The limiting values may seem to be something purely theoretical and not related to the actual conduct of business at the enterprise only because of the lack of practice of working with them in the Soviet and perestroika periods. In fact, limit values are the most effective method to track the opportunities for potential increase in profits, which is what all enterprises strive for without exception. As for their logic and calculation, it is nothing more complicated than elementary algebra.
Marginal revenue is the amount a company earns from selling an additional unit of a product. It is one of the main marginal values that have a direct relationship with profit and price - two of the most important indicators of a company's performance. Marginal revenue is a value that has a different meaning depending on the company. Thus, to carry out an analysis using marginal revenue, it is necessary to compile a table reflecting the change in this value with a change in sales volumes.
To make it clearer, let's define marginal revenue. Marginal revenue is the change in the total income of the company, as a result of an increase in sales by one conventional unit. For example, your company sold 20 units of products for 10 rubles each. Then they increased by one, but the price remained the same. In this case, the marginal income will be equal to 20 rubles.
It may seem that at a constant price, marginal revenue will always be equal to the value of this very price, and therefore it makes no sense to carry out a further calculation of this indicator. However, it is not. As you know, with the growth of sales volumes, the company is forced to reduce the price in order to attract those buyers who will not buy the goods at this price. It turns out that you benefit from the increase in volumes, but lose from the fact that all products are slightly cheaper. Marginal revenue, also known as marginal revenue, is used to determine what outweighs gain or loss.
Let us give an example: as a result of an increase in sales volumes from twenty units to twenty-one units of production, the price of one unit decreased to 9 rubles and 50 kopecks. In this case, our new one will be equal to 199.5 rubles, which is 50 kopecks less than the income with the old volumes. It turns out that the marginal revenue is -50 kopecks. As it turned out, it is not profitable for the company to increase sales volumes.
This example has shown how limit values are used in management. If a limit values revenues fall below zero, which means that the company needs to stop and restrain the growth of production volumes in order to keep prices at an acceptable level. As long as marginal revenue remains positive, there is room for growth.
However, this analysis is somewhat incomplete. If marginal revenue is positive, we need to analyze businesses as well. Marginal cost measures how much cost has changed as a result of an increase in sales. According to elementary logic, this value will be positive, since each new unit of production requires costs for its production. On the other hand, the more units of goods produced, the less per unit of output until the production capacity is fully loaded.
In any case, if marginal revenue is greater than marginal cost, then we receive marginal profit, which means that we need to increase sales. This usually happens until new production equipment is needed, either active sales will not reduce market prices.
Profit maximization conditions for perfect competition.
ANSWER
According to the traditional theory of the firm and the theory of markets, profit maximization is the main goal of the firm. Therefore, the firm must choose such a volume of supplied products in order to achieve maximum profit for each period of sales.
PROFIT is the difference between gross (total) income (TR) and total (gross, total) production costs (TC) for the sales period:
profit = TR - TS.
Gross income- this is the price (P) of the goods sold, multiplied by the volume of sales (Q).
Since the price is not affected by a competitive firm, it can affect its income only by changing the volume of sales. If the firm's gross income is greater than its total costs, then it makes a profit. If the total cost exceeds the gross income, then the firm incurs losses.
total costs is the cost of all factors of production used by the firm in the production of a given volume of output.
Maximum Profit achieved in two cases:
a) when the gross income (TR) exceeds the total costs (TC) to the greatest extent;
b) when marginal revenue (MR) is equal to marginal cost (MC).
Marginal Revenue (MR) is the change in gross income resulting from the sale of an additional unit of output. For a competitive firm, marginal revenue is always equal to the price of the product:
The marginal profit maximization is the difference between the marginal revenue from the sale of an additional unit of output and the marginal cost:
marginal profit = MR - MC.
marginal cost Additional costs that increase output by one unit of the good. Marginal cost is entirely variables costs, because fixed costs do not change with release. For a competitive firm marginal cost equal market price goods:
The marginal condition for profit maximization is the level of output at which price equals marginal cost.
