Refer to Table 16-6. When maximizing profit, what price does Beatrices charge for a cake?

Learning Objectives

• Determine profits and costs by comparing total acquirement and total cost
• Employ marginal revenue and marginal costs to find the level of output that will maximize the house's profits

How Perfectly Competitive Firms Make Output Decisions

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

[latex]\begin{array}{l}\text{Turn a profit}=\text{Total revenue}-\text{Total cost}\hfill \\ \text{ }=\left(\text{Cost}\correct)\left(\text{Quantity produced}\right)-\left(\text{Average cost}\correct)\left(\text{Quantity produced}\correct)\hfill \end{array}[/latex]

Since a perfectly competitive business firm must have the toll for its output equally adamant by the product's market need and supply, it cannot choose the price it charges. Rather, the perfectly competitive firm can choose to sell any quantity of output at exactly the aforementioned price. This implies that the firm faces a perfectly elastic demand curve for its product: buyers are willing to buy any number of units of output from the firm at the marketplace price. When the perfectly competitive firm chooses what quantity to produce, and so this quantity—forth with the prices prevailing in the market place for output and inputs—volition determine the business firm'due south full revenue, total costs, and ultimately, level of profits.

Determining the Highest Profit by Comparison Full Acquirement and Total Toll

A perfectly competitive firm tin can sell as large a quantity as it wishes, as long as it accepts the prevailing marketplace price. Full revenue is going to increase equally the house sells more, depending on the toll of the product and the number of units sold. If you lot increase the number of units sold at a given price, then total revenue will increase. If the price of the product increases for every unit sold, and then total revenue also increases.

Equally an example of how a perfectly competitive house decides what quantity to produce, consider the case of a pocket-sized farmer who produces raspberries and sells them frozen for $4 per pack. Sales of 1 pack of raspberries will bring in $4, two packs will exist $8, three packs will be $12, and then on. If, for example, the cost of frozen raspberries doubles to $8 per pack, then sales of 1 pack of raspberries volition be $8, two packs will be $sixteen, iii packs will be $24, and so on.

Total acquirement and total costs for the raspberry farm are shown in Tabular array 1 and too appear in Figure 1.

Table 1. Total Acquirement, Full Price, and Profit at the Raspberry Subcontract

Quantity (Q)	Total Acquirement (TR)	Total Toll (TC)	Turn a profit
0	$0	$62	−$62
10	$twoscore	$xc	−$fifty
20	$80	$110	−$30
30	$120	$126	−$half-dozen
xl	$160	$138	$22
fifty	$200	$150	$50
60	$240	$165	$75
lxx	$280	$190	$90
eighty	$320	$230	$ninety
ninety	$360	$296	$64
100	$400	$400	$0
110	$440	$550	$−110
120	$480	$715	$−235

In Figure 1, the horizontal centrality shows the quantity of frozen raspberries produced. The vertical axis shows both total revenue and total costs, measured in dollars. The full cost curve intersects with the vertical axis at a value that shows the level of fixed costs, so slopes upward, first at a decreasing rate, then at an increasing charge per unit. In other words, the toll curves for a perfectly competitive business firm have the aforementioned characteristics as the curves that we covered in the previous module on production and costs.

Try It

Figure i. Total Revenue, Total Price and Profit at the Raspberry Farm. Total revenue for a perfectly competitive firm is an up sloping straight line. The gradient is equal to the price of the skilful. Total toll as well slopes upwards, but with some curvature. At higher levels of output, total cost begins to slope up more than steeply because of diminishing marginal returns. Graphically, profit is the vertical distance betwixt the full revenue curve and the full cost curve. This is shown as the smaller, downwards-curving line at the lesser of the graph. The maximum turn a profit volition occur at the quantity where the difference betwixt total revenue and total cost is largest.

