Purpose. Development of a procedure for determining the optimal capitallabor ratio within the framework of twofactor pro duction functions, as well as an analysis of the conditions for its implementation in practice. Methodology. In the process of the conducted mathematical analysis, the search for the extrema of the most popular in eco nomic studies, of twofactor production functions, namely the CobbDouglas production function, CESfunction, linear func tion, Allen's function in terms of capital assets, was performed. The limit rate of the technological substitution of factors in condi tions of optimal capitallabor ratio was found, which proved to be unique in all investigated production functions. The indicated relationship was verified on the basis of microeconomic theory, in particular, using the equilibrium principle. Findings. The hypothesis of the single marginal rate of technological substitution in conditions of optimal capitallabor ratio is verified. On the basis of the microeconomic theory, the procedure for determining the optimal capitallabor ratio in the framework of any twofactor production functions is substantiated due to the marginal rate of technological substitution. The proposed pro cedure consists in determining the marginal rate of technological substitution as the ratio of the marginal products of the produc tion factors and equating it to one unit. The obtained ratio makes it possible to deduce the formula of optimal capitallabor ratio, provided that the indicators of the dynamics of realized products, main assets and labor remuneration in the enterprise are ade quately described by the corresponding production function with nonzero substitution. Originality. Development of a procedure for optimization of capitallabor ratio within the framework of substitutional two factor production functions based on the formulas of their marginal rate of technological substitution. Practical value. Theoretical conclusions and proposals were tested on the example of a Ukrainian enterprise in the field of mechanical engineering. The results of the research can be used to manage capitallabor ratio by determining its optimal volume in production, which opens the possibility of rational use of basic productive assets and labor at domestic enterprises which are characterized by relative overequipment with high moral and physical equipment decay.

Аbstrаct. The аrtіcle іs аbоut іnvestіgаtіng аnd fоrmulаtіng methods оf digitalization of the HR-management system of the enterprise in the context of globalization changes by means of HR-technologies and HR-functions transformation analysis. The оbject оf the reseаrch іs the mоdіfіcаtіоn оf the HR-technologies, factors influencing the development of the HR-function in times of digitalization. Reseаrch methоds аre а set оf theоretіcаl аnd methоdоlоgіcаl, ecоnоmіc аnd аpplіed іssues оf defіnіtіоn, develоpment аnd іmplementаtіоn оf the process of digitalization of the HR-management system of the enterprise in the context of globalization changes. Іt wаs аnаlysed scіentіfіc аrtіcles cоnnected wіth digitalization processes, digital products and HR-solutions, directions of changes in HR-management digitalization process, influence ofglobalization changes at the HR-management system of the enterprise. The аrtіcle prоvіdes аn understаndіng оf the rоle оf digital technologies in HRМ, opportunities provided by digital transformation of HR-management system. It is proved that in today’s conditions, the HR-function of the enterprise should be implemented through flexibility, integration into the business and be able to attract, retain and develop talent. It is analysed how globalization changes and actualization of existing HR-technologies influence human capital market. Among the total investment in digitalization of HR-processes, about half (49%) is aimed at implementing software solutions for human capital management, a third (32%) covers the implementation of cloud services, and in the near future plans to increase investment in forecasting, improved solutions process automation, artificial intelligence. It is investigated the evolution of HR-functions under the influence of digitalization and found out the relevance and directions of digital technologies implementation in HR processes. The article reveals the main directions of HR-management digitalization changes: digital workforce, digital workplace, digital HR. The key opportunities that digitalization brings to HR-management have been substantiated. To get the most out of advanced technologies, HR-competencies must be clearly defined, correlated with business requirements, differentiated by functions, roles and levels, updated at the right time, applied to perform any HR-management functions. It is analysed opportunities provided by digital transformation of HR-management system. Digital economy, human capital and information technology play a crucial role in ensuring sustainable economic development. The mаіn results оf the reseаrch cаn be аpplіed іn the prаctіcаl аctіvіty оf enterprіses іn оrder tо implement HR-management system digitization path. Further reseаrch needs tо be tаken in the field of the HR-technologies development due to fast-moving digital decisions and in accordance with specifics of the domestic countries’ globalization and digitalization influence. Keywоrds: digitalization, HR-management system, globalization, globalization changes, sustainability, HR-technologies, human capital, digital HR, HR-functions, artificial intelligence. JEL Classification L86 Formulas: 0; fig.: 4; tabl.: 1; bibl.: 20.

