Marginal revenue is greater than one. Marginal revenue and its importance in making management decisions

Revenue is zero when the price is $6 because nothing is being sold at that price. However, at a price of $5, 1 unit of output is sold and income in this case is $5. An increase in sales from 1 to 2 units increases income from $5 to $8, so marginal revenue is $3. When  

Algebraically, if the demand for a product is P = 6-Q, then the total income received by the firm is PQ = 6Q - Q2. Average income is equal to PQ/Q =6 - Q, which is the demand curve for the product. The marginal revenue is equal to DR (Q) /AQ, or 6-2Q. This can be checked using the data in Table. 8.1.  

When an individual firm faces a demand represented on a graph by a horizontal line, as in Fig. 8.2a, then it can sell an additional unit of production without reducing the price. As a result, total income increases by an amount equal to the price (one bushel of wheat sold for $4 gives an additional income of $4, i.e. MR = AR(q)/Aq = A(4q)/ Aq = 4 ). At the same time, the average income received by the firm is also $4, since each bushel of wheat produced will be sold for $4 (AR = Pq/q = P == $4). Therefore, the demand curve for an individual firm in a competitive market is expressed by both average and marginal revenue curves.  

Rice. Figure 8.3 shows this graphically. In Fig. Figure 8.3a shows the firm's income R(q) as a straight line passing through the origin. Its slope is the ratio of the change in income to the change in output, i.e., it is equal to the marginal income. Similarly, the slope of the total cost (TC) line represents the ratio of the change in production costs to the change in the volume of output, i.e. marginal cost.  

This condition also follows from the data in table. 8.2. For all output volumes up to 8, marginal revenue is higher than marginal cost. For any volume of output up to 8 units, the company should increase output, as profits increase. At output of 9 units, however, marginal cost becomes greater than marginal revenue, and so additional output will reduce rather than increase profits. In table 8.2 does not show the volume of output at which marginal revenue exactly coincides with marginal costs. At the same time, from the above data it follows that when MR(q) > M (q), the volume of output needs to be increased, and when MR(q)

AR(q)/Aq is the ratio of the change in income to the change in output, or marginal revenue, and AT(q)/Aq is marginal cost. Thus, we conclude that profits are maximized when  

The marginal revenue and marginal cost curves in Fig. 8.4 also illustrate this rule of profit maximization. The average and marginal revenue curves are drawn as horizontal lines at a price of $40. In this figure, we have drawn the average cost curve AC, the average variable cost curve AV, and the marginal cost curve MC to better show the firm's profits.  

Profit reaches its maximum at point A, associated with a production volume of q = 8 and a price of $40, since at this point marginal revenue equals marginal cost. At lower output (say, q, = 7), marginal revenue is greater than marginal cost, and so profits can be further increased by increasing output. The shaded area between qi = 7 and q shows the lost profit associated with production at qi. At higher output levels (say qs), marginal cost is higher than marginal revenue. In this case, reducing the volume of output produces cost savings that exceed the marginal revenue. The shaded area between q and q2 == 9 shows the lost profit associated with production at q2.  

The application of the rule that marginal revenue must equal marginal cost depends on the manager's ability to estimate marginal cost. To properly estimate costs, managers need to keep three key points in mind.  

Careful study of Fig. Figure 8.18 shows that an output tax can have two effects. First, if the tax is less than the firm's marginal revenue, it will maximize its profit by choosing the level of production at which its marginal cost plus tax equals the price of output. The firm's output falls from qi to q2, and the indirect effect of the tax is to shift the short-run supply curve upward (by the amount of the tax). Secondly, if the tax is painful  

But AR/AQ is marginal revenue and A/AQ is marginal cost, and so the condition for profit maximization is  

Rice. Figure 10.2b shows the corresponding average and marginal revenue curves, as well as the average and marginal cost curves. The marginal revenue and marginal cost curves intersect at Q =10. For a given volume of production, average costs are $15 per unit, price is $30 per unit, and therefore average profit is $30 - $15 = $15 per unit. Since 10 units are sold, the profit is $10-$15-$150 (area of ​​the shaded rectangle).  

To do this, we must rewrite the marginal revenue formula as follows  

Now, since the firm's goal is to maximize profit, we can equate marginal revenue to marginal cost  

On the graph, we shift the marginal cost curve up by an amount t and find a new intersection point with the marginal revenue curve (Figure 10.4). Here Qo and Po are, respectively, the volume of production and the price before the tax, and Qi and PI are the volume of output and the price after the introduction of the tax.  

