Marginal revenue equals competitive price. Demand, price and marginal revenue of a monopolist
According to traditional theory of the firm and market theory, profit maximization is the primary goal of the firm. Therefore, the company must choose the volume of products supplied to achieve maximum profit for each sales period. PROFIT is the difference between gross (total) income (TR) and total (gross, total) production costs (TC) for the sales period:
profit = TR - TS.
Gross revenue is the price (P) of goods sold multiplied by sales volume (Q).
Since the price is not influenced by a competitive firm, it can only influence its income by changing sales volume. If a firm's gross revenue is greater than total costs, then it makes a profit. If total costs exceed gross income, the firm incurs losses.
Total costs are the costs of all factors of production used by a firm to produce a given volume of output.
Maximum profit is achieved in two cases:
- a) when gross income (TR) exceeds total costs (TC) to the greatest extent;
- b) when marginal revenue(MR) equals marginal cost (MC).
Marginal revenue (MR) is the change in gross revenue obtained by selling an additional unit of output. For a competitive firm, marginal revenue is always equal to the price of the product:
Marginal profit maximization is the difference between marginal revenue from selling an additional unit of output and marginal cost:
marginal profit = MR - MC.
Marginal costs are additional costs that lead to an increase in output by one unit of a good. Marginal costs are entirely variable costs because fixed costs do not change with release. For a competitive firm, marginal cost equals the market price of the product:
The limiting condition for maximizing profit is the volume of output at which price equals marginal cost.
Having determined the limit for maximizing the firm's profit, it is necessary to establish the equilibrium output that maximizes profit.
The maximum profitable equilibrium is a position of the firm in which the volume of goods offered is determined by the equality of the market price to marginal costs and marginal revenue:
The maximum profitable equilibrium under perfect competition is illustrated in Fig. 26.1.
Rice. 26.1. Equilibrium output of a competitive firm
The firm chooses the volume of output that allows it to make maximum profit. At the same time, it must be borne in mind that the output that ensures maximum profit does not at all mean that the largest profit is made per unit of this product. It follows that it is incorrect to use profit per unit as a criterion for overall profit.
In determining the profit-maximizing level of output, it is necessary to compare market prices with average costs.
Average costs (AC) - costs per unit of production; equal to the total cost of producing a given quantity of output divided by the quantity of output produced. There are three types of average costs: average gross (total) costs (AC); average fixed costs (AFC); average variable costs (AVC).
The relationship between market price and average production costs can have several options:
- price is greater than the profit-maximizing average cost of production. In this case, the company makes economic profit, that is, its income exceeds all its costs (Fig. 26.2);
- the price is equal to the minimum average production costs, which ensures the company’s self-sufficiency, i.e. the company only covers its costs, which gives it the opportunity to make a normal profit (Fig. 26.3);
- the price is below the minimum possible average costs, i.e. the company does not cover all its costs and incurs losses (Fig. 26.4);
- the price falls below the minimum average cost, but exceeds the minimum average variable cost, that is, the company is able to minimize its losses (Fig. 26.5); the price is below the minimum average variable cost, which means the cessation of production, because the firm's losses exceed fixed costs (Fig. 26.6).
Rice. 26.2. Profit maximization by a competitive firm
Rice. 26.3. Self-sustaining competitive firm
Rice. 26.4. Competitive firm incurring losses
G.S. Bechkanov, G.P. Bechkanova
The concepts of “marginal costs” and “marginal revenue” are discussed in paragraph 1 of this topic: these are the costs and income associated with the production and sale of an additional unit of product, i.e. These are incremental values.
IN market economy These concepts are very important for determining the optimal price level and production volumes.
The famous American economist P. Samuelson formulated the rule of equality of marginal income to marginal costs: only when the price of goods is equal to marginal costs, the economy squeezes the maximum possible out of the limited available resources and technologies.
Thus, the rule of equality of marginal revenue to marginal costs means the condition of profit maximization.
This rule is a guide to profit maximization for all types of markets: pure competition, monopolistic (imperfect) competition, oligopoly, monopoly. However, the conditions for its use change and will be discussed further.
