How to determine the optimal production volume. Determining the optimal volume of production

Engineering systems 12.10.2019

Engineering systems

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10.3. The theory of the optimal volume of output. Definition of marginal cost of production

Table 3

Table 4

marginal cost.

Table 5

marginal cost.

The optimal volume of production is such a volume that ensures the fulfillment of concluded contracts and obligations for the production of products on time with a minimum of costs and the highest possible efficiency.

The optimal production volume can be determined by two methods:

Gross indicators comparison method;

The method of comparing limit indicators.

The following assumptions apply when using these methods:

the company produces and sells only one product;

the purpose of the enterprise is to maximize profits in the period under review;

only the price and volume of production are optimized, since it is assumed that all other parameters of the enterprise's activity remain unchanged;

the volume of production in the period under review is equal to the volume of sales.

However, despite the strict limits of the above assumptions, the use of these methods greatly increases the likelihood of accepting right decisions.

Consider the example of determining the optimal volume of production by the above methods.

In table. 3 shows the initial data for determining the optimal volume of production.

Table 3

The volume of sales of products and the costs of its production

The application of the method of comparing gross indicators to determine the optimal volume of production involves the following sequence of actions:

The value of the volume of production is determined, at which zero profit is achieved;

The volume of production with maximum profit is established.

Consider the volume of sales of products (Table 4)

Table 4

The volume of sales of products with maximum profit

Based on the data in the table, we can draw the following conclusions:

Zero profit is achieved with the volume of production and sales in the range from 30 to 40 thousand pieces. products;

The maximum amount of profit (1140 thousand rubles) is obtained with a volume of production and sales of products of 90 thousand pieces, which is in this case optimum production volume.

Before moving on to determining the optimal volume of production using the method of comparing marginal indicators, one should consider such a concept as marginal costs. When forming the production plan of an enterprise, it is important to establish the nature of the increase in production volumes when additional production variables are added to the already available fixed resources, and how, in this case, the total costs of production and sales will be formed. The answer to this question is the law of diminishing returns. Its essence lies in the fact that, starting from a certain moment, the sequential addition of units of a variable resource (for example, labor) to an unchanged fixed resource (for example, fixed assets) gives a decreasing additional, or marginal, product per each subsequent unit of the variable resource. Consider this statement with an example (Table 5).

Table 5

Dynamics of performance indicators of the enterprise

The table shows that the more additional workers are involved, the more products are produced. However, each time the attraction of another additional worker gives an unequal increase in the increase in output. This increase is the marginal product of the labor of one worker. It is calculated by simply subtracting the level of production in question from the subsequent increase in output. In our example, the marginal product per additional worker raised increases to a third worker and then starts to fall. This change in the growth of marginal product is explained by the decrease in the growth of average labor productivity per worker. This is due to the fact that with an increase in the number of employees, fixed assets remain unchanged.

Based on the situation considered, one should not make hasty conclusions about the termination of the production of additional products, since a decrease in the value of the increase in production volumes for each one employee involved does not yet indicate that the production of additional units of output is unprofitable. It all depends on whether profit increases when hiring another employee. For example, if the price of a product in the market is unchanged, then the business will receive income as a result of having more products to sell, provided that the value of the additional cost associated with hiring an additional worker will be less price goods.

From the above example, we can assume that the cost of a unit of production produced by attracting additional work force decreases to a certain point, and then starts to rise again. The fall or rise in the cost of each additional unit of output is called marginal cost.

The concept of marginal cost is practical value, because it shows the costs that the company will have to incur in the event of an increase in production by one unit. However, at the same time, this concept shows the costs that the company will "save" in the event of a reduction in production by this last unit. Thus, the costs of production in the conditions of market relations should be considered not just as the costs incurred for the acquisition of everything necessary for the production of products and their manufacture, but also as the establishment of the best opportunity for their use, i.e., in other words, it is necessary to form such costs, which give the best result.

Let us return to the determination of the optimal volume of production by the method of comparing marginal indicators. The calculation of the optimal volume of production is presented in table. 6.

Table 6 Calculation of the optimal volume of production by comparing marginal indicators

In our case, the marginal revenue per unit of output is the market price of the unit. Marginal cost is the difference between the next total cost and the previous total cost (see Gross Comparison Method) divided by the output. Marginal profit is found as the difference between marginal revenue and marginal cost.

Thus, based on the data in the table, the following conclusions can be drawn:

Expansion of production volumes efficiently (profitably) up to 90 thousand units;

Any increase in production volumes over 90 thousand units. production at a constant price will lead to a decrease in gross profit, since the amount of additional costs will exceed the amount of additional income per unit of output.