The article deals with the features of the controlling implementation in trade enterprises in the context of the international dimension, the possibility of adapting international approaches to the Ukrainian conditions of business. The essential concept of controlling and its connection with realization of the general functions of management is defined. It is established that controlling is a management subsystem that ensures the achievement of the mission and system of goals of the enterprise, covers all areas of activity, business processes and business facilities. It is determined that effective business processes are the driving force of success of a trading company, so the implementation of processes should be monitored and any deviations should be corrected in a timely manner. It was found that the concept of controlling is not limited to pure control. The impossibility of considering controlling only at the final stage of management is substantiated. Controlling ensures the achievement of the goals of trade networks, directing the functioning of the management system of trade entrepreneurs in a single direction, defined by strategic, tactical and operational plans. The experience of other countries in controlling conducting at trade enterprises is studied. The tools of foreign practice that can be used in the implementation of controlling of different areas (marketing controlling, procurement and logistics controlling, financial activities controlling, sales controlling, financial activities controlling) are defined: kaizen system, Just-in-time system, CRM, benchmarking, ABS-analysis and XYZ-analysis, PIMS, outsourcing matrix, DPS method, profitability chart «Maisigma», PEST-analysis, Monte Carlo method, methodology of «quality circles», sensitivity analysis, construction of a map of strategic groups, quality standards, performance indicators, calculation of inventory levels, comparison of costs in the value chain, change management, management of «weak» signals, hierarchy of strategies, building a map of business processes. Implementation of controlling provides an increase in trade to 25%; increase in profit from 10 to 12%; increase in profitability from 8 to 20%; increase labor productivity to 30%.

The article is devoted to topical issues of business protection through the prism of forensics (financial investigations). This new line of financial fraud and fraud investigation services is used to investigate and assist clients in identifying the facts and causes of fraud that may occur due to the absence or inadequate and ineffective system of internal control. The types of economic crimes faced by companies during 2017—2019 were analyzed and it was established that bribery and corruption are the leaders among economic crimes. The article reveals the essence of the concept of «forensic» as the identification of potential problems through legal and financial audit. Forensic procedures as a promising way to protect business in the context of global transformations and emerging cyber risks in an increasingly complex digital business environment have been studied. The article outlines the main directions of forensics in risk management, among which are: investigation of fraud; support in court proceedings; corporate intelligence; computer forensics; compliance with anti-corruption legislation, as well as to use preventive measures to prevent fraud. The classical methods and algorithm of financial investigation are outlined and it is noted that they may differ depending on the purpose for which forensics is conducted, the industry in which the company operates, and others. It is established that forensics for an economic entity ends with a reporting stage, during which the customer is provided with evidence of fraud, as well as the proposed recommendations. It is proposed to use the forensic mechanism when business owners: doubt an important decision; there is a leak of commercial information; mechanisms for working with suppliers have not been established; a large deal is envisaged.

The article is about revealing the content and role of HR crisis management at trade enterprises. The article provides an understanding of organizational changes, crisis phenomena, and crisis management. It is stated, that management of enterprises in a crisis state is one of the main problems of economy and legislation not only of economically developed countries, but also of countries with fragile economies, to which Ukraine still applies. A set of measures for HR crisis management at a trading company was identified. At the basis of research, it is possible to identify consistent ways to implement the steps of HR crisis management at a trading company. It is established, that as a result of a crisis, organizations may lose employees, workers, along with key talent and organizational knowledge, from low morale, fear, physical relocation or death. In this case, there are outlined the core messages to decision makers that employee’s development and rewards are the major dimensions of the content of an Human Resource Management (HRM) system and that consistency and distinctiveness are the principal features of the process of HRM system, even in cases where an organization is operating under an economic crisis environment. It is stated, that the essence of crisis management of an enterprise is to provide such conditions for the functioning of an enterprise, when financial, production, marketing, personnel and other difficulties are not permanent and are quickly resolved by means of special measures. It is investigated, that HR crisis management at trade enterprises involves not only the formal organization of the work with the staff, but also a set of factors of social and psychological, moral character - democratic style of management, caring attitude to the needs of a person, attention to his/her individual characteristics, etc. It is proved, that an important factor that can contribute to effective crisis management is a well-selected, managed personnel, who respond quickly and flexibly to any changes in the environment. The article establishes the HR management in the conditions of unstable or crisis state of an enterprise as a comprehensive, planned activity, based on a system of scientifically grounded principles, experience and intuition of managers of an enterprise. There are investigated the stages for HR crisis management in the market conditions as: analysis of the problem situation and state of an enterprise, diagnostics of human resources state, development and implementation of HR marketing measures, development of a HR crisis strategy and system of its marketing support, design of a HR crisis policy, development and organization of implementation of HR crisis decisions, development of measures to overcome and prevent conflicts, determination of HRM risk and ways of their overcoming, control over the implementation of HR-crisis decisions. There is created a list of actions of HR managers while crisis management, including establishment of a crisis management team, development of recovery plans, provision of communications.