The easiest way to illustrate the rule of equality of marginal revenue to marginal costs is by the example of pure competition (Table 3.1). In this case, attention should be paid to the identity of the concepts “total”, “gross”, “full” income. The terms “total”, “gross” and “full” costs are also synonymous.
Table 3.1\r\nVolume Total Total Average Total Marginal Marginal\r\noutput income, costs at- costs, income,\r\nproduct rub. ki, rub. units Products, rub. rub./unit rub./unit\r\ntion, units tions, rub. Products Products\r\nQ TR=PQ TC AC=TC/Q H=TR-TC MC=ATC/AQ MR=ATR/AQ\r\n1 2 3 4 5 6 7\r\n15 7500 5880 392 1620 340 500\ r\n16 8000 6220 388 1780 380 500\r\n17 8500 6600 388 1900 425 500\r\n18 9000 7025 390 1975 475 500\r\n*
19 *
9500 *
7500 394 *
2000 *
530 *
500\r\n20 10000 8030 401 1970 590 500\r\n21 10500 8620 410 1880 655 500\r\n22 11000 9275 421 1725 725 500\r\n23 11500 1000 0 434 1500 \r\n* - maximum profit values and corresponding them parameters.
Conditions for maximizing profits in the short term under pure competition
In table 3.1, production parameters are determined as follows (the designations in the formulas correspond to those generally accepted in the books of Western economists).
Total income = price volume of output:
TR = PQ.
Gross, or full, costs = fixed costs + variable costs:
TC = FC + VC.
Average costs = gross costs: volume of output:
TC
AC = -. Q
Gross (total) profit = total income - gross costs:
P = TR - TC.
5. Marginal costs = change (increase) in costs: change (increase) in output:
MS = *TC.
AQ
6. Marginal income = change (increase) in income: change (increase) in output:
MR = -.
Q
Analysis of the table 3.1 shows that total (gross) income (column 2) is obtained by increasing the volume of output (column 1) by the same price, equal to 500 rubles. This is due to the fact that in the example under consideration, conditions of pure competition are accepted, under which the company cannot influence the price, but only adjust to it.
As a result, price (P) and marginal revenue (MR) are equal (P = MR).
As can be seen from table. 3.1, the maximum value of gross profit (2000 rubles) corresponds to a production volume equal to 19 units. In this case, marginal revenue (MR) is equal to marginal cost (MC): MR = MC.
An increase in production volume above 19 units, for example, to 20 units, leads to the fact that marginal cost (MC) exceeds marginal revenue (MR): 590>500 (MC>MR).
This example illustrates the rule of equality of marginal revenue to marginal costs, i.e. MR = MS. Since in conditions of pure competition, price equals marginal revenue, we can write:
P = MR = MS,
which means: price equals marginal revenue and marginal cost.
Thus, price determination is based on the rule of equality of marginal revenue to marginal costs, which corresponds to the maximum gross profit.
Graphically this rule is shown in Fig. 3.5. At point A the MC and MR curves intersect, i.e. MR = MS.
Thus, we can conclude that in conditions of pure competition, the company does not face the problem of determining the price of its products, since the price is determined in the market under the influence of supply and demand, and the share of products produced by the company cannot influence it.
Subject economic analysis and regulation in this case is only the optimization of production volumes at the current price.
Since pure competition, like pure monopoly, is ideal model and are extremely rare, the majority market structures lies somewhere between these extremes.
Rice. 3.5. The profit-maximizing position of a firm under pure competition
The principles of pricing under different market models are given in Table. 3.2.
In conclusion, it should be noted that the above provisions are somewhat conventional and debatable.