Based on its full acquirement and full cost curves, a perfectly competitive firm like the raspberry subcontract can summate the quantity of output that will provide the highest level of profit. At any given quantity, total revenue minus full cost will equal profit. One mode to determine the virtually profitable quantity to produce is to run across at what quantity total revenue exceeds total price past the largest corporeality.

Figure 1 shows total revenue, total cost and turn a profit using the data from Table 1. The vertical gap between total revenue and total cost is profit, for example, at Q = sixty, TR = 240 and TC = 165. The divergence is 75, which is the acme of the profit bend 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 so over this range of output, the business firm will be making losses. At output levels from 40 to 100, total revenues exceed total costs, so the firm is earning profits. However, at whatever output greater than 100, full costs again exceed total revenues and the house is making increasing losses. Total profits appear in the final column of Table 1. Maximum profit occurs at an output between lxx and lxxx, when profit equals $ninety.

Effort Information technology

A higher price would mean that total revenue would exist higher for every quantity sold. Graphically, the total revenue curve would exist steeper, reflecting the higher price as the steeper slope. A lower price would flatten the total revenue bend, pregnant that total revenue would be lower for every quantity sold. What happens if the price drops low enough and then that the total acquirement line is completely beneath the full price curve; that is, at every level of output, full costs are higher than total revenues? In this instance, the best the firm can do is to suffer losses. Withal, a turn a profit-maximizing house volition adopt the quantity of output where total revenues come up closest to total costs and thus where the losses are smallest.

Comparing Marginal Revenue and Marginal Costs

The approach that nosotros described in the previous section, using total revenue and full cost, is non the just approach to determining the turn a profit maximizing level of output. In this section, we provide an alternative approach which uses marginal revenue and marginal toll.

Firms often exercise not accept 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 expect like if they, say, doubled production or cut production in half, because they accept non 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 means examining how changes in production affect revenues and costs.

In the module on production and dosts, nosotros introduced the concept of marginal cost—the change in total cost from producing one more unit of measurement of output. Similarly, we can define marginal revenue as the change in total acquirement from selling one more unit of measurement of output. Equally mentioned before, a firm in perfect competition faces a perfectly rubberband demand bend for its product—that is, the business firm'due south demand curve is a horizontal line drawn at the market price level. This also means that the firm'due south marginal revenue curve is the same as the firm'south need bend. Every time a consumer demands one more unit, the firm sells one more unit of measurement and revenue increases by exactly the same corporeality equal to the marketplace price. In this instance, every fourth dimension the firm sells a pack of frozen raspberries, the firm'southward revenue increases by $4, every bit y'all can encounter in Table 2. This condition merely holds for price taking firms in perfect competition where:

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

The formula for marginal revenue is:

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

Table 2. Marginal Revenue for Raspberries
Price	Quantity	Total Acquirement	Marginal Revenue
$iv	1	$4	–
$iv	2	$viii	$iv
$4	three	$12	$4
$4	iv	$16	$4

Try It

Notice that marginal revenue does non change as the firm produces more output. That is considering the price is determined by supply and demand and does non alter as the farmer produces more (keeping in listen that, due to the relative small size of each house, increasing their supply has no impact on the full market place supply where toll is determined).

Figure two. Market Price. The equilibrium price of raspberries is adamant through the interaction of marketplace supply and marketplace demand at $4.00.

Since a perfectly competitive firm is a price taker, it can sell whatsoever quantity information technology wishes at the market-adamant price. Marginal price, the toll per additional unit of measurement sold, is calculated by dividing the change in full toll by the change in quantity. The formula for marginal cost is:

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

Dissimilar marginal acquirement, unremarkably, marginal cost changes as the firm produces a greater quantity of output. At starting time, marginal toll decreases with boosted output, but then it increases with additional output. Over again, note this is the same every bit nosotros found in the module on production and costs.

Table 3 presents the marginal revenue and marginal costs based on the full acquirement and total cost amounts introduced earlier. The marginal acquirement curve shows the additional revenue gained from selling one more than unit of measurement, as shown in Effigy 3.