Having determined the profit maximization limit of the firm, it is necessary to establish an equilibrium output that maximizes profit.
The most profitable equilibrium This is the position of the firm in which the volume of goods offered is determined by the equality of the market price to marginal cost and marginal revenue:
The most 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 extract the maximum profit. At the same time, it should be borne in mind that the output that provides the maximum profit does not mean at all that the largest profit is extracted per unit of this product. It follows that it is wrong to use unit profit as a measure of total profit.
In determining the level of output that maximizes profit, it is necessary to compare market prices with average costs.
Average cost (AC)- costs per unit of output; equal to the total cost of producing a given quantity of output divided by the quantity of output produced. Distinguish three type of average costs: average gross (total) costs (AC); average fixed costs (AFC); average variable costs (AVC).
The ratio of market price and average production costs can have several options:
The price is greater than the average cost of production, maximizing profit. In this case, the firm extracts economic profit, i.e., its income exceeds all its costs (Fig. 26.2);
Rice. 26.2. Profit maximization by a competitive firm
The price is equal to the minimum average production costs, which provides the company with self-sufficiency, i.e., the company only covers its costs, which makes it possible for it to receive a normal profit (Fig. 26.3);
Rice. 26.3. Self-sustaining competitive firm
The price is below the minimum possible average cost, that is, the firm does not cover all its costs and incurs losses (Fig. 26.4);
The price falls below the minimum average cost, but exceeds the average minimum variables costs, i.e. the firm is able to minimize its losses (Fig. 26.5); price below average low variables costs, which means the cessation of production, because the company's losses exceed fixed costs (Fig. 26.6).
Rice. 26.4.Competitive Firm incurring losses
Rice. 26.5. Minimizing the losses of a competitive firm
Rice. 26.6. Termination of production by a competitive firm
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Every firm strives to maximize profits. Its size depends on maximizing the difference between the company's income and costs. Therefore, the second element (along with costs) that determines profit is the income received by the company from the sale of its products. They act as the most important economic indicator the work of enterprises (firms) and other organizations, reflecting their financial receipts from all types of activities.
In a market economy, represented by the movement of commodity-money flows, income always appears in the form of a certain amount of money. Income is the monetary value of the performance of a firm (or individual individual) as a subject market economy. This is the amount of money that comes to her direct disposal. It reflects the economic performance economic activity firms. This means that the condition for receiving cash income is effective participation in the economic life of society. The very fact of receiving it is an objective evidence of such participation, and its size is an indicator of the scale of this participation.
The desire to maximize one's income dictates the economic logic of behavior for any market entity. It acts as ultimate goal and powerful incentive entrepreneurial activity.
The receipt by the firm of income indicates the sale of products, the expediency of the costs incurred, and the public recognition of the consumer properties of the product.
According to the types of costs of the company, revenues are also divided. Therefore, it is customary to allocate total, average and marginal income.
Total (cumulative, gross) income is the amount of money received from the sale of a certain amount of
vara. It is determined by multiplying the price of a good by the corresponding quantity of output that the firm is able to sell, and can be expressed by the corresponding formula:
TR = Р Q, where TR is total revenue;
P is the price of a unit of production;
Since, under conditions of pure (perfect) competition, the firm sells products at a constant price, then, consequently, its income will be directly proportional to the quantity of products sold (the more products sold, the greater the income). In other words, the gross income of the firm will increase in this case by a constant amount for each additional unit of goods sold (Table 11.1).
Table 11.1. Firm's earnings under pure competition
| Unit price (P) | | Total Revenue (TR) | Income Growth (MR) |
| 5 | 0 | 0 | 0 |
| 5 | 1 | 5 | 5 |
| 5 | 2 | 10 | 5 |
| 5 | 3 | 15 | 5 |
| 5 | 4 | 20 | 5 |
| 5 | 5 | 25 | 5 |
Since the demand curve for a product under perfect competition is perfectly elastic, each additional unit sold increases gross income by the same amount (in our example, by 5 monetary units). Graphically, it is depicted by a straight ascending line (Fig. 11.1).