Table 3.2
Principles of pricing under different market models\r\nCharacteristic Type of market\r\nfeature Pure Monopolistic Oligopoly Pure\r\n competition monopoly\r\nBasic price Developed Developed on Developed on Absent\r\n in the market market by market groups or \r\n similar products are installed on \r\n the basis of secret \r\n collusion \r\nAdjustment Absent Adjusted according to the base price Absent \r\nlevel of competitiveness \r\nSubject (over- Optimization Search for the interval Level of average Level\r\nlast) of economic volumes about changes in production costs and satisfactory averages from\r\nproduction analysis at a given price of satisfactory support and\r\n the existing economic fair\r\ n price of profit profit\r\nState- Absent Absent Antitrust Antimonopoly regulation- laws Polar laws\r\n
More on topic 3. Gross and marginal costs. Marginal revenue and price. The rule of equality of marginal revenue to marginal costs is the basis for determining the free price:
- 1.2. Concepts of monetary policy and their implementation in modern Russia
- 3.1. The concept of pricing services of a modern commercial bank
- Concept and classification of state financial regulation of the economy
- § 2. Indicators of economic efficiency of legal norms: theoretical and applied approach
- Copyright - Advocacy - Administrative law - Administrative process - Antimonopoly and competition law - Arbitration (economic) process - Audit - Banking system - Banking law - Business - Accounting - Property law - State law and administration - Civil law and process - Monetary law circulation, finance and credit - Money - Diplomatic and consular law - Contract law - Housing law - Land law - Electoral law - Investment law - Information law - Enforcement proceedings - History of state and law - History of political and legal doctrines - Competition law - Constitutional law - Corporate law - Forensics -
Monopolist demand function. The price of a monopolist's product depends on sales volume and is an inverse function of demand: . To increase sales volume, the monopolist is forced to reduce the price. Therefore, the monopolist's demand curve is downward sloping.
The monopolist's gross income is equal to and is a function of output. Gross income can be expressed as a function of price. Marginal revenue, by definition, is measured by the first derivative of the gross income function:
The quantity characterizes the change in price caused by a change in output and measures the slope of the demand curve. In conditions of perfect competition, since the price is set by the market and any quantity of products is sold at the same price. There are monopolies in the market, i.e. The slope of the demand curve is negative. This means that the monopolist's marginal income from the sale of any product is always lower than its price: . This means that the curve is always below the demand curve.
Let us consider the relationship between the gross and marginal income of a monopolist if the demand function is linear.
Demand function: , the slope of the demand line is equal to. Let's write the inverse demand function: . Then the gross income is equal to: . The total revenue curve is a parabola extending from the origin. Let us determine the marginal income of the monopolist:
The slope of the marginal revenue line is negative and in absolute value is twice the slope of the demand line. In general, the marginal revenue function has the form:
A necessary condition for the maximum value of a function of one variable is that its first derivative is equal to zero. The firm's gross income reaches its maximum value if... From the last equality we find the volume of production at which gross income is maximum. On the demand line there is a single point corresponding to the value at which. Thus, if, then a reaches a maximum. If it takes positive values, and demand is elastic, then it grows. On segments of the line of demand and gross income where the above conditions are met, the monopolist produces products. If marginal revenue is negative and demand is inelastic, then as output increases, gross revenue decreases.
For any price reduction, an area similar to the area ABC in Fig. 2, equals Q 1 (Dр). This is the income lost when a unit of goods is not sold at a higher price. Square DEFG equals P 2 (DQ). This is the increase in income from the sale of additional units of a good minus the income that was sacrificed by giving up the opportunity to sell previous units of the good at higher prices. For very small changes in price, changes in total revenue can therefore be written as
where Dр is negative and DQ is positive. Dividing equation (2) by DQ, we obtain:
(3)
where Dр/DQ is the slope of the demand curve. Since the demand curve for a monopolist's product is downward sloping, marginal revenue must be less than price.
