The Optimal Technological Progress Path

This paper analyzes firm's optimal technology progressing trajectory under dynamic optimizing. In this paper, technology progressing is represented by the improvement of product quality and is divided into two elementary decision-making problems. One is cost minimization, which requires firms to find an optimal combination of researching and technology importing in order to reach specific technology levels efficiently. Another problem is profit maximization. That is, firms have to choose proper product quality dynamically to maximize its profit. Solutions to these two problems, once combined together, form a complete description of firm's decision on technology progressing.This paper considers technology progressing in two situations. Firstly, a firm is assumed to make decisions with optimizing and it is assumed that its capability of innovation can accumulate as it makes efforts on technology progressing, which implies the existence of long-term effects in firm's dynamic choices. Under certain conditions, the optimal trajectory of technology progressing consists of two stages which is further examined by case studies. In the first stage, the firm employs technology importing as the only way of making technology progress, while in the second stage, researching also becomes feasible.In the second situation, firms are postulated to have constant innovating capabilities and, all firms make strategic decisions with considerations of each other's reaction. Under such conditions, the analysis shows that,either firms are homogeneous or not, their product quality increases by time with decreasing speed. That is, the amount of quality improvement in each period decreases, which further leads to decreasing numbers of new researching projects. However, since the former variance decreases faster, the proportion of researching with respect to aggregate technology progressing projects increasingly converges to a positive value.Moreover, this paper discusses games between heterogeneous firms in different situations. In one situation, firms are the same in all aspects but the maximum quality improvement they can make in each period. This difference gives the firm with higher constraint stronger incentive to improving its product quality and therefore, no technology convergence happens. In another situation, firms have different capabilities of researching. But this difference does not necessarily enlarge technology gaps between firms, since the low-capability-firm will progress relatively faster near the end of the game. The effects of patent protecting also turn out to be ambiguous.