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Profits and Losses With the Average Cost Curve

Profits and Losses with the Average Cost Curve

Does maximizing profit (producing where MR = MC) imply an actual economic profit? The answer depends on 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 will earn profits. Conversely, if the price that a firm charges is lower than its average cost of production, the firm will suffer losses. 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 continue to produce and incur a loss. This figure illustrates three situations: (a) where price intersects marginal cost at a level above the average cost curve, (b) where price intersects marginal cost at a level equal to the average cost curve, and (c) where price intersects marginal cost at a level below the average cost curve.

Price and Average Cost at the Raspberry Farm

The three graphs show how profits are affected depending on where total cost intersects average cost.

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 90, which is labeled as e in figure (a). 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 large shaded rectangle from the origin over to a quantity of 90 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 80 packs is shown by point C or about $3.50. Total costs will be the quantity of 80 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. It should be clear from examining the two rectangles that total revenue is greater than total cost. Thus, profits will be the blue shaded rectangle on top.

It can be calculated as:

\(\begin{array}{lll}\text{profit}& =& \text{total revenue}-\text{total cost}\\ & =& (90)(\text{\$5.00})-(90)(\text{\$3.50})\\ & =& \text{\$135}\end{array}\)

Or, it can be calculated as:

\(\begin{array}{lll}\text{profit}& =& \text{(price}–\text{average cost) × quantity}\\ & =& (\$5.00–\$3.50) × 90\\ & =& \text{\$135}\end{array}\)

Now consider figure (b), where the price has fallen to $3.00 for a pack of frozen raspberries. Again, the perfectly competitive firm will choose the level of output where Price = MR = MC, but in this case, the quantity produced will be 70. At this price and output level, where the marginal cost curve is crossing the average cost curve, the price received by the firm is exactly equal to its average cost of production.

The farm’s total revenue at this price will be shown by the large shaded rectangle from the origin over to a quantity of 70 packs (the base) up to point E (the height), over to the price of $3, and back to the origin. The average cost of producing 70 packs is shown by point C’. Total costs will be the quantity of 70 times the average cost of $3.00, which is shown by the area of the rectangle from the origin to a quantity of 70, up to point E, over to the vertical axis and down to the origin. It should be clear from that the rectangles for total revenue and total cost are the same. Thus, the firm is making zero profit. The calculations are as follows:

\(\begin{array}{lll}\text{profit}& =& \text{total revenue}–\text{total cost}\hfill \\ & =& (70)($3.00)–(70)($3.00)\hfill \\ & =& $0\hfill \end{array}\)

Or, it can be calculated as:

\(\begin{array}{lll}\text{profit}& =& \text{(price}–\text{average cost)}×\text{quantity}\hfill \\ & =& ($3.00–$3.00)×70\hfill \\ & =& $0\hfill \end{array}\)

In this figure (c), the market price has fallen still further to $2.00 for a pack of frozen raspberries. At this price, marginal revenue intersects marginal cost at a quantity of 50. The farm’s total revenue at this price will be shown by the large shaded rectangle from the origin over to a quantity of 50 packs (the base) up to point E” (the height), over to the price of $2, and back to the origin. The average cost of producing 50 packs is shown by point C” or about $3.30. Total costs will be the quantity of 50 times the average cost of $3.30, which is shown by the area of the rectangle from the origin to a quantity of 50, up to point C”, over to the vertical axis and down to the origin. It should be clear from examining the two rectangles that total revenue is less than total cost. Thus, the firm is losing money and the loss (or negative profit) will be the rose-shaded rectangle.

The calculations are:

\(\begin{array}{lll}\text{profit}& =& \text{(total revenue}–\text{total cost)}\hfill \\ & =& (50)($2.00)–(50)($3.30)\hfill \\ & =& –$77.50\hfill \end{array}\)

Or:

\(\begin{array}{lll}\text{profit}& =& \text{(price}–\text{average cost) × quantity}\hfill \\ & =& ($1.75–$3.30) × 50\hfill \\ & =& –$77.50\hfill \end{array}\)

If the market price received by a perfectly competitive firm leads it to produce at a quantity where the price is greater than average cost, the firm will earn profits. If the price received by the firm causes it to produce at a quantity where price equals average cost, which occurs at the minimum point of the AC curve, then the firm earns zero profits. Finally, if the price received by the firm leads it to produce at a quantity where the price is less than average cost, the firm will earn losses. This is summarized in the table below.

If…Then…
Price > ATCFirm earns an economic profit
Price = ATCFirm earns zero economic profit
Price < ATCFirm earns a loss

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