The relationship between marginal revenue and the slope of the demand curve can easily be converted into a relationship that relates marginal revenue to the price elasticity of demand. The price elasticity of demand at any point on the demand curve is
Substituting this into the marginal revenue equation, we get:
Hence,
(4)
Equation (4) confirms that marginal revenue is less than price. This is true because E D is negative for a downward sloping demand curve for the monopolist's output. Equation (4) shows that, in general, the marginal revenue of any output depends on the price of the good and the elasticity of demand with respect to price. This equation can also be used to show how total income depends on market sales. Let's assume that e D = -1. This means unit elasticity of demand. Substituting e D = -1 into equation (4) gives zero marginal revenue. There is no change in total income in response to a change in price when the price elasticity of demand is -1. Likewise, when demand is elastic, the equation shows that marginal revenue is positive. This is so because the value of e D would be less than -1 and greater than minus infinity when demand is elastic. Finally, when demand is inelastic, marginal revenue is negative. Table 1.2.2 summarizes the relationships between marginal revenue, price elasticity of demand, and total revenue.
Marginal Revenue
Marginal revenue (MR from the English marginal revenue) is the income received as a result of the sale of an additional unit of production. Also called additional income- this is the additional income to the total income of the company received from the production and sale of one additional unit of goods. It makes it possible to judge the efficiency of production, as it shows the change in income as a result of an increase in output and sales of products by an additional unit.
Marginal revenue allows you to evaluate the possibility of recoupment of each additional unit of output. In combination with the marginal cost indicator, it serves as a cost guide for the possibility and feasibility of expanding the production volume of a given company.
Marginal revenue is defined as the difference between the total income from the sale of n + 1 units of goods and the total income from the sale of n goods:
MR = TR(n+1) - TRn, or calculated as MR = ДTR/ДQ,
where DTR is the increment in total income; DQ - increment in output by one unit.
Perfect competition
Gross (total), average and marginal revenues of the company
This chapter assumes that a firm produces a single type of product. At the same time, in its behavior when making certain decisions, the company strives to maximize its profits. The profit of any company can be calculated based on two indicators:
- 1) total income (total revenue) received by the company from the sale of its products,
- 2) total costs, which the company bears in the process of producing these products, i.e.
where TR is the total revenue of the company or total income; TC - the total costs of the company; P - profit.
In conditions of perfect competition, for any volume of output, products are sold at the same price set by the market. Therefore, the average income of the firm is equal to the price of the product.
For example, if a company sold 10 units of products at a price of 100 rubles. per unit, then its total income will be 1000 rubles, and average income-- 100 rubles, i.e. it is equal to the price. Moreover, the sale of each additional unit of product means that total income increases by an amount equal to the price. If a company sells 11 units, then an additional unit of this product will bring it an additional income of 100 rubles, which is again equal to the price of a unit of product. It follows that under conditions of perfect competition the equality P = AR = MR is maintained.
Let's illustrate this equality with our example, presenting it in the form of table 1-5-1.
Table 1-5-1 - Total, average and marginal revenue of the company.
Table 1-5-1 shows that the increase in sales volume from 10 units. up to 11 units, and then up to 12 units. at a price of 100 rub. per unit does not change average and marginal income. Both remain equal to 100 rubles, i.e. the price of 1 unit.
Now let's present the average and marginal income of the company in the form of a graph (Fig. 1-5-1). He assumes that sales volume (Q) is plotted on the abscissa axis, and all cost indicators (P, AR, MR) are plotted on the ordinate axis. In this case, the average and marginal income of the company, as has already been established, remains constant for any value of Q - 100 rubles. Therefore, the average income curve and the marginal income curve coincide. Both of them are represented by one line parallel to the x-axis.
rice. 1 -5-1
As for the total income curve, it represents a ray emanating from the origin of the coordinate system (a line with a constant positive slope - see Fig. 1-5-2). The constant slope is explained by the constant price level of the product.
rice. 1 -5-2
Considering the total, average, and marginal revenue of a firm does not tell us anything about the profit that the firm hopes for. Meanwhile, any company not only expects to make a profit, but also strives to maximize it. It would be wrong, however, to assume that profit maximization is based on the principle “the greater the output, the greater the profit.” In order to get maximum profit, the company must produce and sell the optimal volume of products.
There are two approaches to determining optimal output. Let's consider them using the example of a conventional company selling products at a price of 50 rubles. per unit.
