Geodesic
Production model in the conditions of unstable demand taking into account the influence of trading infrastructure: Ergodicity and its application
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 4, pp. 704-729

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A production model with allowance for a working capital deficit and a restricted maximum possible sales volume is proposed and analyzed. The study is motivated by an attempt to analyze the problems of functioning of low competitive macroeconomic structures. The model is formalized in the form of a Bellman equation, for which a closed-form solution is found. The stochastic process of product stock variations is proved to be ergodic and its final probability distribution is found. Expressions for the average production load and the average product stock are found by analyzing the stochastic process. A system of model equations relating the model variables to official statistical parameters is derived. The model is identified using data from the Fiat and KAMAZ companies. The influence of the credit interest rate on the firm market value assessment and the production load level are analyzed using comparative statics methods. 
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     author = {N. K. Obrosova and A. A. Shananin},
     title = {Production model in the conditions of unstable demand taking into account the influence of trading infrastructure: {Ergodicity} and its application},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     volume = {55},
     number = {4},
     year = {2015},
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     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_4_a16/}
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N. K. Obrosova; A. A. Shananin. Production model in the conditions of unstable demand taking into account the influence of trading infrastructure: Ergodicity and its application. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 4, pp. 704-729. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_4_a16/