according to the table, what is the average total cost of producing 550 pizzas?

Learning Objectives

• Determine profits and costs by comparing total revenue and total price
• Use marginal acquirement and marginal costs to find the level of output that will maximize the firm's profits

How Perfectly Competitive Firms Make Output Decisions

A perfectly competitive business firm has only one major decision to make—namely, what quantity to produce. To empathize why this is so, consider the basic definition of profit:

[latex]\begin{array}{l}\text{Turn a profit}=\text{Total revenue}-\text{Total toll}\hfill \\ \text{ }=\left(\text{Price}\right)\left(\text{Quantity produced}\right)-\left(\text{Boilerplate cost}\right)\left(\text{Quantity produced}\right)\hfill \stop{array}[/latex]

Since a perfectly competitive firm must accept the cost for its output equally determined by the product's market demand and supply, it cannot cull the price information technology charges. Rather, the perfectly competitive firm tin cull to sell whatsoever quantity of output at exactly the aforementioned price. This implies that the firm faces a perfectly rubberband demand bend for its product: buyers are willing to purchase whatever number of units of output from the firm at the market price. When the perfectly competitive firm chooses what quantity to produce, and so this quantity—along with the prices prevailing in the market for output and inputs—volition decide the house's total revenue, total costs, and ultimately, level of profits.

Determining the Highest Profit past Comparing Full Revenue and Total Cost

A perfectly competitive firm can sell as big a quantity as information technology wishes, as long as it accepts the prevailing marketplace toll. Total acquirement is going to increment as the firm sells more than, depending on the price of the production and the number of units sold. If yous increment the number of units sold at a given price, then full revenue volition increase. If the price of the product increases for every unit of measurement sold, then total revenue also increases.

Every bit an example of how a perfectly competitive business firm decides what quantity to produce, consider the case of a small farmer who produces raspberries and sells them frozen for $4 per pack. Sales of one pack of raspberries will bring in $iv, two packs will be $viii, three packs will be $12, and so on. If, for instance, the price of frozen raspberries doubles to $8 per pack, and then sales of one pack of raspberries will be $eight, two packs volition be $16, three packs volition be $24, then on.

Total revenue and full costs for the raspberry farm are shown in Table one and as well appear in Figure ane.

Table 1. Total Revenue, Total Cost, and Profit at the Raspberry Farm

Quantity (Q)	Total Acquirement (TR)	Total Toll (TC)	Profit
0	$0	$62	−$62
10	$twoscore	$90	−$l
20	$lxxx	$110	−$30
30	$120	$126	−$6
forty	$160	$138	$22
l	$200	$150	$l
60	$240	$165	$75
70	$280	$190	$90
lxxx	$320	$230	$90
90	$360	$296	$64
100	$400	$400	$0
110	$440	$550	$−110
120	$480	$715	$−235

In Figure one, the horizontal axis shows the quantity of frozen raspberries produced. The vertical axis shows both full revenue and full costs, measured in dollars. The total cost curve intersects with the vertical axis at a value that shows the level of fixed costs, and so slopes upward, first at a decreasing charge per unit, then at an increasing charge per unit. In other words, the cost curves for a perfectly competitive business firm have the same characteristics every bit the curves that we covered in the previous module on product and costs.

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Figure 1. Total Revenue, Total Cost and Profit at the Raspberry Farm. Total revenue for a perfectly competitive business firm is an upward sloping straight line. The slope is equal to the price of the good. Full toll also slopes upwardly, but with some curvature. At higher levels of output, total cost begins to slope upward more steeply because of diminishing marginal returns. Graphically, profit is the vertical distance between the total revenue bend and the total price curve. This is shown as the smaller, downward-curving line at the bottom of the graph. The maximum profit will occur at the quantity where the difference between total revenue and total cost is largest.

Based on its total acquirement and total cost curves, a perfectly competitive firm similar the raspberry farm tin can summate the quantity of output that volition provide the highest level of profit. At any given quantity, total revenue minus full cost will equal profit. One way to determine the most assisting quantity to produce is to see at what quantity total revenue exceeds total cost by the largest amount.

