In the vault section, we analyzed benefit maximization by researching graphs. In this section, we will analyze a purely competitive firm’s benefit maximizing quantity based on data native a table.

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The Firm’s Costs

Let’s look in ~ the following hypothetical firm’s price data.

 Quantity Total solved Cost Total variable Cost Total Cost Marginal Cost Average change Cost Average complete Cost 0 \$50 \$0 \$50 – – – 1 50 30 80 \$30 \$30 \$80 2 50 50 100 20 25 50 3 50 60 110 10 20 36.67 4 50 68 118 8 17 29.50 5 50 80 130 12 16 26 6 50 100 150 20 16.67 25 7 50 130 180 30 18.57 25.71 8 50 165 215 35 20.63 26.88 9 50 220 270 55 24.44 30

The Firm’s Revenue

Case A: The industry Price is above the Firm’s Average full CostLet’s assume that the industry price is \$31. Due to the fact that this for sure is a purely competitive firm, marginal revenue and also average revenue are additionally \$31. Looking in ~ the table above, we deserve to see that at assorted quantities, the price above the average full cost. This method that at this quantities, the firm will make a profit.

The Firm’s profit Maximizing Quantity

In the previous section, us concluded the a firm maximizes its revenues where marginal revenue amounts to marginal cost. Since we have actually discrete data native a table fairly than a consistent curve, we notification that in ~ no amount does the marginal revenue same the marginal cost. In this case, we require to recognize the amount at i m sorry the marginal expense comes closest to the marginal revenue, without exceeding it. If there are values because that marginal cost early on in the table, which also approach marginal revenue, perform not pick these. Just the marginal cost values in or draw close the increasing part of the marginal cost column room relevant. We additionally have to make sure that the price is over the firm’s lowest typical variable cost; otherwise, it is far better to shut down. The shortest variable price in the table above is \$16, therefore we deserve to see that the price that \$31 is, indeed, over the firm’s typical variable cost. We do not need to shut down. At a quantity of 7, the marginal expense is \$30, is closest come our marginal revenue the \$31, and also the marginal expense values are increasing. This satisfies our profit maximizing rule. Therefore, the firm maximizes earnings at amount 7. If the certain produces 7 products, the will have the many profit compared to any kind of other quantity produced.

The golden Rule of benefit Maximizing or lose Minimizing

Let’s summary the over information.

 A that company maximizes its profits or minimizes that losses at a amount where MC equates to MR, or where a non-falling MC comes as close as feasible to (without exceeding) MR. The price must be over the firm’s lowest typical variable expense for the certain to produce this quantity. If the price is much less than the firm’s shortest AVC, then it need to shut down (produce a quantity of zero) for a if (until conditions improve).

Case B: The market Price is below the Firm’s Average total Cost, but over the Firm’s typical Variable Cost

Let’s assume that industry price drops come \$21. This method that the firm’s typical revenue and also marginal revenue room \$21, together well.

Looking at the table above and making use of the profit maximization/loss minimization rule, we see that at quantity 6, the marginal expense comes closest come the marginal revenue. The marginal cost is in the increase sloping part of the curve. The price is above the lowest typical variable cost, therefore we perform not need to shut down. At quantity 6, the firm’s full profit equals \$126 – \$150 = -\$24. (\$126 is the total revenue: ns x Q = \$21 times 6; \$150 is the cost at amount 6). Thus, the certain is operating at a loss. However, developing 6 systems is much better than shutting down. If we shut down, our loss would be \$50 (the firm’s solved cost). A firm can incur losses throughout some years. However, if losses persist, it will go the end of company in the long run.

Case C: The market Price is below the Firm’s Average complete Cost and below the Firm’s average Variable Cost

Let’s assume that the market price decreases to \$15. Exactly how many products should the firm produce in order to maximize profits or minimize losses?

In this case, we notice that the price is listed below the firm’s lowest median variable cost. Therefore, it is finest to shut down and produce a amount of zero. The marginal cost comes closest come the marginal revenue at amount 5. However, once you calculate total revenue minus total costs, you arrive at a lose of \$55 (\$75 – \$130). When the certain produces in ~ a quantity of zero, its loss is only \$50 (its solved costs).

Profit Maximizing Using complete Revenue and Total expense Data

Instead of utilizing the gold rule of benefit maximization disputed above, girlfriend can likewise find a firm’s maximum benefit (or minimum loss) by feather at full revenue and total cost data. Merely calculate the firm’s total revenue (price time quantity) at each quantity. Then subtract the firm’s total cost (given in the table) at each quantity. At a industry price of \$31, the firm’s total revenue amounts to \$217 in ~ a amount of 7 (\$31 time 7), and also its full cost is given at \$180. Therefore, the firm’s complete profit in ~ this amount is \$37. If you carry out the exact same for the other quantities, girlfriend will find that developing 7 assets results in the greatest profit for the firm.

Drawing Cost and also Revenue Data in a Graph

If we use a industry price of \$31 and also the price data native the table above, and also plot this data, we get In the over example, the firm maximizes its profits once it to produce 7 units, due to the fact that it is whereby MC equates to MR; ATC at this amount is \$25.71.

The vertical distance from the need curve to the average full cost curve represents the firm’s mean profit (price minus average total cost). Mean profit times the number of products sold equals complete profit. Thus, the benefit area is the rectangle indigenous the price (\$31) under to the ATC (\$25.71) and throughout to the vertical axis. In ~ the benefit maximizing quantity of 7 products, this is equal to the shaded area (length x width).

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The Shutdown Point

The firm’s shutdown point is wherein its average variable expense is at its shortest value. The firm need to shut down temporarily if the price drops below the shutdown price of \$16. In ~ a price listed below \$16 the certain not only loses money top top its addressed costs, but likewise on its variable costs. If that did operate at a price below \$16, that loss would certainly be greater than if it produced a amount of zero (shutdown).

Video ExplanationFor a video clip explanation of how to calculate the benefit maximizing quantity and profit because that a firm in pure competition, please watch: