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fixed costs has no effect on the profit maximizing output or price. The firm merely treats short term fixed costs as sunk costs and continues to operate as before. This can be confirmed graphically. Using the diagram illustrating the total cost–total revenue perspective, the firm maximizes profit at the point where the slopes of the total cost line and total revenue line are equal. An increase in fixed cost would cause the total cost curve to shift up rigidly by the amount of the change. There would be no effect on the total revenue curve or the shape of the total cost curve. Consequently, the profit maximizing output would remain the same. This point can also be illustrated using the diagram for the marginal revenue–marginal cost perspective. A change in fixed cost would have no effect on the position or shape of these curves. In simple terms, although profit is related to total cost,
1106:). Then, if marginal revenue is greater than marginal cost at some level of output, marginal profit is positive and thus a greater quantity should be produced, and if marginal revenue is less than marginal cost, marginal profit is negative and a lesser quantity should be produced. At the output level at which marginal revenue equals marginal cost, marginal profit is zero and this quantity is the one that maximizes profit. Since total profit increases when marginal profit is positive and total profit decreases when marginal profit is negative, it must reach a maximum where marginal profit is zero—where marginal cost equals marginal revenue—and where lower or higher output levels give lower profit levels. In calculus terms, the requirement that the optimal output have higher profit than adjacent output levels is that:
638:, which chooses its level of output simultaneously with its selling price. In the case of monopoly, the company will produce more products because it can still make normal profits. To get the most profit, you need to set higher prices and lower quantities than the competitive market. However, the revenue function takes into account the fact that higher levels of output require a lower price in order to be sold. An analogous feature holds for the input markets: in a perfectly competitive input market the firm's cost of the input is simply the amount purchased for use in production times the market-determined unit input cost, whereas a
747:. Fixed costs, which occur only in the short run, are incurred by the business at any level of output, including zero output. These may include equipment maintenance, rent, wages of employees whose numbers cannot be increased or decreased in the short run, and general upkeep. Variable costs change with the level of output, increasing as more product is generated. Materials consumed during production often have the largest impact on this category, which also includes the wages of employees who can be hired and laid off in the short run span of time under consideration. Fixed cost and variable cost, combined, equal
856:
2204:) to maximize profit. In the long run, a firm will theoretically have zero expected profits under the competitive equilibrium. The market should adjust to clear any profits if there is perfect competition. In situations where there are non-zero profits, we should expect to see either some form of long run disequilibrium or non-competitive conditions, such as barriers to entry, where there is not perfect competition between firms.
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78:
2463:. Moreover, one must consider "the revenue the firm loses on the units it could have sold at the higher price"—that is, if the price of all units had not been pulled down by the effort to sell more units. These units that have lost revenue are called the infra-marginal units. That is, selling the extra unit results in a small drop in price which reduces the revenue for all units sold by the amount
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3284:. The profit maximization issue can also be approached from the input side. That is, what is the profit maximizing usage of the variable input? To maximize profit the firm should increase usage of the input "up to the point where the input's marginal revenue product equals its marginal costs". Mathematically, the profit-maximizing rule is
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508:), then its total profit is not maximized, because the firm can produce additional units to earn additional profit. In other words, in this case, it is in the "rational" interest of the firm to increase its output level until its total profit is maximized. On the other hand, if the marginal revenue is less than the marginal cost (
618:) functions in terms of output are directly available one can equate these, using either equations or a graph. Fourth, rather than a function giving the cost of producing each potential output level, the firm may have input cost functions giving the cost of acquiring any amount of each input, along with a
761:
The five ways formula is to increase leads, conversation rates, average dollar sales, the average number of sales, and average product profit. Profits can be increased by up to 1,000 percent, this is important for sole traders and small businesses let alone big businesses but none the less all profit
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A firm maximizes profit by operating where marginal revenue equals marginal cost. This is stipulated under neoclassical theory, in which a firm maximizes profit in order to determine a level of output and inputs, which provides the price equals marginal cost condition. In the short run, a change in
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of cost or revenue with respect to the quantity of output. For instance, taking the first definition, if it costs a firm $ 400 to produce 5 units and $ 480 to produce 6, the marginal cost of the sixth unit is 80 dollars. Conversely, the marginal income from the production of 6 units is the income
403:
Measuring the total cost and total revenue is often impractical, as the firms do not have the necessary reliable information to determine costs at all levels of production. Instead, they take more practical approach by examining how small changes in production influence revenues and costs. When a
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revenue equals zero when the total revenue curve has reached its maximum value. An example would be a scheduled airline flight. The marginal costs of flying one more passenger on the flight are negligible until all the seats are filled. The airline would maximize profit by filling all the seats.
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rule implies that output should be produced at the maximum level, which also happens to be the level that maximizes revenue. In other words, the profit-maximizing quantity and price can be determined by setting marginal revenue equal to zero, which occurs at the maximal level of output. Marginal
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Companies can seek to maximize profits through estimation. When the price increase leads to a small decline in demand, the company can increase the price as much as possible before the demand becomes elastic. Generally, it is difficult to change the impact of the price according to the demand,
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In addition to using methods to determine a firm's optimal level of output, a firm that is not perfectly competitive can equivalently set price to maximize profit (since setting price along a given demand curve involves picking a preferred point on that curve, which is equivalent to picking a
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In the accompanying diagram, the linear total revenue curve represents the case in which the firm is a perfect competitor in the goods market, and thus cannot set its own selling price. The profit-maximizing output level is represented as the one at which total revenue is the height of
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showing how much output results from using any combination of input quantities. In this case one can use calculus to maximize profit with respect to input usage levels, subject to the input cost functions and the production function. The first order condition for each input equates the
538:), then too its total profit is not maximized, because producing one unit less will reduce total cost more than total revenue gained, thus giving the firm more total profit. In this case, a "rational" firm has an incentive to reduce its output level until its total profit is maximized.
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2166:) to maximize profit. But when the total cost increases, it does not mean maximizing profit Will change, because the increase in total cost does not necessarily change the marginal cost. If the marginal cost remains the same, the enterprise can still produce to the unit of (
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when implementing a "what if" solution to help in sales and operation planning process, familiarity with the company's operations, including the supply chain, inventory management and sales process is useful. Constraints are required to prevent corporate plans from becoming
2057:). However, moving the production line to a foreign location may cause unnecessary transportation costs. Close market locations for producing and selling products can improve demand optimization, but when the production cost is much higher, it is not a good choice.
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Habitually recording and analyzing the business costs of all products/services sold. There are many miscellaneous items in the cost including labor, materials, transportation, advertising, storage, etc. related to any goods or services sold, which become
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In some cases a firm's demand and cost conditions are such that marginal profits are greater than zero for all levels of production up to a certain maximum. In this case marginal profit plunges to zero immediately after that maximum is reached; hence the
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refer to the midpoints between the old and new values of price and quantity respectively. The marginal revenue from an incremental unit of output has two parts: first, the revenue the firm gains from selling the additional units or, giving the term
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preferred quantity to produce and sell). The profit maximization conditions can be expressed in a "more easily applicable" form or rule of thumb than the above perspectives use. The first step is to rewrite the expression for marginal revenue as
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340:), as shown in the blue part, the firm's overall profit will decrease because the additional unit produced will increase the overall cost. Here too the profit is not maximized and the firm has to lower its output level to maximize profits.
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283:), and the profit is not maximized. The firm has in its interest to raise its output level to maximize profits, because the revenue gained will be more than the cost to pay. However, if the output level is greater than
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each of the variables revenue and cost as functions of the level of output and find the output level that maximizes the difference (or this can be done with a table of values instead of a graph). Second, if specific
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915:). Given a table of costs and revenues at each quantity, we can either compute equations or plot the data directly on a graph. The profit-maximizing output is the one at which this difference reaches its maximum.
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is the amount of money that a company receives from its normal business activities, usually from the sale of goods and services (as opposed to monies from security sales such as equity shares or debt issuances).
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of demand for goods depends on the response of other companies. When it is the only company raising prices, demand will be elastic. If one family raises prices and others follow, demand may be inelastic.
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2347:{\displaystyle {\begin{aligned}{\text{MR}}=&{\frac {\Delta {\text{TR}}}{\Delta Q}}\\=&{\frac {P\Delta Q+Q\Delta P}{\Delta Q}}\\=&P+{\frac {Q\Delta P}{\Delta Q}}\\\end{aligned}}}
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and other behaviors are reflecting the crisis of excessive power of monopolists in the market. In an attempt to prevent businesses from abusing their power to maximize their own profits,
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In other words, the rule is that the size of the markup of price over the marginal cost is inversely related to the absolute value of the price elasticity of demand for the good.
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Cheng, Ho Fung
Griffith (1 September 2020). "An economic perspective on the inherent plausibility and frequency of predatory pricing: the case for more aggressive regulation".
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may be needed to integrate all financial information to record expense reports so that the business can clearly understand all costs related to operations and their accuracy.
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Market quotas reflect the power of a firm in the market, a firm dominating a market is very common, and too much power often becomes the motive for non-Hong behavior.
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3624:. Through this regulation, consumers enjoy a better relationship with the companies that serve them, even though the company itself may suffer, financially speaking.
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The optimal markup rule also implies that a non-competitive firm will produce on the elastic region of its market demand curve. Marginal cost is positive. The term
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If, contrary to what is assumed in the graph, the firm is not a perfect competitor in the output market, the price to sell the product at can be read off the
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of the input (the increment to revenue from selling the product caused by an increment to the amount of the input used) to the marginal cost of the input.
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The company may also have other goals and considerations. For example, companies may choose to earn less than the maximum profit in pursuit of higher
2631:{\displaystyle {\text{MR}}=P+Q\cdot {\frac {\Delta P}{\Delta Q}}=P+P\cdot {\frac {Q}{P}}\cdot {\frac {\Delta P}{\Delta Q}}=P+{\frac {P}{\text{PED}}}}
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1205:{\displaystyle {\frac {\operatorname {d} ^{2}R}{{\operatorname {d} Q}^{2}}}<{\frac {\operatorname {d} ^{2}C}{{\operatorname {d} Q}^{2}}}.}
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The principal difference between short run and long run profit maximization is that in the long run the quantities of all inputs, including
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182:. The firm which produces at this output level is said to maximize profits. If the output produced is less than the equilibrium quantity (
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3132:(that is, if demand is elastic at that level of output). The intuition behind this result is that, if demand is inelastic at some value
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A generic derivation of the profit maximisation level of output is given by the following steps. Firstly, suppose a representative firm
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market or otherwise) which wants to maximize its total profit, which is the difference between its total revenue and its total cost.
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market for its output, the revenue function will simply equal the market price times the quantity produced and sold, whereas for a
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In the real world, it is not easy to achieve profit maximization. The company must accurately know the marginal income and the
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would also lead to lower total cost, profit would go up due to the combination of increased revenue and decreased cost. Thus,
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In an environment that is competitive but not perfectly so, more complicated profit maximization solutions involve the use of
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from the production of 6 units minus the income from the production of 5 units (the latter item minus the preceding item).
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marginal cost. The firm maximises their profit with respect to quantity to yield the profit maximisation level of output:
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approach is taken or not, are defined as either the change in cost or revenue as each additional unit is produced or the
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maximization is a matter of each business stage and greater returns for profit sharing thus higher wages and motivation.
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The general rule is that the firm maximizes profit by producing that quantity of output where marginal revenue equals
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firm produces an extra unit of product, the additional revenue gained from selling it is called the marginal revenue (
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2046:. Because price increases maximize profits in the short term, they will attract more companies to enter the market.
478:), then the firm's total profit is said to be maximized. If the marginal revenue is greater than the marginal cost (
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The marginal revenue product is the change in total revenue per unit change in the variable input, that is,
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1833:{\displaystyle {\frac {\left(\partial \pi _{i}\right)}{\left(\partial q_{i}\right)}}=p_{i}-c_{i}=0}
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To obtain the profit maximizing output quantity, we start by recognizing that profit is equal to
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2920:{\displaystyle {\frac {\left(P-{\text{MC}}\right)}{P}}={\frac {1}{\left(-{\text{PED}}\right)}}}
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Profit maximization using the marginal revenue and marginal cost curves of a perfect competitor
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There are several perspectives one can take on profit maximization. First, since profit equals
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2136:, the enterprise can maximize profit by producing to the maximum profit (the maximum value of
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characterizing the demand curve of the firms' customers, which is negative. Then setting
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Profit maximization using the total revenue and total cost curves of a perfect competitor
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An example diagram of Profit
Maximization: In the supply and demand graph, the output of
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Many companies try to minimize costs by shifting production to foreign locations with
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Marginal product of labor, marginal revenue product of labor, and profit maximization
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often intervene to stop them in their tracks. A major example of this is through
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An equivalent perspective relies on the relationship that, for each unit sold,
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642:’s input price per unit is higher for higher amounts of the input purchased.
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because the demand may occur due to many other factors besides the price.
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3883:"Consumer Surplus as the Appropriate Standard for Antitrust Enforcement"
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is the product of marginal revenue and the marginal product of labor or
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3404:{\displaystyle {\text{MRP}}_{L}={\frac {\Delta {\text{TR}}}{\Delta L}}}
2979:{\displaystyle P={\frac {\text{PED}}{1+{\text{PED}}}}\cdot {\text{MC}}}
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2844:{\displaystyle P={\frac {MC}{1+\left({\frac {1}{\text{PED}}}\right)}}}
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to maximize profit with respect to the output level. Third, since the
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As such, the profit maximisation level of output is marginal revenue
2783:{\displaystyle {\frac {P-{\text{MC}}}{P}}={\frac {-1}{\text{PED}}}}
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3487:{\displaystyle {\text{MRP}}_{L}={\text{MR}}\cdot {\text{MP}}_{L}}
2507:{\displaystyle Q\cdot \left({\frac {\Delta P}{\Delta Q}}\right)}
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denotes total costs. The above expression can be re-written as:
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are known for revenue and cost in terms of output, one can use
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963:; the maximal profit is measured as the length of the segment
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3985:(fourth ed.). Weidenfeld and Nicolson. pp. 214–7.
3510:. Some forms of producer profit maximization are considered
1402:) is the same as the optimum quantity in the first diagram.
1001:. This optimal quantity of output is the quantity at which
1668:{\displaystyle \pi _{i}=p_{i}\cdot q_{i}-c_{i}\cdot q_{i}}
4052:
Three Steps to
Mastering Prescriptive Profit Maximization
1539:{\displaystyle \pi _{i}={\text{TR}}_{i}-{\text{TC}}_{i}}
2129:{\displaystyle {\text{Profit}}={\text{TR}}-{\text{TC}}}
57:
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refers to the commonly assumed variable input, labor.
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more than proportionately, thereby increasing revenue
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has perfect information about its profit, given by:
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levels that will lead to the highest possible total
3718:Karl E. Case; Ray C. Fair; Sharon M. Oster (2012),
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Process to determine the highest profits for a firm
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3321:{\displaystyle {\text{MRP}}_{L}={\text{MC}}_{L}}
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653:decisions. In either case, there are inputs of
3722:(10 ed.), Prentice Hall, pp. 180–181
2093:Changes in total costs and profit maximization
1908:Case in which maximizing revenue is equivalent
3031:{\displaystyle {\frac {PED}{1+{\text{PED}}}}}
8:
4036:Profit Maximization: The Comprehensive Guide
3832:Samuelson, W and Marks, S (2003). p. 103–05.
3820:Besanko, D. and Beautigam, R, (2001) p. 408.
1355:is represented by the area of the rectangle
1013:Marginal revenue – marginal cost perspective
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3568:. Unsourced material may be challenged and
3272:does not give the highest possible profit.
1987:. Unsourced material may be challenged and
823:. Unsourced material may be challenged and
703:. Unsourced material may be challenged and
4026:Profit Maximization in Perfect Competition
3841:Pindyck, R and Rubinfeld, D (2001) p. 341.
3806:Pindyck, R and Rubinfeld, D (2001) p. 333.
531:{\displaystyle {\text{MR}}<{\text{MC}}}
501:{\displaystyle {\text{MR}}>{\text{MC}}}
360:process by which a firm may determine the
333:{\displaystyle {\text{MR}}<{\text{MC}}}
276:{\displaystyle {\text{MR}}>{\text{MC}}}
3859:Samuelson, W and Marks, S (2003). p. 230.
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1222:
1220:
1191:
1180:
1166:
1159:
1148:
1137:
1123:
1116:
1114:
1091:
1089:
1069:
1067:
1044:
1042:
970:
968:
948:
946:
926:
924:
900:
898:
874:
872:
843:Learn how and when to remove this message
723:Learn how and when to remove this message
603:
601:
581:
579:
523:
515:
513:
493:
485:
483:
463:
455:
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433:
431:
411:
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325:
317:
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294:
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238:
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216:
214:
193:
187:
167:
159:
157:
137:
135:
115:
113:
92:
86:
3881:Pittman, Russell W. (17 December 2007).
3868:Samuelson, W and Marks, S (2003). p. 23.
3785:Samuelson, W and Marks, S (2003). p. 52.
3764:Samuelson, W and Marks, S (2003). p. 47.
3742:
3740:
3738:
3620:which effectively outlaws most industry
3876:
3874:
3710:
2687:{\displaystyle {\text{MC}}={\text{MR}}}
2159:{\displaystyle {\text{TR}}-{\text{TC}}}
983:{\displaystyle {\overline {\text{CB}}}}
471:{\displaystyle {\text{MR}}={\text{MC}}}
175:{\displaystyle {\text{MR}}={\text{MC}}}
2023:of the last commodity sold because of
1259:is shown in the next diagram as point
785:Total revenue – total cost perspective
3983:An introduction to positive economics
3850:Besanko and Braeutigam (2005) p. 419.
7:
3566:adding citations to reliable sources
2851:. Thus, the optimal markup rule is:
1985:adding citations to reliable sources
1949:Maximizing profits in the real world
821:adding citations to reliable sources
701:adding citations to reliable sources
58:move details into the article's body
739:may be classified into two groups:
3674:Outline of industrial organization
3392:
3382:
3119:
2600:
2592:
2552:
2544:
2491:
2483:
2407:
2331:
2323:
2293:
2285:
2273:
2249:
2239:
1778:
1755:
1698:denotes price (marginal revenue),
1181:
1163:
1138:
1120:
209:), as shown in the red part, then
25:
4000:Samuelson, W.; Marks, S. (2003).
3964:(ninth ed.). South-Western.
3950:(fifth ed.). South-Western.
3538:
3435:{\displaystyle {\text{MRP}}_{L}}
1957:
1937:{\displaystyle {\text{M}}\pi =0}
941:and total cost is the height of
793:
673:
34:
4030:Wolfram Demonstrations Project
1055:{\displaystyle {\text{M}}\pi }
376:(or just profit in short). In
1:
3958:Price Theory and Applications
3948:Price Theory and Applications
3921:10.1080/17441056.2020.1770478
2084:Planning and actual execution
1029:Price setting by a monopolist
566:for the optimization equates
108:is the intersection point of
3909:European Competition Journal
3634:Utility maximization problem
3079:{\displaystyle {\text{PED}}}
2653:{\displaystyle {\text{PED}}}
1367:
1344:{\displaystyle {\text{ATC}}}
975:
3981:Lipsey, Richard G. (1975).
1586:{\displaystyle {\text{TC}}}
1564:{\displaystyle {\text{TR}}}
1318:{\displaystyle {\text{MR}}}
1252:{\displaystyle {\text{MC}}}
1230:{\displaystyle {\text{MR}}}
1099:{\displaystyle {\text{MC}}}
1077:{\displaystyle {\text{MR}}}
1062:) equals marginal revenue (
908:{\displaystyle {\text{TC}}}
882:{\displaystyle {\text{TR}}}
772:, depending on whether the
611:{\displaystyle {\text{MC}}}
589:{\displaystyle {\text{MR}}}
441:{\displaystyle {\text{MC}}}
419:{\displaystyle {\text{MR}}}
246:{\displaystyle {\text{MC}}}
224:{\displaystyle {\text{MR}}}
145:{\displaystyle {\text{MC}}}
123:{\displaystyle {\text{MR}}}
4099:
4004:(Fourth ed.). Wiley.
3746:Lipsey (1975). pp. 245–47.
3512:anti-competitive practices
2662:price elasticity of demand
1870:equating to marginal cost
1571:denotes total revenue and
1296:{\displaystyle {\text{D}}}
1274:{\displaystyle {\text{A}}}
999:optimal quantity of output
956:{\displaystyle {\text{B}}}
934:{\displaystyle {\text{C}}}
396:" (whether operating in a
3506:can in some cases reduce
2416:{\displaystyle P\Delta Q}
1329:are represented by curve
380:, which is currently the
3218:{\displaystyle P\cdot Q}
3125:{\displaystyle -\infty }
1382:. The optimum quantity (
735:Any costs incurred by a
625:marginal revenue product
3720:Principles of Economics
1084:) minus marginal cost (
574:, if marginal revenue (
152:(Marginal Cost), where
130:(Marginal Revenue) and
3955:Landsburg, S. (2013).
3946:Landsburg, S. (2002).
3679:Rational choice theory
3654:Duality (optimization)
3488:
3436:
3405:
3348:
3328:, where the subscript
3322:
3266:
3239:
3219:
3193:
3173:
3153:
3126:
3103:
3080:
3058:
3057:{\displaystyle P>0}
3032:
2980:
2921:
2845:
2784:
2729:
2688:
2654:
2632:
2508:
2457:
2437:
2417:
2390:
2370:
2348:
2198:
2160:
2130:
1938:
1891:
1864:
1834:
1732:
1712:
1692:
1669:
1587:
1565:
1540:
1480:
1457:
1430:
1396:
1376:
1345:
1319:
1297:
1275:
1253:
1231:
1206:
1100:
1078:
1056:
1030:
1022:
984:
957:
935:
909:
883:
860:
612:
590:
532:
502:
472:
442:
420:
378:neoclassical economics
341:
334:
304:
277:
247:
225:
203:
176:
146:
124:
102:
4028:by Fiona Maclachlan,
3644:Business organization
3618:anti-trust regulation
3530:Government Regulation
3514:and are regulated by
3489:
3437:
3406:
3349:
3323:
3267:
3265:{\displaystyle Q_{1}}
3240:
3220:
3194:
3174:
3154:
3152:{\displaystyle Q_{1}}
3127:
3104:
3081:
3059:
3038:would be positive so
3033:
2981:
2922:
2846:
2785:
2730:
2689:
2655:
2633:
2509:
2458:
2443:brings in revenue of
2438:
2418:
2391:
2371:
2349:
2199:
2161:
2131:
2076:Business intelligence
1939:
1892:
1890:{\displaystyle c_{i}}
1865:
1863:{\displaystyle p_{i}}
1835:
1733:
1713:
1693:
1670:
1588:
1566:
1541:
1481:
1458:
1456:{\displaystyle P_{m}}
1431:
1429:{\displaystyle Q_{m}}
1397:
1377:
1346:
1320:
1298:
1276:
1254:
1232:
1207:
1101:
1079:
1057:
1028:
1020:
985:
958:
936:
910:
884:
858:
632:perfectly competitive
613:
596:) and marginal cost (
591:
564:first order condition
533:
503:
473:
443:
421:
398:perfectly competitive
335:
305:
303:{\displaystyle Q^{*}}
278:
248:
226:
204:
202:{\displaystyle Q^{*}}
177:
147:
125:
103:
101:{\displaystyle Q^{*}}
80:
4078:Financial management
4048:by Tejvan Pettinger.
4002:Managerial Economics
3794:Landsburg, S (2002).
3639:Welfare maximization
3562:improve this section
3502:The maximization of
3446:
3417:
3361:
3347:{\displaystyle _{L}}
3332:
3288:
3249:
3229:
3203:
3183:
3163:
3136:
3113:
3090:
3068:
3042:
2997:
2939:
2858:
2794:
2739:
2698:
2668:
2642:
2518:
2467:
2447:
2427:
2401:
2380:
2360:
2219:
2170:
2140:
2102:
1981:improve this section
1917:
1874:
1847:
1745:
1722:
1702:
1682:
1600:
1575:
1553:
1493:
1470:
1440:
1413:
1386:
1359:
1333:
1307:
1285:
1263:
1241:
1219:
1215:The intersection of
1113:
1088:
1066:
1041:
967:
945:
923:
897:
871:
817:improve this section
697:improve this section
600:
578:
512:
482:
452:
430:
408:
392:is assumed to be a "
314:
287:
257:
235:
213:
186:
156:
134:
112:
85:
4046:Profit Maximisation
3159:then a decrease in
1327:Average total costs
620:production function
350:profit maximization
4083:Capital management
4040:Techfunnel Project
4038:by Richard Gulle,
3484:
3432:
3401:
3344:
3318:
3262:
3235:
3215:
3189:
3169:
3149:
3122:
3102:{\displaystyle -1}
3099:
3076:
3054:
3028:
2976:
2917:
2841:
2780:
2725:
2684:
2650:
2628:
2504:
2453:
2433:
2413:
2386:
2366:
2344:
2342:
2194:
2156:
2126:
1934:
1887:
1860:
1830:
1728:
1708:
1688:
1665:
1583:
1561:
1536:
1476:
1453:
1426:
1392:
1372:
1341:
1315:
1293:
1271:
1249:
1227:
1202:
1096:
1074:
1052:
1031:
1023:
980:
953:
931:
905:
879:
861:
608:
586:
528:
498:
468:
438:
416:
342:
330:
300:
273:
243:
221:
199:
172:
142:
120:
98:
3971:978-1-285-42352-4
3684:Supply and demand
3602:Predatory pricing
3598:
3597:
3590:
3520:predatory pricing
3476:
3467:
3453:
3424:
3399:
3388:
3368:
3310:
3295:
3238:{\displaystyle Q}
3192:{\displaystyle P}
3172:{\displaystyle Q}
3074:
3026:
3023:
2974:
2966:
2963:
2952:
2915:
2908:
2887:
2877:
2839:
2832:
2831:
2778:
2777:
2760:
2754:
2723:
2722:
2704:
2682:
2674:
2648:
2626:
2625:
2607:
2584:
2559:
2524:
2498:
2456:{\displaystyle P}
2436:{\displaystyle P}
2389:{\displaystyle Q}
2369:{\displaystyle P}
2338:
2300:
2256:
2245:
2229:
2192:
2184:
2176:
2154:
2146:
2124:
2116:
2108:
2017:
2016:
2009:
1923:
1796:
1731:{\displaystyle c}
1711:{\displaystyle q}
1691:{\displaystyle p}
1581:
1559:
1528:
1513:
1479:{\displaystyle i}
1405:If the firm is a
1395:{\displaystyle Q}
1370:
1366:
1339:
1313:
1291:
1269:
1247:
1225:
1197:
1154:
1094:
1072:
1047:
978:
974:
951:
929:
903:
877:
853:
852:
845:
733:
732:
725:
665:Basic definitions
606:
584:
526:
518:
496:
488:
466:
458:
436:
414:
328:
320:
271:
263:
241:
219:
170:
162:
140:
118:
75:
74:
54:length guidelines
16:(Redirected from
4090:
4015:
3996:
3975:
3963:
3951:
3933:
3932:
3915:(2–3): 343–367.
3904:
3898:
3897:
3895:
3893:
3878:
3869:
3866:
3860:
3857:
3851:
3848:
3842:
3839:
3833:
3830:
3821:
3818:
3807:
3804:
3795:
3792:
3786:
3783:
3777:
3776:Desai, M (2017).
3774:
3765:
3762:
3747:
3744:
3733:
3732:entrepreneur.com
3730:
3724:
3723:
3715:
3689:Marginal revenue
3659:Market structure
3593:
3586:
3582:
3579:
3573:
3542:
3534:
3508:consumer surplus
3504:producer surplus
3493:
3491:
3490:
3485:
3483:
3482:
3477:
3474:
3468:
3465:
3460:
3459:
3454:
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3430:
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3408:
3407:
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3327:
3325:
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3302:
3301:
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3293:
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3242:
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3236:
3224:
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3216:
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3196:
3195:
3190:
3178:
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3175:
3170:
3158:
3156:
3155:
3150:
3148:
3147:
3131:
3129:
3128:
3123:
3108:
3106:
3105:
3100:
3085:
3083:
3082:
3077:
3075:
3072:
3063:
3061:
3060:
3055:
3037:
3035:
3034:
3029:
3027:
3025:
3024:
3021:
3012:
3001:
2985:
2983:
2982:
2977:
2975:
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2967:
2965:
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2950:
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2926:
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2918:
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2914:
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2883:
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2875:
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2837:
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2812:
2804:
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2787:
2786:
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2779:
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2774:
2766:
2761:
2756:
2755:
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2743:
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2731:
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2651:
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2637:
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2634:
2629:
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2623:
2619:
2608:
2606:
2598:
2590:
2585:
2577:
2560:
2558:
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2542:
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2522:
2513:
2511:
2510:
2505:
2503:
2499:
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2460:
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2434:
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2414:
2395:
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2387:
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2373:
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2367:
2353:
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2345:
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2339:
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2329:
2318:
2301:
2299:
2291:
2268:
2257:
2255:
2247:
2246:
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2237:
2230:
2227:
2203:
2201:
2200:
2195:
2193:
2190:
2185:
2182:
2177:
2174:
2165:
2163:
2162:
2157:
2155:
2152:
2147:
2144:
2135:
2133:
2132:
2127:
2125:
2122:
2117:
2114:
2109:
2106:
2032:price elasticity
2012:
2005:
2001:
1998:
1992:
1961:
1953:
1943:
1941:
1940:
1935:
1924:
1921:
1896:
1894:
1893:
1888:
1886:
1885:
1869:
1867:
1866:
1861:
1859:
1858:
1839:
1837:
1836:
1831:
1823:
1822:
1810:
1809:
1797:
1795:
1791:
1790:
1789:
1772:
1768:
1767:
1766:
1749:
1737:
1735:
1734:
1729:
1717:
1715:
1714:
1709:
1697:
1695:
1694:
1689:
1674:
1672:
1671:
1666:
1664:
1663:
1651:
1650:
1638:
1637:
1625:
1624:
1612:
1611:
1592:
1590:
1589:
1584:
1582:
1579:
1570:
1568:
1567:
1562:
1560:
1557:
1545:
1543:
1542:
1537:
1535:
1534:
1529:
1526:
1520:
1519:
1514:
1511:
1505:
1504:
1485:
1483:
1482:
1477:
1462:
1460:
1459:
1454:
1452:
1451:
1435:
1433:
1432:
1427:
1425:
1424:
1401:
1399:
1398:
1393:
1381:
1379:
1378:
1373:
1371:
1364:
1363:
1350:
1348:
1347:
1342:
1340:
1337:
1324:
1322:
1321:
1316:
1314:
1311:
1302:
1300:
1299:
1294:
1292:
1289:
1280:
1278:
1277:
1272:
1270:
1267:
1258:
1256:
1255:
1250:
1248:
1245:
1236:
1234:
1233:
1228:
1226:
1223:
1211:
1209:
1208:
1203:
1198:
1196:
1195:
1190:
1178:
1171:
1170:
1160:
1155:
1153:
1152:
1147:
1135:
1128:
1127:
1117:
1105:
1103:
1102:
1097:
1095:
1092:
1083:
1081:
1080:
1075:
1073:
1070:
1061:
1059:
1058:
1053:
1048:
1045:
1003:marginal revenue
989:
987:
986:
981:
979:
972:
971:
962:
960:
959:
954:
952:
949:
940:
938:
937:
932:
930:
927:
914:
912:
911:
906:
904:
901:
888:
886:
885:
880:
878:
875:
848:
841:
837:
834:
828:
797:
789:
770:marginal revenue
728:
721:
717:
714:
708:
677:
669:
647:physical capital
630:For a firm in a
617:
615:
614:
609:
607:
604:
595:
593:
592:
587:
585:
582:
568:marginal revenue
556:functional forms
537:
535:
534:
529:
527:
524:
519:
516:
507:
505:
504:
499:
497:
494:
489:
486:
477:
475:
474:
469:
467:
464:
459:
456:
447:
445:
444:
439:
437:
434:
425:
423:
422:
417:
415:
412:
339:
337:
336:
331:
329:
326:
321:
318:
309:
307:
306:
301:
299:
298:
282:
280:
279:
274:
272:
269:
264:
261:
252:
250:
249:
244:
242:
239:
231:is greater than
230:
228:
227:
222:
220:
217:
208:
206:
205:
200:
198:
197:
181:
179:
178:
173:
171:
168:
163:
160:
151:
149:
148:
143:
141:
138:
129:
127:
126:
121:
119:
116:
107:
105:
104:
99:
97:
96:
70:
67:
61:
52:Please read the
38:
37:
30:
21:
4098:
4097:
4093:
4092:
4091:
4089:
4088:
4087:
4058:
4057:
4022:
4012:
3999:
3993:
3980:
3972:
3961:
3954:
3945:
3942:
3937:
3936:
3906:
3905:
3901:
3891:
3889:
3887:Search eLibrary
3880:
3879:
3872:
3867:
3863:
3858:
3854:
3849:
3845:
3840:
3836:
3831:
3824:
3819:
3810:
3805:
3798:
3793:
3789:
3784:
3780:
3775:
3768:
3763:
3750:
3745:
3736:
3731:
3727:
3717:
3716:
3712:
3707:
3630:
3594:
3583:
3577:
3574:
3559:
3543:
3532:
3516:competition law
3500:
3472:
3449:
3444:
3443:
3420:
3415:
3414:
3391:
3381:
3364:
3359:
3358:
3335:
3330:
3329:
3306:
3291:
3286:
3285:
3278:
3252:
3247:
3246:
3227:
3226:
3201:
3200:
3181:
3180:
3179:would increase
3161:
3160:
3139:
3134:
3133:
3111:
3110:
3088:
3087:
3066:
3065:
3040:
3039:
3013:
3002:
2995:
2994:
2953:
2937:
2936:
2931:or equivalently
2901:
2897:
2867:
2863:
2856:
2855:
2820:
2813:
2805:
2792:
2791:
2767:
2744:
2737:
2736:
2696:
2695:
2666:
2665:
2640:
2639:
2599:
2591:
2551:
2543:
2516:
2515:
2490:
2482:
2476:
2465:
2464:
2445:
2444:
2425:
2424:
2399:
2398:
2378:
2377:
2358:
2357:
2341:
2340:
2330:
2319:
2309:
2303:
2302:
2292:
2269:
2265:
2259:
2258:
2248:
2238:
2234:
2217:
2216:
2210:
2168:
2167:
2138:
2137:
2100:
2099:
2095:
2067:Profit analysis
2063:
2013:
2002:
1996:
1993:
1978:
1962:
1951:
1915:
1914:
1910:
1877:
1872:
1871:
1850:
1845:
1844:
1814:
1801:
1781:
1777:
1773:
1758:
1754:
1750:
1743:
1742:
1720:
1719:
1700:
1699:
1680:
1679:
1655:
1642:
1629:
1616:
1603:
1598:
1597:
1573:
1572:
1551:
1550:
1524:
1509:
1496:
1491:
1490:
1468:
1467:
1443:
1438:
1437:
1416:
1411:
1410:
1384:
1383:
1357:
1356:
1353:economic profit
1331:
1330:
1305:
1304:
1283:
1282:
1261:
1260:
1239:
1238:
1217:
1216:
1179:
1162:
1161:
1136:
1119:
1118:
1111:
1110:
1086:
1085:
1064:
1063:
1039:
1038:
1035:marginal profit
1015:
965:
964:
943:
942:
921:
920:
895:
894:
869:
868:
849:
838:
832:
829:
814:
798:
787:
729:
718:
712:
709:
694:
678:
667:
598:
597:
576:
575:
549:, one can plot
510:
509:
480:
479:
450:
449:
428:
427:
406:
405:
312:
311:
290:
285:
284:
255:
254:
233:
232:
211:
210:
189:
184:
183:
154:
153:
132:
131:
110:
109:
88:
83:
82:
71:
65:
62:
51:
48:may be too long
43:This article's
39:
35:
28:
23:
22:
18:Profit function
15:
12:
11:
5:
4096:
4094:
4086:
4085:
4080:
4075:
4070:
4060:
4059:
4056:
4055:
4054:by Riverlogic.
4049:
4043:
4033:
4021:
4020:External links
4018:
4017:
4016:
4010:
3997:
3991:
3978:
3977:
3976:
3970:
3941:
3938:
3935:
3934:
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3861:
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3808:
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3778:
3766:
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3703:
3702:
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3676:
3671:
3666:
3664:Microeconomics
3661:
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3373:
3341:
3337:
3315:
3305:
3300:
3277:
3274:
3259:
3255:
3234:
3225:; since lower
3214:
3211:
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3098:
3095:
3053:
3050:
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2987:
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2678:
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2264:
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2254:
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2241:
2235:
2233:
2225:
2224:
2209:
2208:Markup pricing
2206:
2188:
2180:
2150:
2120:
2112:
2094:
2091:
2090:
2089:
2085:
2082:
2079:
2073:
2069:
2062:
2059:
2015:
2014:
1965:
1963:
1956:
1950:
1947:
1933:
1930:
1927:
1909:
1906:
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1880:
1857:
1853:
1841:
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1800:
1794:
1788:
1784:
1780:
1776:
1771:
1765:
1761:
1757:
1753:
1727:
1718:quantity, and
1707:
1687:
1676:
1675:
1662:
1658:
1654:
1649:
1645:
1641:
1636:
1632:
1628:
1623:
1619:
1615:
1610:
1606:
1547:
1546:
1533:
1523:
1518:
1508:
1503:
1499:
1475:
1450:
1446:
1423:
1419:
1391:
1369:
1213:
1212:
1201:
1194:
1189:
1186:
1183:
1177:
1174:
1169:
1165:
1158:
1151:
1146:
1143:
1140:
1134:
1131:
1126:
1122:
1051:
1014:
1011:
997:at the firm's
977:
851:
850:
801:
799:
792:
786:
783:
745:variable costs
731:
730:
681:
679:
672:
666:
663:
522:
492:
462:
394:rational agent
386:microeconomics
324:
297:
293:
267:
196:
192:
166:
95:
91:
73:
72:
42:
40:
33:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
4095:
4084:
4081:
4079:
4076:
4074:
4071:
4069:
4066:
4065:
4063:
4053:
4050:
4047:
4044:
4041:
4037:
4034:
4031:
4027:
4024:
4023:
4019:
4013:
4007:
4003:
3998:
3994:
3992:0-297-76899-9
3988:
3984:
3979:
3973:
3967:
3960:
3959:
3953:
3952:
3949:
3944:
3943:
3939:
3930:
3926:
3922:
3918:
3914:
3910:
3903:
3900:
3888:
3884:
3877:
3875:
3871:
3865:
3862:
3856:
3853:
3847:
3844:
3838:
3835:
3829:
3827:
3823:
3817:
3815:
3813:
3809:
3803:
3801:
3797:
3791:
3788:
3782:
3779:
3773:
3771:
3767:
3761:
3759:
3757:
3755:
3753:
3749:
3743:
3741:
3739:
3735:
3729:
3726:
3721:
3714:
3711:
3704:
3700:
3699:Marginal cost
3697:
3695:
3694:Total revenue
3692:
3690:
3687:
3685:
3682:
3680:
3677:
3675:
3672:
3670:
3667:
3665:
3662:
3660:
3657:
3655:
3652:
3650:
3647:
3645:
3642:
3640:
3637:
3635:
3632:
3631:
3627:
3625:
3623:
3619:
3615:
3611:
3610:price gouging
3607:
3603:
3592:
3589:
3581:
3571:
3567:
3563:
3557:
3556:
3552:
3547:This section
3545:
3541:
3536:
3535:
3529:
3527:
3525:
3521:
3517:
3513:
3509:
3505:
3497:
3495:
3479:
3469:
3461:
3456:
3427:
3412:
3395:
3376:
3371:
3355:
3339:
3336:
3313:
3303:
3298:
3283:
3282:marginal cost
3275:
3273:
3257:
3253:
3232:
3212:
3209:
3206:
3186:
3166:
3144:
3140:
3116:
3096:
3093:
3051:
3048:
3045:
3017:
3014:
3009:
3006:
3003:
2991:
2968:
2957:
2954:
2945:
2942:
2935:
2934:
2930:
2929:
2911:
2902:
2898:
2894:
2889:
2884:
2880:
2871:
2868:
2864:
2854:
2853:
2852:
2834:
2826:
2821:
2817:
2814:
2809:
2806:
2800:
2797:
2771:
2768:
2762:
2757:
2748:
2745:
2717:
2712:
2709:
2706:
2676:
2663:
2620:
2615:
2612:
2609:
2603:
2595:
2586:
2581:
2578:
2573:
2570:
2567:
2564:
2561:
2555:
2547:
2538:
2535:
2532:
2529:
2526:
2500:
2494:
2486:
2477:
2473:
2470:
2450:
2430:
2410:
2404:
2383:
2363:
2354:
2334:
2326:
2320:
2314:
2311:
2306:
2296:
2288:
2282:
2279:
2276:
2270:
2262:
2252:
2231:
2214:
2207:
2205:
2186:
2178:
2148:
2118:
2110:
2092:
2086:
2083:
2080:
2077:
2074:
2070:
2068:
2065:
2064:
2060:
2058:
2056:
2052:
2047:
2045:
2040:
2036:
2033:
2028:
2026:
2022:
2021:marginal cost
2011:
2008:
2000:
1997:November 2022
1990:
1986:
1982:
1976:
1975:
1971:
1966:This section
1964:
1960:
1955:
1954:
1948:
1946:
1931:
1928:
1925:
1907:
1905:
1903:
1898:
1882:
1878:
1855:
1851:
1827:
1824:
1819:
1815:
1811:
1806:
1802:
1798:
1792:
1786:
1782:
1774:
1769:
1763:
1759:
1751:
1741:
1740:
1739:
1725:
1705:
1685:
1660:
1656:
1652:
1647:
1643:
1639:
1634:
1630:
1626:
1621:
1617:
1613:
1608:
1604:
1596:
1595:
1594:
1531:
1521:
1516:
1506:
1501:
1497:
1489:
1488:
1487:
1473:
1464:
1448:
1444:
1421:
1417:
1408:
1403:
1389:
1354:
1328:
1199:
1192:
1187:
1184:
1175:
1172:
1167:
1156:
1149:
1144:
1141:
1132:
1129:
1124:
1109:
1108:
1107:
1049:
1036:
1027:
1019:
1012:
1010:
1008:
1007:marginal cost
1004:
1000:
996:
991:
916:
892:
866:
865:total revenue
857:
847:
844:
836:
833:November 2022
826:
822:
818:
812:
811:
807:
802:This section
800:
796:
791:
790:
784:
782:
779:
775:
771:
767:
766:Marginal cost
763:
759:
756:
752:
750:
746:
742:
738:
727:
724:
716:
713:November 2022
706:
702:
698:
692:
691:
687:
682:This section
680:
676:
671:
670:
664:
662:
660:
659:raw materials
656:
652:
648:
643:
641:
637:
633:
628:
626:
621:
573:
572:marginal cost
569:
565:
561:
557:
552:
548:
544:
539:
520:
490:
460:
401:
399:
395:
391:
387:
383:
379:
375:
371:
367:
363:
359:
355:
351:
347:
322:
295:
291:
265:
194:
190:
164:
93:
89:
79:
69:
66:November 2022
59:
55:
49:
47:
41:
32:
31:
19:
4001:
3982:
3957:
3947:
3912:
3908:
3902:
3890:. Retrieved
3886:
3864:
3855:
3846:
3837:
3790:
3781:
3728:
3719:
3713:
3599:
3584:
3575:
3560:Please help
3548:
3501:
3413:
3356:
3279:
2992:
2989:
2355:
2215:
2211:
2096:
2048:
2044:market share
2041:
2037:
2029:
2018:
2003:
1994:
1979:Please help
1967:
1911:
1899:
1842:
1677:
1548:
1465:
1404:
1214:
1032:
995:demand curve
992:
917:
862:
839:
830:
815:Please help
803:
764:
760:
753:
734:
719:
710:
695:Please help
683:
644:
629:
540:
402:
384:approach to
349:
343:
63:
46:lead section
44:
3649:Corporation
3614:governments
3086:is between
2088:unfeasible.
