Product innovation with lumpy investment |
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| Authors: | M Chahim D Grass R F Hartl P M Kort |
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| Institution: | 1.Department of Strategy and Policy,Netherlands Organisation for Applied Scientific Research (TNO),Delft,The Netherlands;2.Department of Operations Research and Systems Theory, Institute of Operations Research and Control Systems (ORCOS),Vienna University of Technology,Vienna,Austria;3.Department of Business Administration, Production and Operations Management,University of Vienna,Vienna,Austria;4.Department of Economics,University of Antwerp,Antwerp,Belgium;5.Department of Econometrics and Operations Research, CentER, Dynamic Optimization in Economics and Operations Research,Tilburg University,Tilburg,The Netherlands |
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| 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. |
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