In contrast to pure competition, under conditions of imperfect competition, the volume of sales affects the market price of the product (it decreases with an increase in sales), so the total income of the company does not grow in proportion to the products sold, but at a slower pace, since additional income in this case tends to decrease (Table 11.2).
Table 11.2. The total income of a firm under imperfect competition
| Unit price (P) | Units sold (Q) | Total income (TR) | Growth income |
| 6 | - | - | - |
| 5 | 1 | 5 | 5 |
| 4 | 2 | 8 | 3 |
| 3 | 3 | 9 | 1 |
| 2 | 4 | 8 | -1 |
| 1 | 5 | 5 | -3 |
The table shows that not only the quantity of goods sold, but also the size of the total income of the company depends on the value of the price. At the same time, the maximum gross income is not provided by the highest price (in our example, 5 den. units).
According to the table, you can build a graph showing the dynamics of the total income of the company in conditions of imperfect competition (Fig. 11.2).
As can be seen from the graph, two parts can be distinguished in the change in total income (TR). First, it grows and reaches its maximum value at point E, and then begins to decline. The total income increases as long as the additional
0123456Q Fig. 11.2. The firm's total income curve under imperfect competition
the income from the sale of a new unit of goods is a positive value. Wherein maximum income(9 den. units) the company receives not at the maximum selling price (5 den. units), but at a price of 3 den. units Therefore, the firm's optimal sales volume will be three physical units at a price of 3 den. units
Average income (AR) is the proceeds from the sale of a unit of production, i.e. is the gross income per unit of goods sold. It acts as the price per unit for the buyer and as income per unit for the seller.
Average revenue is the quotient of total revenue (TR) divided by the number of products sold (Q). It can be expressed by the following formula:
where AR is average revenue;
TR - total income;
Q - the number of products sold.
At a constant price (in conditions of pure competition), the average income is equal to the selling price, as can be seen from the above formula, which can be transformed as follows:
AR == --= P .
QQ
Therefore, the price and average income, according to Western economists, act as one and the same phenomenon, which is considered only from different points of view. It makes sense to calculate the average income for certain period only if the prices for manufactured homogeneous products change or if the firm focuses on the production of a number of products, models, etc.
Under conditions of perfect competition (when the price is assumed to be constant), the average income graph looks like a straight line parallel to the x-axis, i.e. horizontal line (Fig. 11.3).
In conditions of imperfect competition (when the price tends to fall with the growth of sales), the average income of the firm decreases. Graphically, this is depicted as a descending line (Fig. 11.4).
Marginal revenue (MR) is the additional (additional) income to the firm's gross income received from the production and sale of one more unit of goods. It refers to the limiting characteristics of the goods being sold and makes it possible to judge the effectiveness of the sale.
Production, as it shows the change in income as a result of an increase in output and sales of products.
Marginal revenue allows you to evaluate the possibility of payback for each additional unit of output. In combination with the indicator of marginal cost, it serves as a cost guide for the possibilities and expediency of expanding the volume of production. Therefore, whenever a firm intends to change its output, it must calculate how its income will change as a result of this change and how much additional income will be from the sale of one more unit of output.
Marginal revenue measures the change in total revenue resulting from the sale of an additional unit of a good. It is defined as the difference between the gross income from the sale of n + 1 units of a product and the gross income from the sale of n units of a product at
following formula: MR = TRn+1 - TRn,
where MR is marginal revenue;
TRn+1 - total income from the sale of n+1 units of goods;
TRn is the total income from the sale of n units of goods.
