Anticipation effects of technological progress on capital accumulation: a vintage capital approach

Abstract

Anticipation effects of technological progress on capital accumulationFeichtinger, G.; Hartl, R.F.; Kort, P.M.; Veliov, V.M. AbstractDue to embodied technological progress new generations of capital goods are more productive. Therefore, in order to study the effects of technological progress, a model must be analyzed in which different generations of capital goods can be distinguished.We determine in what way the firm adjusts current investments to predictions of technological progress. In the presence of market power we show that a negative anticipation effect occurs, i.e. current investments in recent generations of capital goods decline when faster technological progress will take place in the future, because then it becomes more attractive to wait for new generations of capital goods. In case that only investments in new machines are possible, actually a whole wave of anticipation phases arises. Journal of Economic Literature Classification Numbers: D92; O33; C61

Generically distributed investments on flexible projects and endogenous growth

“…Vintage capital models are, clearly, an economic example of such problems [see among others Boucekkine et al (1997) and Feichtinger et al (2006), and the survey on this literature by Boucekkine et al (2011)]. From a methodological viewpoint, most of the papers dealing with this kind of problems use maximum principle techniques.…”

Optimal investment models with vintage capital: Dynamic programming approach

“…The problem falls into the class of infinite horizon optimal control problems of PDE's with age structure that have been studied in various papers (see e.g. [11,12], [30,32]) either in cases when explicit solutions can be found or using Maximum Principle techniques.…”

“…That of optimal control of linear age structured equations is one of the possible approaches undertaken in the literature. Such framework has been introduced in in [11,12] and then studied in various papers, among which we mention [26,27,29,30,31,32]. There the optimal investment problem with vintage capital is treated in two main cases:…”

“…• In [32] the case when the production function is linear and with large representative investor (which leads to an objective function which is nonlinear in the capital stock). In this case the value function is non linear and the optimal investment strategies cannot be explicitly calculated.…”

“…The problem falls into the class of infinite horizon optimal control problems of PDE's with age structure that have been studied in various papers (see e.g. [11,12], [30,32]) either in cases when explicit solutions can be found or using Maximum Principle techniques.The problem is rephrased into an infinite dimensional setting, it is proven that the value function is the unique regular solution of the associated stationary Hamilton-Jacobi-Bellman equation, and existence and uniqueness of optimal feedback controls is derived. It is then shown that the optimal path is the solution to the closed loop equation.…”