to different outcomes.

### Try It

These questions allow you to get as much practice as you need, as you can click the link at the top of the first question (“Try another version of these questions”) to get a new set of questions. Practice until you feel comfortable doing the questions.

### Glossary

break-even point:
the level of output where price just equals average total cost, so profit is zero
profit margin:
at any given quantity of output, the difference between price and average total cost; also known as average profit