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

Quantity	Total Revenue	Marginal Revenue	Total Price	Marginal Cost	Profit
0	$0	$iv	$62	–	-$62
10	$40	$4	$90	$2.80	-$50
20	$80	$4	$110	$2.00	-$thirty
thirty	$120	$4	$126	$1.60	-$half-dozen
40	$160	$4	$138	$1.20	$22
fifty	$200	$4	$150	$1.20	$fifty
60	$240	$4	$165	$1.l	$75
70	$280	$4	$190	$two.50	$90
lxxx	$320	$4	$230	$4.00	$xc
90	$360	$iv	$296	$6.60	$64
100	$400	$4	$400	$10.40	$0
110	$440	$4	$550	$15.00	-$110
120	$480	$4	$715	$sixteen.50	-$235

In the raspberry farm instance, marginal cost at first declines every bit product increases from x to 20 to 30 packs of raspberries. But so marginal costs offset to increase, due to diminishing marginal returns in production. If the house is producing at a quantity where MR > MC, like 40 or 50 packs of raspberries, so it tin can increase profit by increasing output. The reason is since the marginal revenue exceeds the marginal cost, additional output is adding more to turn a profit than information technology is taking abroad. If the house is producing at a quantity where MC > MR, like 90 or 100 packs, so it tin can increment turn a profit by reducing output. The firm's profit-maximizing level of output will occur where MR = MC (or at a level shut to that indicate).

Figure 3. Marginal Revenues and Marginal Costs at the Raspberry Subcontract. For a perfectly competitive business firm, the demand bend s a horizontal line equal to the marketplace price of the practiced, Since toll doesn't change with additional output, the demand bend is also the marginal revenue (MR) curve. The marginal cost (MC) curve is sometimes initially down-sloping, simply is eventually upward-sloping at college levels of output as diminishing marginal returns kick in. The firm will maximize profit at the level of output where MR = MC. In the case of the raspberry subcontract, this occurs at 80 packs of strawberries.

In this example, the marginal revenue and marginal cost curves cross at a cost of $4 and a quantity of 80 produced. If the farmer started out producing at a level of 60, and and then experimented with increasing production to lxx, marginal revenues from the increase in production would exceed marginal costs—and so profits would ascension. The farmer has an incentive to keep producing. At a level of output of eighty, marginal price and marginal acquirement are equal so profit doesn't change. If the farmer then experimented farther with increasing production from 80 to ninety, he would find that marginal costs from the increment in production are greater than marginal revenues, and and so profits would decline.

The profit-maximizing choice for a perfectly competitive firm will occur at the level of output where marginal revenue is equal to marginal cost—that is, where MR = MC. This occurs at Q = lxxx 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 between 70 and lxxx units of output. Simply MR = MC occurs but at 80 units of output. How do we explain this slight discrepancy? As long as MR > MC. a profit-seeking business firm should keep expanding production. Expanding product into the zone where MR < MC reduces economic profits. It'south true that profit is the same at Q = 70 and Q = eighty, simply it's only when the house goes beyond that level, that we meet profits fall. Thus, MR = MC is the signal to end expanding, then that is the level of output they should target.

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

Try It

Scout It

Lookout man this video to practise finding the turn a profit-maximizing point in a perfectly competitive house. Mr. Clifford reminds united states that in a perfectly competitive market, the demand curve is a horizontal line, which also happens to be the marginal acquirement. You tin can utilise the acronym MR. DARP to remember that marginal revenue=demand=boilerplate revenue=price. The ideal production point is the place where MR=MC.

Glossary

marginal revenue:

the additional revenue gained from selling 1 more unit of output

turn a profit:

 the difference betwixt total revenues and total costs

profit-maximizing rule for a perfectly competitive firm:

produce the level of output where marginal revenue equals marginal cost

Contribute!

Did y'all accept an thought for improving this content? We'd love your input.

Improve this pageLearn More

robertsonstord1974.blogspot.com

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