Effigy i shows full revenue, total cost and turn a profit using the information from Tabular array 1. The vertical gap between total revenue and total cost is profit, for example, at Q = 60, TR = 240 and TC = 165. The difference is 75, which is the height of the turn a profit curve at that output level. The firm doesn't make a profit at every level of output. In this example, full costs will exceed total revenues at output levels from 0 to approximately 30, and and then over this range of output, the firm will exist making losses. At output levels from 40 to 100, total revenues exceed total costs, so the business firm is earning profits. All the same, at any output greater than 100, full costs again exceed full revenues and the firm is making increasing losses. Full profits announced in the final column of Table 1. Maximum turn a profit occurs at an output between 70 and 80, when profit equals $90.

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A college price would mean that total acquirement would be higher for every quantity sold. Graphically, the total acquirement curve would be steeper, reflecting the higher price equally the steeper gradient. A lower price would flatten the total acquirement curve, meaning that full revenue would be lower for every quantity sold. What happens if the price drops low enough and then that the total revenue line is completely below the total cost bend; that is, at every level of output, total costs are higher than total revenues? In this instance, the best the firm can do is to endure losses. Even so, a turn a profit-maximizing firm will prefer the quantity of output where full revenues come closest to total costs and thus where the losses are smallest.

Comparing Marginal Revenue and Marginal Costs

The approach that we described in the previous section, using total revenue and total cost, is not the just approach to determining the profit maximizing level of output. In this section, we provide an culling arroyo which uses marginal revenue and marginal price.

Firms often practice not have the necessary information they need to draw a complete total cost curve for all levels of production. They cannot be sure of what total costs would wait like if they, say, doubled production or cutting production in half, because they have not tried information technology. Instead, firms experiment. They produce a slightly greater or lower quantity and observe how it affects profits. In economic terms, this practical approach to maximizing profits ways examining how changes in product touch on marginal revenue and marginal toll.

As mentioned earlier, a business firm in perfect contest faces a perfectly rubberband demand curve for its product—that is, the firm'due south demand curve is a horizontal line drawn at the market place price level. This likewise means that the firm'south marginal acquirement curve is the same every bit the firm'south need curve. Every time a consumer demands ane more unit, the firm sells ane more unit of measurement and revenue increases past exactly the same amount equal to the market toll. In this example, every fourth dimension the firm sells a pack of frozen raspberries, the firm'due south acquirement increases by $four, as y'all can see in Tabular array 2. This condition simply holds for price taking firms in perfect competition where:

[latex]\text{marginal acquirement = price}[/latex]

The formula for marginal revenue is:

[latex]\text{marginal revenue = }\frac{\text{modify in total revenue}}{\text{alter in quantity}}[/latex]

Table 2. Marginal Acquirement for Raspberries
Cost	Quantity	Total Acquirement	Marginal Acquirement
$4	1	$four	–
$4	2	$8	$4
$4	3	$12	$4
$4	four	$16	$4

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Discover that marginal revenue does not change as the firm produces more output. That is considering the price is determined by supply and demand and does not change as the farmer produces more than (keeping in mind that, due to the relative pocket-size size of each firm, increasing their supply has no bear on on the full market place supply where price is determined).

Figure 2. Market Toll. The equilibrium price of raspberries is determined through the interaction of market supply and market demand at $4.00.

Since a perfectly competitive firm is a price taker, it can sell whatever quantity it wishes at the market-adamant toll. Marginal cost, the cost per boosted unit sold, is calculated by dividing the change in total cost past the modify in quantity. The formula for marginal cost is:

[latex]\text{marginal price = }\frac{\text{alter in total cost}}{\text{change in quantity}}[/latex]

Dissimilar marginal revenue, unremarkably, marginal cost changes every bit the business firm produces a greater quantity of output. At first, marginal toll decreases with additional output, simply then it increases with additional output. Again, annotation this is the same equally we plant in the module on production and costs.

Table iii presents the marginal revenue and marginal costs based on the total acquirement and total toll amounts introduced before. The marginal revenue curve shows the boosted revenue gained from selling 1 more unit, as shown in Figure 3.