We can answer this question by comparing consumer and producer surplus in competitive and monopolistic markets (we assume that producers in a freely competitive market and a monopolist have the same cost curves). Rice. Figure 10.7 shows the average and marginal revenue curves and the marginal cost curve for a monopolist. To maximize profits, the firm produces the level of production at which marginal revenue equals marginal cost. The monopoly price and output are denoted by Pm and Qm. In a competitive market, price must equal marginal cost and the competitive price Pc and quantity Q must be at the intersection of the average revenue curve (coinciding with the demand curve) and the marginal cost curve. Now let's see how it changes  

Marginal revenue curve: when the regulated price should not be higher than P,  

The firm's new marginal revenue curve corresponds to its new average revenue curve, and is shown by the thick line. For production volumes up to Qi, marginal revenue is equal to average revenue. For production volumes greater than Qi, the new marginal revenue curve coincides with the previous one. The firm will produce quantity Qi because it is at this point that the marginal revenue curve intersects the marginal cost curve. You can check that at PI price and Qi output quantity, the total net loss from monopoly power decreases.  

First, we need to determine the profit that the firm receives when it charges a single price P (Figure 11.2). To find out, we can add the profit from each additional unit produced and sold with the total output Q. This additional profit is the marginal revenue minus the marginal cost of each unit of output. In Fig. 11.2 this marginal revenue for the first unit is the highest, and the marginal cost is the lowest. For each additional unit, marginal revenue decreases and marginal cost increases. Therefore, the firm produces a total output Q at which marginal revenue equals marginal cost. Producing any quantity greater than Q would raise marginal cost above marginal revenue and thus reduce profit. Total profit is the sum of the profit from each unit of output sold and is therefore represented by the shaded area in Fig. 11.2 between the marginal income and marginal curves  

What happens if a firm engages in perfect price diversification? Since each buyer is charged exactly the price he is willing to pay, the marginal revenue curve is no longer related to the firm's output decision. Instead, the incremental revenue from each additional unit sold represents

Limit values ​​may seem like something purely theoretical and unrelated to the actual conduct of business at an enterprise only due to the lack of practice in working with them during the Soviet and perestroika periods. In fact, limit values- this is the most effective way track opportunities for potential profit increase, which is what all enterprises strive for without exception. As for their logic and calculation, it is nothing more complex than elementary algebra.

Marginal revenue is the amount a company receives from selling an additional unit of a product. It is one of the main limiting values ​​that have a direct connection with profit and price - two of the most important indicators of the company's performance. Marginal revenue is a value that has different meanings depending on the company. Thus, to carry out analysis using marginal income, it is necessary to compile a table reflecting the change in this value as sales volumes change.

To make it clearer, let's give a definition of marginal income. Marginal revenue is the change total income company, as a result of an increase in sales volumes per 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, given a constant price, marginal revenue will always be equal to the value this very price, and therefore it makes no sense to carry out further calculations of this indicator. However, this is not true. As you know, with an increase in sales volumes, an enterprise is forced to reduce the price in order to attract those buyers who will not buy the product at this price. It turns out that you benefit from increased volumes, but you lose from the fact that all goods are slightly cheaper. Marginal revenue, also known as marginal revenue, is used to determine which outweighs the gain or loss.

Let's 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 income is -50 kopecks. As it turned out, increasing sales volumes is not profitable for the enterprise.

The above example showed how limit values ​​are used in management. If the revenue thresholds fall below zero, it means that the company needs to stop and curb the growth of production volumes in order to keep prices at an acceptable level. As long as marginal returns remain positive, there is scope for increasing volumes.

However, this analysis is somewhat incomplete. If marginal revenue is positive, we need to analyze businesses as well. Marginal costs show how much costs have changed as a result of increased sales volumes. 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 a product are produced, the less there is per unit of output until production capacity not fully loaded.

In any case, if marginal revenue is greater than marginal cost, then we receive marginal profit, which means we need to increase sales volumes. As a rule, this occurs until new equipment is required for production or active sales will not reduce prices on the market.

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 get:

(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 be easily 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.

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 revenue along the linear demand curve and the corresponding marginal revenue curve for the monopoly vary along with the quantity demanded by the buyer. Recall that demand is price elastic when a reduction in price 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 so because negative marginal revenue implies that a decrease in price leads to a decrease 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. Maximum total revenue is extracted when 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 if E D tends to minus infinity. This is consistent with the fact that for a competitive firm, price equals marginal revenue.

