Establishing effective cooperation between the manufacturer and reseller as vertical marketing channel participants implies the effective mechanism for the development of the main strategies of their business behaviour, such as price and expenditure forming for the joint promotion of the product. This provides the manufacturer and reseller the ability to select the most appropriate business game scenarios to maximize their profits in the short and long-term perspectives. This issue is relevant in the practice of distribution channels functioning. The purpose of the study is defining the optimal parameters values of expenditure function reaction for the compatible advertising, which will help to maximize the profits of both distribution channel participants. The research takes into account the statistical analysis of empirical data, in particular, data on average monthly sales volumes, as well as retail price for the unit of the product of the manufacturer enterprise. Besides, the paper presents a numerical experiment on the possible values of the advertisement expenditures parameters’ function, calculated on the basis of effectively selected range and step change. It was mathematically substantiated and defined the solutions of Stackelberg's business game, which implies functioning of the manufacturer equilibrium. A numerical experiment was conducted to maximize the possibilities of the manufacturer’s profitability features, reseller and marketing channel from the point of pricing strategies formation, and expenditure strategies for joint advertising of the both participants of the goods turnover channel. Stakelberg's variant of a business game is found to be optimal for the manufacturer, in which the percentage of its participation in the reseller’s expenditures on the joint advertising is non-zero. The obtained results can be the initial information base to form recommendations on possibilities of Stakelberg’s business game application in comparison with other variants of theoretical and game models of marketing channels’ participants interaction
Abstract. Subject of research: assessment and management of economic security of regional foreign trade flows of regions of Ukraine. Methodology: during the research, statistical analysis and analytical analysis (in the study of the main aspects of the formation of foreign trade flows of the region) are used. Mathematical modelling in economics (when creating a model of the two-dimensional normal distribution of regional foreign trade streams) and methods of analysis for risk assessment, conditioned by the formalization of the uncertainty of the operation of regional foreign trade operations are also used. The purpose of scientific research: mathematical modelling in economics in the management of economic security of export-import flows of regions of Ukraine; analysis of the structure of regional foreign trade flows in Ukraine and their respective risks; creation of the field of economic security of foreign trade flows of the region. The conclusion of the research: the study of limits and quantitative analysis of the risk of regional foreign trade flows in some regions of Ukraine is reduced to the creation of the area of crossing the main splicing ellipses of two-dimensional normal laws of export-import flows of these regions. After that, it will be possible to make a comparative assessment of the competitiveness and economic security of the regions. The purpose of the article is to develop an economic-mathematical model of quantitative risk analysis and to find appropriate boundaries of foreign trade flows of the region, which allows setting the thresholds of regional exportimport operations for optimal management of the process of foreign trade flows of the region. The foreign trade flows of Ivano-Frankivsk, Mykolaiv, and Kherson regions of Ukraine based on a two-dimensional normal distribution are modelled. Areas of threshold values of indicators of foreign trade flows of regions from the point of view of economic risk are defined, which, in contrast to existing one-dimensional approaches, takes into account elements of the interconnection of foreign trade flows of the region. The methodical conditions for constructing split ellipses of foreign trade flows of the region for comparative estimation of the risk of competitiveness and economic security of the regions are developed. This will make possible to conduct a systematic analysis of the region's economic development and to take measures both at the local level and at the state level in order to neutralize a number of threats to its economic security.
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