Abstract
The paper provides a framework that enables us to analyze the important topic of capital accumulation under technological progress. We describe an algorithm to solve Impulse Control problems, based on a (multipoint) boundary value problem approach. Investment takes place in lumps and we determine the optimal timing of technology adoptions as well as the size of the corresponding investments. Our numerical approach led to some guidelines for new technology investments. First, we find that investments are larger and occur in a later stadium when more of the old capital stock needs to be scrapped. Moreover, we obtain that the size of the firm’s investments increase when the technology produces more profitable products. We see that the firm in the beginning of the planning period adopts new technologies faster as time proceeds, but later on the opposite happens. Furthermore, we find that the firm does not invest such that marginal profit is zero, but instead marginal profit is negative.
Highlights
In today’s knowledge economy innovation is of prime importance
To do so we employ the Impulse Control modeling approach that is perfectly suitable to take into account the disruptive changes caused by innovations
This paper employs an Impulse Control modeling approach that is perfectly suitable to take into account the disruptive changes caused by innovations
Summary
In today’s knowledge economy innovation is of prime importance. Innovation has led to the extraordinary productivity gains in the 1990s. To do so we employ the Impulse Control modeling approach that is perfectly suitable to take into account the disruptive changes caused by innovations This enables us to determine the length of the time interval that the firm uses a particular technology, when it is time to launch a new product generation, and how these decisions interact with the firm’s capital accumulation behavior. In Boucekkine et al (2004) a two-stage optimal control model is considered, where only one adoption occurs, without adoption (fixed) cost Both Boucekkine et al (2004) and Saglam (2011) incorporate learning, were the firm raises productivity of a given technology over time due to learning and revenue is linear in the capital stock.
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