The first approach to determining the optimal volume of a firm's output is based on comparing total income with total costs. In order to show what this approach consists of, let us first turn to Table. 1-5-2.
Table 1-5-2
First, costs exceed income (the company suffers losses). Graphically, this situation is expressed in the fact that the TC curve is located above the TR curve. When producing 4 units of output, the TR and TC curves intersect at point A. This indicates that total costs are equal to total income (the company receives zero profit). The TR curve then passes above the TC curve. In this case, the company makes a profit, which reaches its maximum value when producing 9 units of output. With a further increase in production, the absolute value of profit gradually decreases, reaching zero when 12 units are produced (the TR and TC curves intersect again). The firm then enters an area of unprofitable operations. Thus, critical production points should be established.
In Fig. 1-5-3 are points A (Q = 4) and B (Q = 12). If a firm produces products in a volume that is represented by values located between these points, it makes a profit. Beyond the specified volumes, it suffers losses.
rice. 1 -5-3
The profit curve (P) reflects the ratio of the TR and TC curves. When the firm suffers losses (profit is negative), the P curve is located below the horizontal axis. It intersects this axis at critical volumes output (points A" and B") and passes above it when receiving a positive profit.
The optimal output level is the output at which the firm maximizes profit. IN in this example it amounts to 9 units of product. At Q - 9, the distances between the TR and TC curves, as well as between the P curve and the horizontal axis, are maximum.
Now consider another approach to determining the optimal level of output and the equilibrium state of a competitive firm. It is based on comparing marginal revenue with marginal cost. In order to determine the optimal output, it is not necessary to calculate the amount of profit for all production volumes. It is enough to compare the marginal revenue from the sale of each unit of product with the marginal costs associated with the production of this unit. If marginal revenue (under perfect competition MR = P) exceeds marginal costs, then production should be increased. If marginal costs begin to exceed marginal revenue, then further increases in production should be stopped.
Let us turn again to the example presented in Table. 1-5-2. Should the firm produce the first unit of product? Of course, since the marginal income from its implementation (50 rubles) exceeds the marginal costs (48 rubles). In the same way, it must produce the second unit (MC = 38 rubles). In the same way, the marginal revenue and marginal costs associated with the production of each subsequent unit are compared. We make sure that the ninth unit of the product should be produced. But already the costs associated with the production of the tenth unit (MC = 54 rubles) exceed the marginal income. Consequently, by releasing the tenth unit, the firm will reduce the amount of profit received, which consists of the excess of marginal revenue over the marginal cost of releasing each previous unit of product. From this we can conclude that the optimal volume of production for this company is 9 units. With this output, marginal revenue equals marginal cost.
The behavior of the company at various ratios of marginal revenue and marginal costs is presented in table. 1-5-3.
Table 1-5-3
Thus, the rule for determining the optimal output of a firm when the product price is equal to the marginal product is expressed by the equality
Since under conditions of perfect competition price is equal to marginal revenue (P = MR), then
P = MS, i.e.
Equality of product price to marginal cost is a condition for equilibrium of a competitive firm.
Determining the optimal level of product output by a company based on the second approach can also be done graphically (Fig. 1-5-4).
rice. 1 -5-4
Conclusion
Gross (total) income (TR) is the product of the price of a product by the corresponding quantity of products sold.
In conditions of perfect competition, the firm sells additional units of output at a constant price, so the gross income graph looks like a straight ascending line (in this case, gross income is directly proportional to the volume of products sold).
At imperfect competition The firm must reduce its price to increase sales. In this case, gross income on the elastic part of demand increases, reaching a maximum, and then - on the inelastic part - decreases.
Marginal revenue (MR) is the amount by which gross income changes as a result of an increase in the quantity products sold per one unit.
In a perfectly competitive market with perfectly elastic demand, marginal revenue is equal to average revenue.
Imperfect competition gives the firm a downward-sloping demand curve. In such a market, marginal revenue is less than both average revenue and price.
Average revenue (AR) is the average revenue from the sale of a unit of goods. It is calculated by dividing total income by the volume of products sold.