Model of indirect Expenses Distribution for Determining Economies of Scale

Changing economic environment, innovative production technologies and the need to obtain relevant information in decisionmaking, management determines the organizations to seek different approaches to identify economies of scale. Economies of scale are manifested as an effect of cost reduction. The article proposes a comparative analysis of two methods of establishing costs that allow the identification and quantification of economies of scale. The research proposes a distribution of indirect costs depending on the cause-effect relationship between activity and product. The research results show a cost difference in the case of implementing the Activity-based costing (ABC) cost system, thus recognizing the usefulness and compatibility of the method.


Introduction
Economies of scale are a feature of a cost function, which describes the impact on total production costs. The analysis of cost efficiency, factor productivity and economies of scale has identified how companies are affected by the current pandemic situation [1][2]. Profitability driven by economies of scale can lead to lower costs [3]. Increasing volumes of goods and services, made with a certain amount of labour and capital, have led to an increase in living standards through the efficient combination of resources [4]. An efficient configuration of the organization's resources can be monitored with the help of economies of scale. The efficiency of companies with high market authority can be achieved by setting up a price monopoly, but its implementation would trigger a reduction in efficiency [5][6]. The existence of economies of scale is dependent on a directly proportional increase in results, depending on the unitary increase in inputs [7]. Such wording indicates the reduction in unit cost obtained as a result of the increase in production [8][9].
Studies have indicated that market power is advantageous to induce economies of scale and would result in higher productivity [10][11]. The definition of economies of scale does not contain the effects of managerial decisions, which would have a major effect on operational characteristics. Economies of scale refer to changing the total cost for a certain value of production. If production doubles and costs increase by less than 100%, then the TC = f(X, Z, P, T, F) (1) where TC is the total cost, X is a vector of input prices, Z is a vector of operating characteristics, P is a measure of the result, T is a vector of effects over time, and F is a vector of firm effects.
The use of such a model does not provide a perspective, if the outputs and the size of the network change by a disproportionate amount. As a result, a model of the following form can be used [37]: TC = f(W, Y, T, F) (2) Another form of the production function can be considered the solution offered by a Cobb-Douglas production function, if the elasticity of the substitution is very close to the unit value, the case [38].
where Y represents the production (gross domestic product), K is the fixed capital, L the employed population, , , și the parameters to be estimated. Starting from the production function (3), the following form of the function was proposed by constraining + ß = 1, the expression thus becoming a productivity function [39].
The translog production function is a class of flexible functional form [40]. An advantage of the production function is that it does not accept rigid situations, such as the perfect substitution between factors of production or ideal competition in the market of factors of production [41]. Such a function allows the transition from a linear to a nonlinear relationship, and can be used to approximate the second order of a homogeneous linear output.
The input price factor (X) takes into account the price of raw materials, labour, transport, operating cost and administrative cost as input variables. These variables were selected because they are representative of society and do not have major corrections. However, the significant correlation becomes an issue in the translog model with the addition of second-order terms.
Relation (5) can be used to estimate the economy in scale , or the impact on the cost of increasing production, while keeping input prices constant and allowing all other factors to vary.
The elasticity of economies of scale E s varies, when is superunitary, unitary, respectively subunitary. The economies of scale in relation 7 are calculated as 1 minus the derivative of the logarithm of costs in relation to the derivative of the logarithm of production. A positive result indicates an increasing profitability, a negative result indicates scale diseconomies. where: elasticity of total cost with respect to output; elasticity of total cost; RTS will refer to the impact on cost of increasing output and network size simultaneously; RTD will refer to the impact on cost of increasing output while holding network size; E E elasticity of scale; P production sold and C costs.

Determination of economies of scale by statistical method
In order to determine the economies of scale, the translog cost function was estimated for a company operating in Romania, Brasov County, which assembles locking systems, CAEN code 4618, 159 employees [42]. The company is characterized by a share of staff costs of 11%, raw materials 73% of the total cost, the difference being transport and administrative costs [42]. The translog cost function will be initially estimated using the Ordinary Least Squares Model (OLS) for a period of one year. The statistical calculations include the total cost of the periods subject to analysis 21596.90 lei, with a standard deviation of 217311.67 lei, considering all 30 products of the company (leu-Romanian currency). The standard deviation is shown because costs vary by product, while production averages 338.07 lei and a standard deviation of 951.83 lei. The data provided by the organization were statistically processed, in order to identify the type of economies of scale of the company (Table 1). In order to carry out the research, an interim balance sheet was prepared as follows: I (January-April), II (May-August), III (September-December). In table 2 the data were statistically processed using the Excel program. The correlation between production and the number of employees is shown in Figure 1. Identifying the degree of association of the variables, in this case the result shows a perfect positive association. The linear relationship between the independent variable (number of employees) and the dependent variable (production) was highlighted with a linear regression equation. Bravis-Pearson correlation indices were used to express the causal relationship. The graph shows a linear relationship between production and the number of employees. The correlation coefficient is 0.9449. It can be stated that approximately 94% of the production variation is explained by the participation of employees. In addition, for each increase in the number of employees (with one employee), the value of production increases by 51692  significant differences between the compared means, for the alternative hypothesis there are statistically significant differences between them, because the value of p is greater than 0.05. The calculations show that there are no statistically significant differences between the means compared with two exceptions. In the case of the average labour force in the first period compared to the second period, because p is 0.03, less than 0.05 there are statistically significant differences between the labour force in the first period and the labour force in the second period and in the case the average administrative cost in the second period compared to the third period, because p is 0.01, less than 0.05. The results indicate that the allocation of resources according to the models that rejected the null hypothesis in order to represent the production structure is indicated.