Under perfect competition, a firm sells up to
additional units of production at a constant (constant) price, since any seller cannot influence the established market price by selling an additional quantity of goods. Therefore, marginal revenue is equal to the price of the good, and its curve coincides with the curve of perfectly elastic demand and average income, i.e. MR=AR=P (Fig. 11.5).
In conditions of imperfect competition, marginal REVENUE does not coincide with the price of an additional unit of goods sold (it will be less than the price). This is due to the fact that with an increase in the supply of additional quantity of goods in an imperfect market, the price has to be reduced. At the same time, the price of each previous unit of goods also decreases. This price reduction (loss on n units) is taken into account in the price of n + 1 units of the good. Therefore, the marginal revenue of an additional unit of good is equal to the price of that unit minus the loss on previous units of output caused by the decrease in price.
Graphically, the marginal revenue of an imperfect competitor is a sloping line, reflecting its fall as a result of a price decrease (Fig. 11.6).
The figure shows that the line of average income and the line of marginal income with the production of additional units of output gradually decrease, since the demand line in this case goes down (it coincides with the line of average income), and
The individual income falls below the price as the volume of sales influences the market price.
The income of the firm in practice consists of two parts. Firstly, from the proceeds from the sale of products (goods or services). It is a certain amount Money from the main and non-core activities of the company, the end result of which is manufactured and sold products or services rendered (work performed), paid for by the buyer or customer.
Secondly, from non-operating income, which is a side financial income of the company. They are not directly related to the main production activities. Their sources can be: dividends on invested shares or acquired shares and other securities, fines received from counterparties, penalties, forfeits, interest for keeping funds in a bank and other unplanned income.
Gross income or the company's revenue () is the product of the price of the goods () by the volume of output (sales) ():
Average income firms () is the quotient of dividing revenue by sales volume:
Therefore, average income is just another name for the price of a commodity.
Under conditions of perfect competition, the price is determined by the market, and an individual firm, occupying a negligible share of the market, accepts it as given (is price taker), i.e. can sell any quantity of its products at a fixed market price. Therefore, the revenue function of a perfectly competitive firm from output is linear, and the tangent of the slope of the line TR is equal to the price of the goods (Fig. 10.1).
Rice. 10.1. Revenue of a perfectly competitive firm
Accordingly, as the price increases, the slope increases, and the revenue curve shifts from position to position. And vice versa.
marginal revenue firms (MR) is the increase in gross income with an increase in sales by one unit:
It can also be said that marginal revenue is the additional revenue that a firm will receive from producing an additional unit of output.
If the output revenue function is known (TR = f(q)), the marginal revenue function can be obtained by taking the derivative of revenue with respect to output:
Since the price is set by the market, and an individual firm can sell any quantity of output at that price, the market demand curve for the firm's product is a horizontal line: at the slightest increase in price by the firm, the demand for its product drops to zero, as buyers go to other sellers. It also follows from this that The marginal revenue of a perfectly competitive firm is equal to the price of the good:MR= R.
Let's verify this with an example. Let the store sell beer for 10 rubles. for a bottle. This means that each next bottle sold increases the store's revenue by exactly the price of the bottle. Let's make a table of revenue and marginal income of the store, depending on the number of bottles sold (Table 10.1).
Table 10.1. Revenue and marginal revenue of a competitive firm
The demand curve for a competitive firm's product is shown in Fig. 10.2.
Rice. 10.2. Equilibrium market price and demand curve for an individual firm's product
On fig. 10.2a curves in the market of the given goods are represented. Hundreds of sellers and thousands of buyers collide here, respectively, the quantities of supply and demand (q) are measured in many thousands, and maybe even millions of units of production. As a result of the interaction of supply and demand, the equilibrium market price of the goods (P*) is formed. On fig. 10.26 we observe the position of an individual firm, which is a grain of sand on a market scale. The firm accepts the market price as given and is able to sell any quantity of its product at that price. In other words, buyers can purchase any quantity of the firm's product at the equilibrium market price: the market demand curve for the product of an individual perfectly competitive firm is a horizontal line.
