A Vintage Capital Approach to the Dynamics of the Firm

Why are new technologies often adopted so slowly? Why do firms often invest in old technologies even when apparently superior technologies are available? How are decisions to adopt new technologies affected by the prospect that even better tech-nologies become available in the future? These three questions raised by Chari and Hopenhayn (1991) illustrate some of the problems we attempt to solve in the present research proposal. In standard capital accumulation models all capital goods are equally productive and produce goods of the same quality. However, due to ageing and technological progress, in reality it holds that newer capital goods are either more productive or produce better quality. In this research proposal we intend to study the implications of process innovation for a firm`s investment policy. In particular, the capital accumulation process will be analyzed under the occurrence of a business cycle. In this way the effect of output price developments on the investment profile will be studied, i.e. does the firm invest in new machines rather than in older capital goods during an expansion phase or is it the other way round? And what happens during a recession? Furthermore, we will try to answer the three questions above for also firms with significant market power. To incorporate all the above features for the firm`s investment policy we develop an optimal control model that distinguishes the vintages of the capital goods, technical progress, and where, unlike most of the recent contributions, it is possible to keep on investing in older technologies. For an investigation of such optimal control models with distributed parameters we developped a new maximum principle which can be successfully applied to a number of problems where the known methods failed. Based on that a numerical algorithm will be developped to support the theoretical conclusions by numerical results and investigate different scenarios. Our preliminary methods show that (i) learning is one of the reasons why a firm may invest in old technologies even when apparently superior technologies are available, (ii) investments in machines of a given age increase more over time under fast technological progress, (iii) under fast technological progress investments are more vulnerable to output price developments, and (iv) on average, machines are older during recessions.

Why are new technologies often adopted so slowly? Why do firms often invest in old technologies even when apparently superior technologies are available? How are decisions to adopt new technologies affected by the prospect that even better technologies become available in the future? These three questions raised by Chari and Hopenhayn (1991, JPE 99, 1142-1165) illustrate some of the problems we solved in the present research proposal. In standard capital accumulation models all capital goods are equally productive and produce goods of the same quality. However, due to ageing and technological progress, in reality it holds that newer capital goods are either more productive or produce better quality. In this research proposal we studied the implications of process innovation for a firm`s investment policy. In particular, the capital accumulation process was analyzed under the occurrence of a business cycle. In this way the effect of output price developments on the investment profile was studied, i.e. does the firm invest in new machines rather than in older capital goods during an expansion phase or is it the other way round? And what happens during a recession? Furthermore, we answered the three questions above also for firms with significant market power. To incorporate all the features above for the firm`s investment policy we developed an optimal control model that distinguishes the vintages of the capital goods, technical progress, and where, unlike most of the recent contributions, it is possible to keep on investing in older technologies. For an investigation of such optimal control models with distributed parameters we developped a new maximum principle which can be successfully applied to a number of problems where the known methods failed. Based on that a numerical algorithm was developped to support the theoretical conclusions by numerical results and investigate different scenarios. Our methods show that (i) learning is one of the reasons why a firm may invest in old technologies even when apparently superior technologies are available, (ii) investments in machines of a given age increase more over time under fast technological progress, (iii) under fast technological progress investments are more vulnerable to output price developments, and (iv) on average, machines are older during recessions.