مدل‌سازي رياضي توليد نوآوري، تقليد نوآوري و اثرات آن بر رفاه اجتماعي

MATHEMATICAL MODELING OF INNOVATION DEVELOPMENT, INNOVATION IMITATION AND THE EFFECTS ON SOCIAL WELFARE

اين مقاله يك مدل رياضي جديد و كاملاً نوآورانه براي تحليل اثرات ميزان تقليد‌پذيري نوآوري بر ميزان توليد و تقليد نوآوري، و نيز بر ميزان رفاه اجتماعي حاصل از نوآوري ارايه مي‌كند. هسته‌ي اصلي اين مدل، رقابت بين دو بنگاه است كه هر دو توانايي خلق نوآوري و نيز توانايي تقليد آن را دارند. هدف، بررسي اثر پارامترهاي مختلف بر تصميم‌گيري دو بنگاه در رابطه با ميزان توليد و ميزان تقليد نوآوري است. نتايج حل مدل نشان مي‌دهد كه هزينه‌هاي تقليد بالا (كم‌تر تقليد‌پذير‌بودن نوآوري) نه‌تنها توليد نوآوري را زياد مي‌كند، بلكه مي‌تواند تقليد نوآوري را هم افزايش دهد. به‌كمك مدل، سياست حق انحصاري نوآوري نيز مورد تحليل قرار گرفته است. نتايج تحليل مدل نشان مي‌دهد براي نوآوري‌هاي بسيار تقليد‌پذير، اعمال سياست حق انحصاري موجب افزايش رفاه مي‌شود. به‌خصوص اگر قيمت فروش نوآوري به ميزان كم‌تر از هزينه‌ي تمام‌شده‌ي نوآوري تعيين ‌شود.

The tradeoff between innovation development and innovation imitation has been widely studied in the literature of technology diffusion. In this paper, a mathematical model is developed to investigate how innovation imitability affects the amount of developed innovations, imitated innovations and, also, social welfare, resulted from innovations. For the sake of simplicity, it is considered that there are two firms producing the same product with the same price in the market and with equal market shares, while their production costs are different. The market is assumed competitive, thus, the cost reduction of one firm results in lower prices and, consequently, less profit for the other firm. As obvious in the model, the problem is captured by linking the production cost of one firm to the profit of the other firm. By the aid of this model, we have presented barriers to innovation development and diffusion. The model is based on competition between two firms in the context of a strictly competitive game, and both are able to develop and imitate innovations simultaneously. The greatest challenge in this model is to understand how firms endogenously decide on, not only how much innovation to develop, but, also, how much innovation to imitate. The results of the model solution point out that higher imitation costs (less imitability) not only increase innovation development, but, also, may increase innovation imitation. We have further used the model to investigate the effectiveness of an apparently anti-innovation imitation policy: Intellectual Property Right (IPR). This is a routine policy which governments can easily consider toward innovation imitation between firms. Two points considered are: First, how the policy is modeled and entered into the model equations, and, second, how that policy affects the solution results. The main criteria for investigating this effects of this policy is its effect on social welfare resulting from innovations. While the IPR policy is implemented, developed innovations are available in the market for other firms to be used. However, firms have to pay a pre-determined amount of money to the innovation developer firm. This policy changes to parts of the model: firstly, the imitation cost increases as much as the innovation buying price, and, secondly, the indirect costs of the innovation developer firm decreases. Whether it is the first or the second firm, the same changes happen to the innovator and imitator firms. Solution results bear the testimony that for highly imitable innovations, implementing IPR results in higher social welfare, especially if the price of buying that innovation is set to an amount less than the cost of developing that innovation.