For any price cut, area like area ABDC in fig. 2 is equal to Q 1 (Dp). 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 product minus the income that was sacrificed by giving up the opportunity to sell previous units of the product at higher prices. For very small changes in price, the changes in total income can therefore be written as
where Dp is negative and DQ is positive. Dividing equation (2) by DQ, we get:
(3)
where Dp/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 translated into a relationship that relates marginal revenue to price elasticity of demand. The price elasticity of demand at any point on the demand curve is
Plugging this into the marginal revenue equation, we get:
Consequently,
(4)
Equation (4) confirms that marginal revenue is less than price. This is so because E D is negative for a downward-sloping demand curve for the monopolist's product. Equation (4) shows that, in general, the marginal revenue from any output depends on the price of the good and the elasticity of demand to price. This equation can also be used to show how total revenue 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. In the same way, 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. Tab. 1.2.2 summarizes the relationship between marginal revenue, price elasticity of demand, and total revenue.
TABLE 1.2.2. Marginal revenue, total revenue, and price elasticity of demand for a product
You can see that the relationship implied by Equation (4) is logical by analyzing how total income changes along a linear demand curve and the corresponding marginal revenue curve for a monopoly along with the quantity a buyer needs. Recall that demand is price elastic when a price reduction leads to an increase in total income. If total revenue increases when price decreases, then marginal revenue must be positive. Thus, whenever the marginal revenue from a price decrease is positive, demand is price elastic. This is true because negative marginal revenue implies that a decrease in price leads to a reduction in total revenue. Finally, when marginal revenue is zero, a change in price does not change total revenue, and demand has unit elasticity. This is shown at the bottom of Fig. 3. The maximum total revenue is extracted when the marginal revenue is zero. At this point on the linear demand curve, the price elasticity of demand is -1.
Equation (4) also implies that the more elastic demand is, the smaller the difference between marginal revenue and price. In the extreme case, if demand is infinitely elastic, then the difference between price and marginal revenue becomes zero. This is so because the value of 1/E D in equation (4) tends to zero as E D tends to minus infinity. This is in line with the fact that in a competitive firm price equals marginal revenue.
We also note in Table. 1.2.1 and according to the graphs in fig. 2 and 3 that marginal revenue falls faster than price as the monopolist produces more product. For a linear demand curve, marginal revenue will fall exactly twice as fast as price. Note that for every $100,000 reduction in the price of a concert, marginal revenue always decreases by $200,000 after the first concert. Marginal revenue becomes zero at the level of output corresponding to half of the amount of goods (services) that would be sold at a price equal to zero. (For a linear demand curve, the slope of the curve is constant. Equation (3) shows that the change in marginal revenue in response to any change in Q is such that:
D mR/ DQ = D [P + Q( D R/ DQ )] / DQ= (Dр + DQ(DP/DQ))/DQ = 2(DP/DQ). The rate of change of MR relative to Q is twice the rate of its change relative to Q.
Rice. 3. Demand for a monopolist, marginal revenue, total revenue and elasticity
With a linear demand curve, when more goods are sold, marginal revenue falls twice as fast as price. When marginal revenue is positive, total revenue increases as price decreases. When marginal revenue is negative, total revenue decreases whenever price falls. Total revenue peaks when marginal revenue MR = 0. When MR > 0, demand is elastic. When MR< 0, спрос является неэластичным. Спрос обладает единичной эластичностью, когда МR = 0, а общий доход в этой точке достигает максимума.