The goal of the firm is profit maximization. Profit(P) is the difference between the revenue (TR) and the firm's total costs (TC):

Since, in the revenue function (TR = P × Q), the market price is not under the control of a perfectly competitive firm, the latter's task is to determine the output at which its profit will be maximized.

Firm maximizes profit at an output where its marginal revenue equals its marginal cost:

wherein production volume is optimal

According to the profit maximization rule, a firm that produces products in volumes at which MR=MC receives the maximum profit possible at given prices, i.e. optimal production volume is the volume at which marginal cost (MC) and marginal revenue (MR) are equal.

The equality of MR and MC is profit maximization condition for any firm regardless of the market structure in which it operates (perfect or imperfect competition).

Equality MR=MC as a condition for profit maximization can be justified logically. Each additional unit of output brings some additional income (marginal revenue), but also requires additional costs (marginal cost). As long as marginal revenue exceeds marginal cost, an extra unit of output increases profits.

Accordingly, at the moment when marginal cost becomes equal to marginal revenue, profit reaches maximum. Further rise output at which marginal cost exceeds marginal revenue will result in lower profits.

In its decisions, the company seeks to achieve the best results - to get the maximum profit at the lowest cost. In this case, the firm is said to be in a state equilibrium .

Firm equilibrium condition is the equality of marginal cost, marginal revenue and factor price:

The point at which the market price crosses the marginal cost curve defines the equilibrium position.

To the left of point E (Fig. 2) MC > MR, it is profitable for the company to increase production, because on each unit of output, it receives more than it spends. Having produced less than at point E, the firm incurs losses from underproduction.

Figure 2. Firm equilibrium in production

To the right of point E MC > MR. For each additional unit of output, the firm incurs losses, because its costs exceed its income. It is unprofitable to increase production to the right of point E. Consequently, optimum production volume is Q 0 .

Thus, at the volume of production Q 0 , the firm achieves maximum profit.

Consequently. To achieve maximum profit, the firm must produce this volume of output. where marginal revenue equals marginal cost.

The equality of marginal revenue and marginal cost characterizes the equilibrium of the firm in any market structures and is used to maximize profits. minimizing losses and obtaining zero economic profit.

Conclusions on question 3

The volume of production at which marginal revenue is equal to marginal cost (optimum output) ensures maximum profit. If the actual output is below the optimum, then the firm should expand production - profits will increase; If output is greater than optimal, then the firm should reduce production to increase profits.

the method of comparing gross indicators;
the method of comparison of limit indicators.

The following assumptions apply when using these methods:
the company produces and sells only one product;

the purpose of the enterprise is to maximize profits in the period under review;
only the price and volume of production are optimized, since it is assumed that all other parameters of the enterprise's activity remain unchanged;
the volume of production in the period under review is equal to the volume of sales.

However, despite the rigid framework of the above assumptions, the use of these methods greatly increases the likelihood of making the right decisions.
Consider the example of determining the optimal volume of production by the above methods.
In table. 7.1 shows the initial data for determining the optimal volume of production.
Table 7.1
The volume of sales of products and the costs of its production

Volume	Permanent	Variables	Gross
0	1200	0	1200
10	1200	200	1400
20	1200	360	1560
30	1200	490	1690
40	1200	610	1810
50	1200	760	1960
60	1200	960	2160
70	1200	1220	2420
80	1200	1550	2750
90	1200	1980	3180
100	1200	2560	3760

The application of the method of comparing gross indicators to determine the optimal volume of production involves the following sequence of actions:

the value of the volume of production is determined, at which zero profit is achieved;
the volume of production with maximum profit is established. Consider the volume of sales of products (Table 7.2)

Table 7.2
The volume of sales of products with maximum profit

Volume	Price,	Gross	Gross	Profit,
implementation, thousand pieces	rub-	revenue, thousand rubles	costs, thousand roubles.	thousand roubles.
0	-	0	1200	-1200
10	48	480	1400	-920
20	48	960	1560	-600
30	48	1440	1690	-250
40	48	1920	1810	110 440
50	48	2400	1960	720
60	48	2880	2160	940
70	48	3360	2420	1090
80	48	3840	2750	1140
90	48	4320	3180	1040
100	48	4800	3760

Based on the data in the table, we can draw the following conclusions:

zero profit is achieved with the volume of production and sales in the range from 30 to 40 thousand pieces. products;
the maximum amount of profit (1140 thousand rubles) is obtained with a volume of production and sales of 90 thousand pieces, which in this case is the optimal volume of production.