Determining the cost by the global method
The analysed company obtained during a management period, carried out during a year, 10142 pieces for which expenses of 20678674 lei were incurred. The standard cost used as a registration price is 2039 lei/piece. (20679538 lei -total standard cost). The statement of expenditure in the accounts is shown in Table 3 [39]. Establishing the cost of production is achieved with the additional information forwarded by the production department summarized in Table 4 [42]. The sequence of accounting entry, between the two modes of accounting, revealed in the case of the calculation of actual cost, in which administrative expenses are not included in the cost, expenses of the period remain (not included in cost, in the balance of account 9240). Thus, the expenses that form the production cost are, in this situation, of 20668700 lei. It is observed that the value of the production cost is equal to the sum of the expenses from class 6, of 20678674 lei, from which the administration expenses 4174139 lei were eliminated. Following the cost calculation by the global method, the cost of the quantity of 10142 pcs. is 20668700 lei. The actual unit cost is 2037.93 lei/piece, if the product is registered in the accounting at a standard (default) cost. The cost differences between the calculated actual cost of 20668700 lei and the standard cost of 20679538 lei must be established. The cost difference -10838 lei is a saving because the actual cost is lower than the standard cost. Analysing the turnover of account 711, it is observed that it is equal to the credit turnover of account 902, resulting from the sum of the amounts registered on its credit of 20679538 lei. (registration of production at standard cost), and registration of cost differences being -5480 lei, respectively -10838 lei.
The value of the two accounts reflects, in fact, the actual production cost established in both variants, of 20674058 lei and 20668700 lei. The balances of the two accounts are equal and close to each other, reflecting the amount of administrative expenses not included in the cost of production. Indirect costs are included in costs as well as direct costs. These items of expenditure may be absorbed by the cost items and the cost allocation is based on an absorption basis (RAI) thus: where quantity manufactured, machine operating hours, THFU total machine operating hours.
The calculation of the unit and overall cost of production was performed in Table 7. The cost of production is the sum of direct and indirect costs, and the direct cost consists of the cost of raw materials and direct labour [7].
(10) (11) (12) (13) where C p production cost, C d direct cost, C i indirect manufacturing cost, C RM raw material cost, C L labor costs and q quantity manufactured.

Determination of cost calculation by indirect cost absorption method and ABC method
The ABC method of calculating costs is used in different areas of activity due to the ability to organize cost accounting according to the activities of the organization. This method will identify the main differences in cost allocation and identify the reasons why the ABC method contributes to improving costing. The data provided by the organization are in table 7. According to the method, the enterprise is no longer considered a set of entities, but an accumulation of activities.
The products are assembled and then sold in batches of 120 pieces, and the orders of materials were 15 pieces for each type of product [42]. Indirect costs are absorbed in the cost of products according to the number of operating hours of the machines identified in Table 5. The calculation of the unit cost of inductors was performed in Table 8 [43] with respect to: (14) where C ui unit cost of inductors. Calculation of unit and global production cost using relationships (Table 9): where: Cp production cost, C d direct cost, C i indirect manufacturing cost, C RM raw material cost, C L labour costs, q quantity manufactured, C EC equipment cost, C uif unit cost inductor machine operating hours, h operating hours of equipment/pcs., C l launch cost, n number of units sold per lot, C uil unit cost inductor launch in manufacturing, C R reception cost, C uir cost unit inductor material reception, n p number of orders for each product, C C cost control, C uic unit cost inductor control, C MM material management cost and C uigm unit cost inductor material management.

Results
The paper presents the existence of economies of scale in an organization, confirming the initial expectations. The extension of the vision related to the relationship between production and production factors can be achieved by estimating the parameters of a translog production, thus making the transition from a linear to a nonlinear system. Accelerating the dynamics of factors of production, in order to increase the level of production, taking into account the context generated by a weak collinearity and an accelerated dynamics of the factor of production, will determine a subunit economy, while a sub-exponential dynamics will determine a economies of scale with a score higher than 1.
The differences identified as a result of the allocation of costs by the two methods identify the best allocation of indirect costs (Figure 2). Comparative situation of unit costs, calculated by the two methods (Table 10). These are due to indirect cost absorption conventions and can influence price if calculated on the basis of cost plus margin and can influence profit if the price level influences sales and last but not least of the benefit if the level of stocks fluctuates from a period to period.

Conclusions
The results of this study show that the presence of economies of scale in the industry market indicates inefficiency in operations, and unit production costs could be reduced by increasing the scale of operations. As long as unit costs can be reduced by increasing production, this approach would be more effective, leading to greater profitability for the organization.
The strategy is only a viable option if additional production can be sold, which may not be the case in a competitive market, but the company has economies of scale, which can be improved by the measures identified by the analysis, ie a cost allocation that to benefit from increased profitability. With the main purpose of illustrating the application of these theoretical relations and to show the importance of potential errors, this paper presents an empirical study conducted on a company operating in Romania. This research can be continued by expanding the analysis by addressing economies of scale by expanding the field of research.