Table 3. Marginal Revenues and Marginal Costs at the Raspberry Farm

Quantity	Full Revenue	Marginal Revenue	Total Cost	Marginal Toll	Profit
0	$0	$four	$62	–	-$62
ten	$40	$iv	$ninety	$2.80	-$50
20	$80	$4	$110	$two.00	-$30
30	$120	$four	$126	$1.60	-$6
twoscore	$160	$4	$138	$1.xx	$22
50	$200	$4	$150	$1.twenty	$l
60	$240	$4	$165	$1.l	$75
seventy	$280	$4	$190	$2.fifty	$90
lxxx	$320	$4	$230	$4.00	$90
90	$360	$4	$296	$6.sixty	$64
100	$400	$four	$400	$x.forty	$0
110	$440	$4	$550	$15.00	-$110
120	$480	$iv	$715	$16.fifty	-$235

In the raspberry subcontract example, marginal cost at showtime declines as production increases from x to 20 to thirty packs of raspberries. But and then marginal costs outset to increase, due to diminishing marginal returns in production. If the firm is producing at a quantity where MR > MC, similar 40 or fifty packs of raspberries, then information technology tin can increase profit past increasing output. The reason is since the marginal revenue exceeds the marginal cost, additional output is adding more to profit than information technology is taking away. If the firm is producing at a quantity where MC > MR, like 90 or 100 packs, then it tin can increase profit by reducing output. The firm'southward profit-maximizing level of output volition occur where MR = MC (or at a level close to that bespeak).

Effigy iii. Marginal Revenues and Marginal Costs at the Raspberry Subcontract. For a perfectly competitive firm, the demand curve southward a horizontal line equal to the market price of the skillful, Since price doesn't change with additional output, the demand bend is also the marginal acquirement (MR) bend. The marginal cost (MC) curve is sometimes initially downward-sloping, but is somewhen upward-sloping at higher levels of output as diminishing marginal returns boot in. The firm volition maximize profit at the level of output where MR = MC. In the instance of the raspberry farm, this occurs at eighty packs of strawberries.

In this example, the marginal acquirement and marginal cost curves cross at a price of $4 and a quantity of 80 produced. If the farmer started out producing at a level of 60, and and so experimented with increasing product to seventy, marginal revenues from the increase in product would exceed marginal costs—and and so profits would rise. The farmer has an incentive to go along producing. At a level of output of lxxx, marginal toll and marginal revenue are equal and then profit doesn't change. If the farmer then experimented further with increasing product from 80 to xc, he would find that marginal costs from the increase in product are greater than marginal revenues, and and then profits would decline.

The turn a profit-maximizing choice for a perfectly competitive firm will occur at the level of output where marginal revenue is equal to marginal toll—that is, where MR = MC. This occurs at Q = 80 in the figure.

Does Profit Maximization Occur at a Range of Output or a Specific Level of Output?

Table 1 showed that maximum profit occurs at any output level betwixt lxx and 80 units of output. But MR = MC occurs just at lxxx units of output. How can practice nosotros explain this slight discrepancy? Every bit long as MR > MC. a profit-seeking business firm should proceed expanding production. Expanding production into the zone where MR < MC reduces economic profits. It'due south truthful that profit is the same at Q = 70 and Q = 80, but it'south simply when the firm goes beyond that that see that profits autumn. Thus, MR = MC is the signal to finish expanding, so that is the level of output they should target.

Because the marginal acquirement received by a perfectly competitive house is equal to the price P, we can besides write the turn a profit-maximizing rule for a perfectly competitive firm as a recommendation to produce at the quantity of output where P = MC.

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Watch It

Sentinel this video to practice finding the profit-maximizing indicate in a perfectly competitive firm. Mr. Clifford reminds us that in a perfectly competitive market, the demand curve is a horizontal line, which besides happens to be the marginal revenue. You can use the acronym MR. DARP to remember that marginal revenue=demand=average acquirement=price. The ideal production point is the place where MR=MC.

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These questions permit you to become as much do every bit you need, equally you tin click the link at the top of the start question ("Effort another version of these questions") to get a new gear up of questions. Practise until y'all feel comfortable doing the questions.

Try It

These questions allow you to get every bit much exercise equally you lot need, as yous can click the link at the peak of the first question ("Effort another version of these questions") to get a new fix of questions. Practice until y'all feel comfortable doing the questions.

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These questions let you lot to get as much practice as you need, every bit y'all tin click the link at the top of the first question ("Try another version of these questions") to get a new set of questions. Do until you lot feel comfy doing the questions.

Glossary

marginal acquirement:

the additional acquirement gained from selling ane more unit of output

profit:

 the divergence betwixt total revenues and full costs

profit-maximizing rule for a perfectly competitive house:

produce the level of output where marginal acquirement equals marginal cost

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Source: https://courses.lumenlearning.com/wmopen-microeconomics/chapter/profit-maximization-in-a-perfectly-competitive-market/

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