The method of comparing marginal indicators allows you to establish to what extent it is cost-effective to increase production and sales. It is based on a comparison of marginal cost and marginal revenue. In this case, the rule applies: if the value of marginal revenue per unit of output exceeds the value of marginal cost per unit of output, then the increase in production and sales will be profitable.
Before moving on to determining the optimal volume of production using the method of comparing marginal indicators, one should consider such a concept as marginal cost. When forming the production plan of an enterprise, it is important to establish the nature of the increase in production volumes when additional production variables are added to the already available fixed resources, and how, in this case, the total costs of production and sales will be formed. The answer to this question is the law of diminishing returns. Its essence lies in the fact that, starting from a certain moment, the sequential addition of units of a variable resource (for example, labor) to an unchanged fixed resource (for example, fixed assets) gives a decreasing additional, or marginal, product per each subsequent unit of the variable resource. Consider this statement with an example (Table 7.3).
Table 7.3.
Dynamics of performance indicators of the enterprise
The table shows that the more additional workers are involved, the more products are produced. However, each time the attraction of another additional worker gives an unequal increase in the increase in output. This increase is the marginal product of the labor of one worker. It is calculated by simply subtracting the level of production in question from the subsequent increase in output. In our example, the marginal product per additional worker raised increases to a third worker and then starts to fall. This change in the growth of marginal product is explained by the decrease in the growth of average labor productivity per worker. This is due to the fact that with an increase in the number of employees, fixed assets remain unchanged. Based on the situation considered, one should not make hasty conclusions about the cessation of the production of additional products, since a decrease in the value of the increase in production volumes for each one employee involved does not yet indicate that the production of additional units products are unprofitable. It all depends on whether profit increases when hiring another employee. For example, if the price of a product in the market is unchanged, then the business will receive income as a result of having more products to sell, provided that the value of the additional cost associated with hiring an additional worker is less than the price of the product.
From the above example, it can be assumed that the unit cost of production produced by attracting additional labor decreases to a certain point, and then starts to rise again. The fall or rise in the cost of each additional unit of output is called the marginal cost.
The concept of marginal cost is of great practical importance, since it shows the costs that an enterprise will have to incur if production is increased by one unit. However, at the same time, this concept shows the costs that the company will "save" in the event of a reduction in production by this last unit. Thus, the costs of production in the conditions of market relations should be considered not just as the costs incurred for the acquisition of everything necessary for the production of products and their manufacture, but also as the establishment of the best opportunity for their use, i.e., in other words, it is necessary to form such costs, which give the best result.
Let us return to the determination of the optimal volume of production by the method of comparing marginal indicators. The calculation of the optimal volume of production is presented in Table 7.4.
Table 7.4
Calculation of the optimal volume of production by the method of comparison of marginal indicators

Sales volume, thousand units	Marginal income, rub.	Marginal costs, rub.	Marginal profit, rub.
10	48	20	28
20	48	16	32
30	48	13	35
40	48	12	36
50	48	15	33
60	48	20	28
70	48	26	22
80	48	33	15
90	48	43	5
100	48	58	-10

expansion of production volumes efficiently (profitably) up to 90 thousand units;
any increase in production volumes over 90 thousand units. production at a constant price will lead to a decrease in gross profit, since the amount of additional costs will exceed the amount of additional income per unit of output.

The goal of the firm is profit maximization. Profit(P) is the difference between the revenue (TR) and the firm's total costs (TC):

Firm maximizes profit at an output where its marginal revenue equals its marginal cost:

wherein production volume is optimal

According to the profit maximization rule, a firm that produces products in volumes at which MR=MC receives the maximum profit possible at given prices, i.e. optimal production volume is the volume at which marginal cost (MC) and marginal revenue (MR) are equal.

The equality of MR and MC is profit maximization condition for any firm regardless of the market structure in which it operates (perfect or imperfect competition).

Accordingly, at the moment when marginal cost becomes equal to marginal revenue, profit reaches maximum. A further increase in output, at which marginal cost exceeds marginal revenue, will lead to lower profits.

In its decisions, the company seeks to achieve the best results - to get the maximum profit with minimal cost. In this case, the firm is said to be in a state equilibrium .

Firm equilibrium condition is the equality of marginal cost, marginal revenue and factor price:

The point at which the market price crosses the marginal cost curve defines the equilibrium position.

Figure 2. Firm equilibrium in production

Thus, at the volume of production Q 0 , the firm achieves maximum profit.

Consequently. To achieve maximum profit, the firm must produce this volume of output. where marginal revenue equals marginal cost.

Conclusions on question 3

Conclusion

Lecture conclusions:

1. The ultimate goal and main result of the company's activities is profit. The degree of profitability of the company depends on many factors: rational use resources, the efficiency of the technology used, the organization of production and labor, the validity of decisions made, etc. Solving the problem of increasing profitability, the firm is guided by the rule of least cost and the rule of profit maximization, using a comparison of such quantities as marginal cost, marginal revenue and resource prices.

A sign of production optimization is the achievement of the most profitable output at the lowest possible cost. The result of an optimal production process depends on the influence of external and internal factors.