We also note from the 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 of the good. For a linear demand curve, marginal revenue will fall at exactly twice the rate of price. Note that for every $100,000 reduction in the price charged per concert, after the first concert, the marginal revenue always decreases by $200,000. Marginal revenue becomes zero at the level of output corresponding to half the quantity 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. From equation (3) it can be seen 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 of a good is sold, marginal revenue falls at twice the rate of price. When marginal revenue is positive, total revenue increases as price decreases. When marginal revenue is negative, total revenue falls whenever the price decreases. Total revenue is maximum when marginal revenue MR = 0. When MR > 0, demand is elastic. When M.R.< 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 the marginal cost of production equals the marginal revenue. Although a monopoly can influence the price of its product, the marginal analysis of profit maximization is the same under both competition and a monopoly. Profit maximization implies that marginal revenue must equal marginal cost of the quantity produced. However, the monopolist's marginal revenue from additional output 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 the necessary condition for the existence of the second derivative is satisfied, the maximum profit is achieved where [P + Q (dP/dQ)]=dTC/dQ. marginal revenue. This expression for marginal revenue is similar to equation (3) for cases where the changes in Q are infinitesimal. The right side of the equation represents marginal cost.)

Table 1.3.1 provides data on the costs of a concert performance. The total cost per year for all performances 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 the data on marginal income from table. 1.2.1. Fixed (economic - Ed.) costs are equal to $100,000 per year. They consist of depreciation and interest (forgone interest on the provision of the corresponding funds on a loan, for example, when investing them in a bank. - Ed.) on durable equipment - such as musical instruments, sound equipment, costumes, vehicles used for transporting 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 total profit, therefore indicating that if you decide not to play any concerts, you will lose $100,000 per year. If you price your shows 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, you will find a buyer for one show per year. Total costs will be $500,000. You will therefore make $500,000 in profit from this gig. The marginal cost of the first concert is $400,000. They are equal to the average variable costs this concert. They consist of the salaries 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 maximum income from the first concert is $1 million. The marginal profit indicated in the penultimate column of the table. 10.3 is therefore equal to $600,000. As a reminder, marginal profit is the difference between marginal revenue and marginal cost.

After the first show, marginal revenue falls below price because you have to lower your target price to be able to perform more shows. Gross income from two concerts, according to table. 10.3, equal to 1.8 million dollars. You must value your concerts at $900,000 each if you want to sell two shows a year to the promoters.

Total costs for two concerts are equal to 1 million dollars. The marginal cost of the second concert is therefore $1 million less $500,000 divided by one. This gives marginal cost. Since the marginal revenue from the second gig is $800,000, your marginal benefit is positive. In this case, your marginal profit is $300,000, and your total profit increases from $500,000 per year to $800,000.

As long as marginal revenue exceeds 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 your concert output per year. This is true because the marginal cost of the third concert is $550,000, while its marginal revenue is $600,000. Your marginal profit for the third gig is therefore $50,000, and your total profits increase to $850,000 per year. If you wanted to do three concerts a year, then you would have to value each of them at $800,000.

Are you interested in lowering your price below $800,000? If you brought the price down to $700,000, you could do four shows a year. But this shouldn't be done. The marginal cost of the fourth concert would be $700,000, but its marginal revenue would be only $400,000. Your marginal profit would be,

TABLE 1.3.1 Costs and determination of the volume of commodity output of a profit-maximizing monopoly

hence $300,000. By lowering your price to $700,000, you would reduce your profits from $850,000 to $550,000 per year.

As indicated in table. 1.3.1, for any output greater than three concerts per year, marginal cost will exceed marginal revenue. Your equilibrium price is therefore $800,000 per gig. The amount of equilibrium output that will be demanded at this price is three. Profits at this price are $850,000 per year. The marginal cost of the concert at this output is $550,000. Therefore, at equilibrium output, marginal cost is less than price. This follows from the fact that the marginal revenue under a monopoly is less than the price.

Just as we distinguish between total, average and marginal costs, it is necessary to distinguish between total, average and marginal income.

Total income(gross, total, total income, sales revenue) ( TR)– is the product of price ( r) by the number of products sold ( Q):

TR=p´ Q.

Thus, income is always a function of price and production volume. Moreover, depending on the nature of the market (perfect or imperfect competition), on which the company operates, the price is either a constant value that the company cannot influence (the firm is a price taker), or a variable value that the company can influence (the company is a price setter).

Hence: the income of a firm operating in a perfectly competitive market depends entirely on the volume of production chosen by it and changes in proportion to the change in output, while at the same time the income of a firm selling its products in an imperfectly competitive market depends on the chosen volume of production and on price. A monopolist company, in order to sell more products, is forced to reduce the price, so the total income of the company, as sales volume increases, first increases, then begins to decrease.

Graphically, the total income of a perfect competitor firm is a straight line rising from the origin; monopolist firm - a parabola, the top of which characterizes the maximum total income received by the firm (Fig. 7.5).

