# Calculation of Profit or Loss in the Short Run

In a situation of perfect competition, whether a company earns profits or suffers losses depends on whether price is greater or less than the average cost of production.

To maximize profit in perfect competition, a firm must set its production output such that marginal revenue (the income earned by selling one additional unit of a good) is equal to marginal cost (the cost of producing one additional unit of a good). However, maximizing profit does not necessarily mean that economic profit will be earned. That depends on whether or not total revenues are greater or less than total costs. That, in turn, depends on whether the price set by the market for a unit of product is greater or less than the average cost per unit of producing that product incurred by the firm.

The equivalency of these two ways of conceptualizing and calculating profit and loss can be stated in the following way:
\begin{aligned}\text{Profit}&=\text{Total Revenue} -\text{Total Cost}\\&=(\text{Price per Unit} \times \text{Quantity Produced)} - \text{Average Cost per Unit} \times \text{Quantity Produced})\\&=(\text{Price per Unit} - \text{Average Cost per Unit}) \times \text{Quantity Produced} \end{aligned}
Using these equations, when the price per unit is greater than the average cost per unit, the result is a positive number, meaning that the firm is earning profit from selling its goods or services. Conversely, when the price per unit is less than the average cost per unit, the result is a negative number. This means that the firm is operating at a loss, even though it has maximized the amount of possible profit through setting its output levels at the point where marginal revenue is equal to marginal cost. For example, suppose a candy bar company is producing candy bars for which the market price is $1. In a situation of perfect competition, market price is equal to marginal revenue, so the marginal revenue is$1 as well. The candy bar company determines that at this price, its marginal cost equals $1 when it produces and sells 80 candy bars. (Remember, perfect competition assumes a firm will be able to sell all the goods or services it produces if the firm sets its prices equal to the market price.) Because the company is attempting to make marginal revenue equal to marginal cost, it produces and sells exactly 80 candy bars. That makes its total revenue equal to: $\1\times80=\80$ . Suppose that at a production level of 80 candy bars, the average cost of producing each candy bar is$0.60. That makes total cost equal to $\0.60\times80=\48$ . So, profit in this case is equal to $\80-\48=\32$ .

#### Economic Profit in the Short Run

Another way to calculate that profit would be to multiply the difference between price (P) and average total cost (ATC) by the quantity produced (Q), using the formula $(\text {P}-\text{ATC})\times \text{Q}$ . The difference between the price of $1.00 and the average total cost of$0.60 is $0.40. Multiplying$0.40 by the quantity produced, 80 candy bars, once again gives a profit earned of $32. Now suppose the market price drops to$0.40 per candy bar. The candy bar company determines that marginal cost equals $0.40 at a production level of 60 candy bars, so it produces and sells 60 candy bars to maximize profit. That brings in revenue of $\0.40 \times 60 = \24$ . However, at a production level of 60 candy bars, the average cost of producing and selling a candy bar is$0.55. So, the total cost for the company to produce 60 candy bars is $\0.55 \times 60 = \33$ . That makes the profit equal to $\24 -\33 = -\9$, meaning the company is operating at a loss.

### Short-Run Supply Curve of a Firm

In a situation of perfect competition, the supply curve for an individual firm is equal to the marginal cost curve, above a minimum point on the average variable cost curve.
The supply curve for a product is a graphical representation that shows the quantity supplied at different prices, which can also be used to show the maximum amount of a good or service that an individual producer (or the supply side of the market) would be willing to produce. It describes the relationship between that product's price and the quantity of the product produced. It slopes upward because the greater the price, the more of a product a firm will be motivated to make, all other things being equal.
Because a firm maximizes profits by producing output at a quantity where the price is equal to the marginal cost, the marginal cost curve is equal to the supply curve. However, if the revenue earned at a particular price is less than the average variable cost at that price, the company will shut down production to minimize loss. (That point on the marginal cost curve is thus called the shutdown point.) Therefore, the supply curve and the marginal cost curve are only identical above the minimum point on the average variable cost curve where price is equal to or greater than average variable cost.