The optimal volume of output is achieved as a result of the relationship between the technological and managerial tasks built on analysis and mathematical approach.

Ensuring the ultimate goal of the manufacturer - making a profit requires an analysis of:

The consumer market in the context of categories and product characteristics.
Composition of permanent and variable costs.
The impact of a change in the cost structure on optimal release products.
The minimum allowable price of products at the break-even point.
Determining the relationship of factors influencing the volume of output.

Conducting research is focused on a specific type of product unit, which allows you to obtain accurate analysis data.

Balance of consumer demand and supply

Dynamics of change market demand on products affects the strategy of the company for the production of goods. decreases:

Enterprises independently determine the composition of costs and fix the structure in the accounting policy. For operational analysis, costing is performed by item.

The impact of the composition of costs on the pricing mechanism

At a constant selling price of products, a decrease in unit costs leads to an increase in part of the profit. One form of optimization is to change the balance between fixed and variable costs. The growth in output affects the increase in variable costs, fixed types of costs remain unchanged. Regulating quantitative composition shares, an optimal balance of costs is achieved.

The structure of constants and variable costs differs when calculating the parameters:

Planned release, in which the value of each component is clearly defined. Actual data are used for the calculation.
An additional release based on market demand.

With additional release, a reduction in the price of products is achieved. Share fixed costs in an additional batch of products is absent (covered by the planned release) and the resulting difference goes into the category of profit. As a result, a reserve of the minimum allowable price is provided, which allows for competitive discounts and seasonal sales of goods.

Determining the level of break-even production

The optimal level of output is located within the boundaries of the minimum allowable and maximum possible output. To plan the quantity of output, it is important to determine the minimum level - the lower break-even limit.

The calculation of the break-even point (TB) is carried out by assigning indicators of variables, fixed costs on the volume of output (quantity of goods) and the price of a unit of production. The critical point is calculated graphically.

Defining a critical release level allows you to:

Maintain the minimum allowable output during a period unfavorable for the sale of products. The need may arise in conditions of seasonality or high competitive offer market.
identify weaknesses and possible problems quantity output. The indicator makes it possible to vary the parameters of costs and volume.
Exclude from production products with unprofitable indicators.

An exact indicator and the use of calculated data can only be used if the data remain unchanged in a certain unit of time. If you change the structure of manufactured goods, the sales price or the amount of costs, you will need to make a new calculation.

The objective of the production process is to obtain the maximum return on capacity and human resources. Technical and economic indicators are influenced by external and internal factors. Non-manufacturing causes arise when:

Changes in commodity and consumer market;
increase in transport costs.

Internal factors are based on:

The technical level of equipment of the enterprise;
providing warehousing materials and finished products;
system of management and organization of work.

To determine the optimal level of production, it is not enough to determine the total break-even volume of revenue and costs. In practice, an important indicator is optimal size parties. Costs are taken into account:

Required for the implementation of the order;
necessary for the safety of stocks and products.

For example, you can determine the impact of capacity utilization on variable costs. The value of the share of costs decreases in the total value with a more complete use of capacities and increases with a decrease in productivity, which, in turn, affects . In turn, the increase in output will require the use of large areas for stock storage.

The search for relationships between indicators allows you to work out the degree of influence on the optimal output. A frequent option for searching for the interaction of factors is a combination of labor automation and capital investment. The selection of options is carried out for the same type of units of goods. Comparative analysis carried out in a quantitative or valuation.

For ease of perception, analysts use materials in the form of tables or diagrams. Most visual way achieved using graphs and curved lines - isoquant. The graphical method allows you to obtain information about the possible substitution when the original data changes.

The practical benefit of obtaining information on substitution allows us to consider, for example, the possibility of increasing automation and mechanization of labor in comparison with the use of costs handmade. In a common version, the method is used in the selection of raw materials or materials as a share of variable costs in the cost of finished products.

Basis for determining the optimal level of production output

The strategy of the enterprise to achieve the optimal level of production is reduced to the relationship of factors influencing the process. With the help of summary data of assessment and analysis, the following is achieved:

Determining the volume of output at which financial stability arises. The indicator is based on the calculation of the break-even point.
Obtaining data on the feasibility of producing a number of types of products. The assortment policy is determined on the basis of the ratio of average costs to the cost of producing a unit of output.
Search for internal and external factors that affect pricing.
Definition of entrepreneurial risk as a result of the study of conjectural demand.

The combination of factors allows you to get the optimal level of production of assortment units and the enterprise as a whole.

The value of the optimal level of production determines the profit and enterprises. Obtaining data on optimization is achieved by calculation, in which indicators of the volume of revenue, costs, demand, and other interrelated parameters are compared. By analyzing external and internal factors of influence, maximum output is achieved at minimum cost.

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