Rice. 7.5. Total income

a) a competitive company; b) non-competitive firm

Average income (AR ) – This is the income received per unit of product sold:

AR = TR: Q.

It is obvious that the average income of the company equal to price product:

AR = (p´ Q): Q =p.

Finally, the third indicator characterizing the company’s income and widely used in economic analysis, is the marginal revenue ( M.R.). Marginal Revenue characterizes the increase in total income with an increase in production volume by one unit.

MR =Δ TR: Δ Q.

IN conditions competitive market The firm's marginal revenue is equal to the average revenue and price, i.e. M.R. = AR = r(Fig. 7.6).

0 Number of products, units. Q

Rice. 7.6. Average, marginal income and product price

competitive firm

Marginal Revenue non-competitive firm less than average income (price), i.e.

M.R.< р.

This relationship between marginal revenue and price is explained as follows. In order to sell an additional unit of product, the company is forced to reduce the price for it, but the company cannot sell identical copies of products at different prices, so it is forced to reduce prices for everything. previous copies. As a result, using the income received from the sale of an additional unit of production, the company must cover losses from lower prices for previous copies. Under imperfect competition, the marginal revenue of a noncompetitive firm is equal to the price of an additional unit of output minus the losses resulting from the reduction in the price of previous units.

Let's assume that the firm sells the first unit of output for 124 deniers. units, in order to sell the second unit, she is forced to reduce the price to 114 den. units, but reducing the price for the second unit to 114 den. units, the company is forced to reduce the price for the previous (first) unit. As a result, having sold the second unit for 114 den. units, the company will receive marginal income equal to 104 den. units , i.e. marginal revenue is less than price.

Thus, if a firm needs to reduce its price to sell more of a good, the average revenue curve will slope downward and the marginal revenue curve will be below the average revenue curve (Figure 7.7).

Rice. 7.7. Average, marginal income and product price

non-competitive firm

See also:

By selling its products, the company receives income, or revenue.

Income is the amount of money received by a company as a result of the production and sale of goods or services over a certain period of time. The amount of income and its change indicate the degree of efficiency of the company.

Distinguish total, average and marginal income.

Total (gross) income (TR ) is the total amount of cash revenue received by the company as a result of the sale of its products. It is calculated by the formula: TR = P Q, Where R– selling price per unit of production; Q– the number of units of products produced and sold. As we see, the amount of total income, other things being equal, depends on the volume of output and sales prices.

Average Income (AR) is the amount of cash revenue per unit of products sold. It is calculated by the formula: AR = TR / Q = (P  Q) / Q = P . The calculation of average income is usually used when prices change over a certain time interval or in cases where the range of products produced by a company consists of several or many goods or services.

Marginal Revenue (MR) is an increase in gross income resulting from the production and sale of an additional unit of product. It is calculated by the formula MR = TR/ Q, whereTR is the increase in gross income as a result of the sale of an additional unit of product;Q is the increase in production and sales volume per unit.

Comparison of marginal income and marginal costs for a commodity producer is important in developing its economic policy.

5. Company profit: concept and types

The profit of the company largely depends on the amount of income.

Profit represents the difference between total revenue and total costs, that is π= TR – TC, Where π – profit. The firm can calculate total profit (TR – TC), average profit (AR – ATC) and marginal profit (MR – MC).

Since there are accounting and economic costs, there are also accounting and economic profits.

Accounting profit – the difference between total revenue and external (accounting) costs. Let us recall that the latter include explicit, actual costs: wages, costs of fuel, energy, auxiliary materials, interest on loans, rent, depreciation, etc.

Economic profit - this is the part of the company’s income that remains after subtracting all costs from income: explicit (external) and implicit (internal), that is economic costs. Economic profit is also called net profit .

Economic profit is a certain excess of total income over economic costs. Its presence interests the manufacturer in this particular area of ​​business. At the same time, it encourages other firms to enter this field.

The essence of economic profit can be explained by the innovation of the entrepreneur, his use of innovative solutions in business affairs, and his willingness to bear full responsibility for the economic decisions made. Therefore, sometimes profit itself is defined as a payment for risk.

Depending on how income and costs are related, the company's profit can be positive(TR>TS), null(TR=TC) and negative(TR<ТС). Положительная прибыль означает, что фирма добилась самоокупаемости. Все издержки производства стали возмещаться полученным доходом.

Zero (normal) profit is income that reimburses the minimum costs of the entrepreneurial factor after the entrepreneur has reimbursed all production costs. It was previously noted that it is this profit that keeps the entrepreneur in this field of activity. However, at this moment there is no economic profit yet.

Negative profits mean the firm is making losses. The proceeds only partially cover production costs.