Average, gross and marginal income. Conditions for profit maximization under perfect competition Marginal cost is...

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.

Just as there is a distinction between total, average, and marginal cost, it is necessary to distinguish between total, average, and marginal cost. income.

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

TR=p´ Q.

Thus, income is always a function of price and output. At the same time, depending on the nature of the market (perfect or imperfect competition) in which the firm operates, the price is either a constant value that the firm cannot influence (the firm is the price taker), or a variable value that the firm can influence (the firm is the price taker). price maker).

Hence: the income of a firm operating in the market of perfect competition depends entirely on the volume of production chosen by it and changes in proportion to the change in output, while the income of a firm selling its products in the market of imperfect competition depends on the chosen volume of production and on the price. The monopoly firm has to lower the price in order to sell more products, so the total income of the firm, as the volume of sales increases, first rises, then begins to decline.

Graphically, the total income of a perfect competitor's firm is a straight line ascending from the origin; monopoly firms - 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 firm b) a non-competitive firm

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

AR = TR: Q.

Obviously, the average revenue of the firm is equal to the price of the product:

AR= (p´ Q): Q=p .

Finally, the third indicator that characterizes the income of the firm and is widely used in economic analysis is the marginal income ( MR). marginal revenue characterizes the increase in total income with an increase in output per unit.

MR=Δ TR: Δ Q.

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

0 Number of products, units Q

Rice. 7.6. Average, marginal revenue and product price

competitive firm

marginal revenue non-competitive firm less than the average income (price), i.e.

MR< р.

This relationship between marginal revenue and price is explained as follows. In order to sell an additional unit of output, the firm has to lower the price of that unit, but the firm cannot sell the same product at different prices, so it has to lower the price of everything. previous instances. As a result, at the expense of the income received from the sale of an additional unit of production, the company must cover the losses from lower prices for previous copies. In conditions of imperfect competition, the marginal revenue of a non-competitive firm is equal to the price of an additional unit of output minus the losses arising from a decrease in the price of previous units.

Suppose the firm sells the first unit of output for 124 den. unit, 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 firm is forced to reduce the price of the previous (first) unit. As a result, having sold the second unit for 114 den. unit, the firm will receive a marginal revenue of 104 den. units , i.e. marginal revenue is less than price.

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

Rice. 7.7. Average, marginal revenue and product price

non-competitive firm

See also:

Conditions for profit maximization under 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:

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 output. For a competitive firm, marginal cost is equal to the market price of the good:

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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Monopolist's demand function. The price of a monopolist's product depends on the volume of sales and is an inverse function of demand: . To increase the volume of sales, the monopolist is forced to reduce the price. Therefore, the monopolist's demand curve is downward.

The monopolist's gross income is equal to and is a function of output. Gross income can be thought of as a function of price. Marginal income, by definition, is measured by the first derivative of the gross income function:

The quantity characterizes the change in price caused by the 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 number of products are sold at the same price. In the monopoly market, i.e. the slope of the demand curve is negative. This means that the marginal revenue of a monopolist from the sale of any product is always below its price: . This means that the curve is always below the demand curve.

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 income curve is a parabola starting from the origin. Define the marginal revenue of a 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 is:

A necessary condition for the maximum value of a function of one variable is the equality of its first derivative 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. There is only one point on the demand line corresponding to the value at which. Thus, if, then, a reaches a maximum. If and takes positive values, and demand is elastic, then it grows. On segments of the line of demand and gross income, where these conditions are met, the monopolist produces products. If marginal revenue is negative and demand is inelastic, then as output increases, gross revenue decreases.

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, marginal values ​​are the most effective way to track the potential increase in profits that all enterprises, without exception, are striving for. 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 revenue margins fall below zero, then 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 produced, the less there is per unit of output as long as the production capacity is not 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. As a rule, this happens until new equipment is required for production or active sales do not reduce prices in the market.