Perfect Competition

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:
Profit=TotalrevenuesTotalcost=(Priceperunit×Quantityproduced)(Averagecostperunit×Quantityproduced)=(PriceperunitAveragecostperunit)×Quantityproduced\begin{array}{l}\mathrm{Profit}\;=\;\mathrm{Total}\;\mathrm{revenues}\;-\;\mathrm{Total}\;\mathrm{cost}\\\;\;\;\;\;\;\;\;\;\;\;=\;(\mathrm{Price}\;\mathrm{per}\;\mathrm{unit}\;\times\;\mathrm{Quantity}\;\mathrm{produced})\;-\;(\mathrm{Average}\;\mathrm{cost}\;\mathrm{per}\;\mathrm{unit}\;\times\;\mathrm{Quantity}\;\mathrm{produced})\\\;\;\;\;\;\;\;\;\;\;\;=\;(\mathrm{Price}\;\mathrm{per}\;\mathrm{unit}\;-\;\mathrm{Average}\;\mathrm{cost}\;\mathrm{per}\;\mathrm{unit})\;\times\;\mathrm{Quantity}\;\mathrm{produced}\end{array}
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 $1×80=$80\$1\;\times\;80=\$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 $0.60×80=$48\$0.60\;\times\;80\;=\;\$48 . So, profit in this case is equal to $80$48=$32\$80\;-\;\$48\;=\;\$32 .

Economic Profit in the Short Run

The factors affecting the firm in perfect competition are marginal cost (MC), marginal revenue (MR), price (P), quantity (Q), and average total cost (ATC). The firm will always choose an output where marginal revenue equals marginal cost. If the market price for the good is above average total cost, the firm will make a profit in the short-run. In the numerical example, the firm is producing 80 candy bars, and selling them for $1 a bar ($80 in total revenue). The average cost per bar at this production level is 60 cents, so total cost is $48. The shaded area represents a profit of $32 (Total revenue - Total cost = $80 - $48 = $32 profit).
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 (PATC)×Q(\mathrm P\;-\;\mathrm{ATC})\;\times\;\mathrm 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 $0.40×60=$24\$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 $0.55×60=$33\$0.55\;\times\;60\;=\;\$33 . That makes the profit equal to $24 – $33 = –$9, meaning the company is operating at a loss.

Economic Loss in the Short Run

If the market price for the good is below average total cost (ATC), there will be a loss in the short-run. In the numerical example, the firm is producing 60 candy bars, and selling them for $0.40 a bar ($24 in total revenue). The average cost per bar at this production level is $0.55, so total cost is $33. The shaded area represents a loss of $9 (Total revenue - Total cost = $24 - $33 = -$9, or $9 loss).
As in the previous example, another way to calculate that profit would be to multiply the difference between price and average total cost by the quantity produced, using the formula (PATC)×Q(\mathrm P\;-\;\mathrm{ATC})\;\times\;\mathrm Q . The difference between the price of $0.40 and the average total cost of $0.55 is -$0.15. Multiplying -$0.15 by the quantity produced, 60 candy bars, once again gives a profit earned of -$9. In a third case, (after a period of entry and exit) the price is $0.50 per bar and the average cost per bar is also $0.80. The production level where marginal revenue and marginal cost are equal is 70 units. This is a point of zero economic profit (also known as the break even point). Total revenue minus total cost would equal zero, and price (P) per bar minus average cost (AC) per bar would also equal zero. At this point, the company is breaking even in terms of economic profit, and there is no incentive for this firm or any other in the market to enter or exit.

Zero Economic Profit in the Short Run

This graph shows the factors affecting the firm in perfect competition: marginal cost (MC), marginal revenue (MR), price (P), quantity (Q), and average total cost (ATC). In the long run, the equilibrium price and quantity in a perfectly competitive market occur when marginal cost equals marginal revenue at the minimum average total cost. In the numerical example, total revenue is $56 and total cost is $56 (both are $0.80 times 70 units). Given the market price and cost structure, the firm is making zero economic profit. This is a long-run equilibrium for perfectly competitive markets, as there is no incentive for firms to enter or exit the market.