2051:cheap labor
1902:game theory
741:fixed costs
640:monopsonist
551:graphically
4062:Categories
4011:0470000449
3940:References
3622:monopolies
2055:Nike, Inc.
1407:monopolist
891:total cost
778:derivative
749:total cost
651:investment
636:monopolist
382:mainstream
3929:1744-1056
3892:24 August
3578:June 2023
3549:does not
3498:Criticism
3470:⋅
3393:Δ
3383:Δ
3210:⋅
3120:∞
3117:−
3094:−
2969:⋅
2903:−
2872:−
2769:−
2749:−
2601:Δ
2593:Δ
2587:⋅
2574:⋅
2553:Δ
2545:Δ
2539:⋅
2492:Δ
2484:Δ
2474:⋅
2408:Δ
2332:Δ
2324:Δ
2294:Δ
2286:Δ
2274:Δ
2250:Δ
2240:Δ
2149:−
2119:−
2072:expenses.
1968:does not
1926:π
1812:−
1779:∂
1760:π
1756:∂
1653:⋅
1640:−
1627:⋅
1605:π
1522:−
1498:π
1368:¯
1185:
1173:
1142:
1130:
1050:π
976:¯
804:does not
684:does not
354:short run
346:economics
296:∗
195:∗
94:∗
56:and help
3628:See also
3522:such as
3064:only if
2638:, where
2514:. Thus,
2356:, where
1351:. Total
889:) minus
774:calculus
560:calculus
358:long run
4073:Pricing
3669:Pricing
3570:removed
3555:sources
3524:dumping
2660:is the
1989:removed
1974:sources
1005:equals
825:removed
810:sources
755:Revenue
705:removed
690:sources
543:revenue
352:is the
4068:Profit
4008:
3989:
3968:
3927:
2694:gives
2107:Profit
2053:(e.g.
1678:where
1549:where
545:minus
388:, the
374:profit
370:output
3962:(PDF)
3705:Notes
3606:tying
2191:Price
2078:tools
2061:Tools
655:labor
366:input
362:price
4006:ISBN
3987:ISBN
3966:ISBN
3925:ISSN
3894:2024
3553:any
3551:cite
3109:and
3049:>
2790:and
2376:and
2030:The
1972:any
1970:cite
1365:PABC
1237:and
1157:<
808:any
806:cite
768:and
743:and
737:firm
688:any
686:cite
657:and
570:and
547:cost
521:<
491:>
390:firm
368:and
323:<
266:>
3917:doi
3564:by
3452:MRP
3423:MRP
3367:MRP
3294:MRP
3073:PED
3022:PED
2962:PED
2951:PED
2907:PED
2830:PED
2776:PED
2735:so
2721:PED
2647:PED
2624:PED
1983:by
1463:).
1338:ATC
819:by
699:by
356:or
344:In
4064::
3923:.
3913:16
3911:.
3885:.
3873:^
3825:^
3811:^
3799:^
3769:^
3751:^
3737:^
3608:,
3604:,
3526:.
3494:.
3475:MP
3466:MR
3411:.
3387:TR
3309:MC
2973:MC
2876:MC
2753:MC
2703:MC
2681:MR
2673:MC
2523:MR
2244:TR
2228:MR
2183:MC
2175:MR
2153:TC
2145:TR
2123:TC
2115:TR
2027:.
2025:MR
1904:.
1897:.
1580:TC
1558:TR
1527:TC
1512:TR
1312:MR
1246:MC
1224:MR
1093:MC
1071:MR
1009:.
973:CB
902:TC
876:TR
751:.
661:.
605:MC
583:MR
525:MC
517:MR
495:MC
487:MR
465:MC
457:MR
435:MC
413:MR
364:,
348:,
327:MC
319:MR
270:MC
262:MR
240:MC
218:MR
169:MC
161:MR
139:MC
117:MR
4042:.
4032:.
4014:.
3995:.
3974:.
3931:.
3919::
3896:.
3591:)
3585:(
3580:)
3576:(
3572:.
3558:.
3480:L
3462:=
3457:L
3428:L
3396:L
3377:=
3372:L
3340:L
3314:L
3304:=
3299:L
3258:1
3254:Q
3233:Q
3213:Q
3207:P
3187:P
3167:Q
3145:1
3141:Q
3097:1
3052:0
3046:P
3018:+
3015:1
3010:D
3007:E
3004:P
2986:.
2958:+
2955:1
2946:=
2943:P
2912:)
2899:(
2895:1
2890:=
2885:P
2881:)
2869:P
2865:(
2835:)
2827:1
2822:(
2818:+
2815:1
2810:C
2807:M
2801:=
2798:P
2772:1
2763:=
2758:P
2746:P
2718:P
2713:+
2710:P
2707:=
2677:=
2621:P
2616:+
2613:P
2610:=
2604:Q
2596:P
2582:P
2579:Q
2571:P
2568:+
2565:P
2562:=
2556:Q
2548:P
2536:Q
2533:+
2530:P
2527:=
2501:)
2495:Q
2487:P
2478:(
2471:Q
2451:P
2431:P
2411:Q
2405:P
2384:Q
2364:P
2335:Q
2327:P
2321:Q
2315:+
2312:P
2307:=
2297:Q
2289:P
2283:Q
2280:+
2277:Q
2271:P
2263:=
2253:Q
2232:=
2187:=
2179:=
2111:=
2010:)
2004:(
1999:)
1995:(
1991:.
1977:.
1932:0
1929:=
1922:M
1883:i
1879:c
1856:i
1852:p
1828:0
1825:=
1820:i
1816:c
1807:i
1803:p
1799:=
1793:)
1787:i
1783:q
1775:(
1770:)
1764:i
1752:(
1726:c
1706:q
1686:p
1661:i
1657:q
1648:i
1644:c
1635:i
1631:q
1622:i
1618:p
1614:=
1609:i
1532:i
1517:i
1507:=
1502:i
1474:i
1449:m
1445:P
1422:m
1418:Q
1390:Q
1290:D
1268:A
1200:.
1193:2
1188:Q
1182:d
1176:C
1168:2
1164:d
1150:2
1145:Q
1139:d
1133:R
1125:2
1121:d
1046:M
1037:(
950:B
928:C
893:(
867:(
846:)
840:(
835:)
831:(
827:.
813:.
726:)
720:(
715:)
711:(
707:.
693:.
461:=
310:(
292:Q
253:(
191:Q
165:=
90:Q
68:)
64:(
60:.
50:.
20:)
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