Profit maximization by monopoly firms in the short run
A competitive firm maximizes profit by adjusting the quantity sold at the market price so that marginal cost of production equals marginal revenue. Although a monopoly can influence the price of its product, the marginal analysis of profit maximization is the same in the case of competition and in the presence of a monopoly. Profit maximization implies that the marginal revenue must equal the marginal cost of producing the quantity of goods. However, the marginal revenue from additional output of a monopolist is always less than the price at which this quantity is sold. (For a firm with monopoly power, the price it can charge is a function of the quantity offered for sale, Q. Profit is p = PQ - TC since P = f(Q) and TC = f(Q), dp/ dQ=P+Q(dP/dQ)-dTC/dQ Assuming that necessary condition the existence of the second derivative is satisfied, maximum profit is achieved where [P + Q (dP/dQ)]=dTC/dQ. The left side of equality is marginal revenue. This marginal revenue expression is similar to equation (3) for cases where changes in Q are infinitesimal. The right side of the equation represents marginal cost.)
Tab. 1.3.1 presents data on the cost of a concert performance. The total cost per year for all submissions is shown in the third column of the table. The fourth column shows the average cost per performance. Marginal cost is calculated in the fifth column as the change in total cost from each additional submission. The sixth column reproduces data on marginal income from Table. 1.2.1. Fixed (economic. - Ed.) Costs are $100,000 a year. They consist of depreciation and interest (forgone interest from the provision of appropriate funds in a loan, for example, when investing them in a bank. - Ed.) on durable equipment - such as musical instruments, sound equipment, costumes, vehicles used to transport personnel and equipment (including bodyguards). Even if there are no concerts at all for a year, you still bear these costs. The last column is the total profit, so it indicates that if you choose not to play any gigs, you will lose $100,000 a year. If you value your performances at more than $1 million each, there will be no buyers for them. You will therefore lose an amount equal to your fixed costs.
If your price is $1 million, then you will find a buyer for one gig a year. The total cost will be $500,000. You will therefore make $500,000 in profit from this concert. The marginal cost for the first gig is $400,000. They are equal to the average variable costs this concert. They consist of the salary paid to your assistants, accompanists, bodyguards who protect you on the road, and the cost of fuel for the transport in which you move from one place to another. The marginal revenue from the first gig is $1 million. The marginal profit indicated in the penultimate column of Table. 10.3 is therefore $600,000. Remember that marginal profit is the difference between marginal revenue and marginal cost.
After the first gig, the marginal revenue drops below the price because you have to lower your planned price to be able to give more performances. Gross income from two concerts, according to Table. 10.3 is equal to 1.8 million dollars. You must value your concerts at $900,000 each if you are willing to sell two performances a year to the organizers.
The total cost of the two concerts is $1 million. The marginal cost of the second gig is therefore $1 million minus $500,000 divided by one. This gives marginal cost. Since the marginal revenue from the second gig is $800,000, your marginal revenue is positive. AT this case marginal profit is $300,000 and your total profit rises from $500,000 a year to $800,000.
As long as the marginal revenue exceeds the marginal cost of the gig, profits increase. Profit begins to decline as soon as marginal cost exceeds marginal revenue. You will increase your annual profits if you increase the output of concerts per year. This is true because the marginal cost of the third gig is $550,000, while the marginal revenue from it is $600,000. Your marginal profit for the third concert is therefore $50,000, and your total profits rise to $850,000 per year. If you want to give three concerts a year, then you must value each of them at $800,000.
Are you interested in getting your price below $800,000? If you could bring the price down to $700,000, you could play four gigs a year. But that shouldn't have been done. The marginal cost of the fourth concert would be $700,000; the marginal revenue from it would be only $400,000. Your marginal profit would be,
TABLE 1.3.1 Costs and determination of the amount of commodity output of a profit-maximizing monopoly
hence $300,000. By lowering your price to $700,000, you would cut your profits from $850,000 to $550,000 a year.
As indicated in Table. 1.3.1, for any release greater than three concerts per year, marginal cost will exceed marginal revenue. Your equilibrium price is thus equal to $800,000 per concert. The equilibrium output that will be demanded at this price is three. Profits at this price are $850,000 a year. The marginal cost per concert for this release is $550,000. Therefore, at equilibrium output, marginal cost is less than price. This follows from the fact that marginal revenue under monopoly is less than price.