Profit and Loss Calculations in the Candy Bar Market

Market Price of Candy Bar $1.00 Market Price of Candy Bar $0.40
Marginal revenue $1.00 $0.40
Quantity produced and sold 80 60
Marginal cost $1.00 $0.40
Total revenue $80 ($1.00 × 80) $25 ($0.40 × 60)
Average cost $0.60 $0.55
Total cost $48 ($0.60 × 80) $33 ($0.55 × 60)
Profit $32 ($80 – $48) –$9 ($24 – $33)

The formula for calculating profit or loss is Revenueperunit×UnitssoldCostperunit×Unitsproduced\mathrm{Revenue}\;\mathrm{per}\;\mathrm{unit}\;\times\;\mathrm{Units}\;\mathrm{sold}\;-\;\mathrm{Cost}\;\mathrm{per}\;\mathrm{unit}\;\times\;\mathrm{Units}\;\mathrm{produced} . (The cost per unit rises with fewer units produced because of the costs of beginning production.) A positive figure represents a profit, and a negative figure represents a loss.

Shutting Down in the Short Run

Experiencing a loss does not necessarily mean a company should shut down production. Whether to shut down depends on whether revenue is great enough to cover the average variable cost of production.
In certain situations it makes economic sense for a firm to shut down production of a product immediately. Operating at a loss does not necessarily mean that shutting down is the best option; whether or not to shut down depends on how revenue compares with variable costs. A variable cost is the cost of variable inputs, which changes as output changes, such as labor and the cost of materials used for manufacture. (This is in contrast to fixed costs. A fixed cost is the cost of fixed inputs, which does not change as output changes, such as rent and infrastructure costs.) The question of whether a company operating at a loss should shut down production depends on whether the company is still able to cover and exceed its variable costs with the revenue from additional production.
In a perfectly competitive market, a producer breaks even at the price point where the marginal cost curve (MC) intersects the average total cost (ATC) curve (P1). Below that price point the producer operates at a loss, but should still operate when price is above the shutdown point (P2), where the marginal cost is equal to the average variable cost (AVC). Below the shutdown point the producer minimizes loss by ending production.
Total costs for a company are equal to the sum of variable costs and fixed costs. Fixed costs are assumed to stay the same at every level of production, whereas variable costs increase as output increases. Because the average cost per unit of production takes both fixed and variable costs into consideration, a firm can earn more revenue per unit of production than the variable cost of producing that unit and still be operating at a loss. In that situation, it makes sense for a firm to continue producing, as over time the revenue earned over the amount of variable costs will cover more and more of the fixed costs. When the price of a good is greater than that good's variable costs (the costs the firm incurs by producing that good), that means the firm is covering its variable costs and some of its fixed costs even if the price is less than the total cost of producing that good. However, if the firm is earning less revenue per unit of production than the variable cost of producing that unit, it makes more sense for the firm to shut down production. The "shutdown rule" for a firm in the short term is that the firm should stop production of a good when the price of that good is less than the average variable cost. For example, suppose a candy bar company pays $1,000 per month for rent, insurance, and other fixed costs. Suppose additionally that the candy bars it produces have a variable cost of $0.50 per unit, and the market price for candy bars is $1 per unit. The company has determined, by setting marginal revenue equal to marginal cost, that to maximize profit it must produce 500 candy bars per month; producing any other number of candy bars would result in less profit. After producing these 500 candy bars and selling them at the market price of $1 per unit, the firm's total revenue per month equals $1×500=$500permonth\$1\;\times\;500\;=\;\$500\;\mathrm{per}\;\mathrm{month} . The variable cost per month at the level of 500 candy bars equals $0.50×500=$250permonth\$0.50\;\times\;500\;=\;\$250\;\mathrm{per}\;\mathrm{month} . The firm's total costs per month would thus be equal to $1,000(fixedcost)+$250(variablecosts)=$1,250\$1,000\;(\mathrm{fixed}\;\mathrm{cost})\;+\;\$250\;(\mathrm{variable}\;\mathrm{costs})\;=\;\$1,250 . This results in a loss for the company of $750 per month ($500 total revenue – $1,250 total costs = -$750). So, it might be concluded that because the business is operating at a loss, it should shut down production to reduce variable costs to zero. However, if the business shuts down, revenue also falls to zero while fixed costs remain. So, in that case, the firm would suffer losses of $1,000 per month ( $0totalrevenue$1,000totalcosts=$1,000\$0\;\mathrm{total}\;\mathrm{revenue}\;-\;\$1,000\;\mathrm{total}\;\mathrm{costs}\;=\;-\$1,000 ). Despite operating at a loss, the company should not shut down production. Continuing to produce and sell its product minimizes the loss the company suffers. The loss created by shutting down (-$1,000 per month) would be greater than the loss of staying in business (-$750 per month).

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.
In a perfectly competitive market, the supply curve is the same as the part of the marginal cost curve (MC) above the point of intersection with the average variable cost curve. This is the case because a firm maximizes profits by producing output at a quantity where the price is equal to the marginal cost.
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.