Vladimir M. Veliov

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

Abstract Due 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.

Capital accumulation under technological progress and learning: A vintage capital approach☆

Abstract In standard capital accumulation models all capital goods are equally productive and produce goods of the same quality. However, due to technological progress, in reality it holds most of the time that newer capital goods are either more productive (process innovation) or produce goods of better quality (product innovation). Implications of process innovation for the firm’s investment policies are investigated while the output price development is subject to a business cycle, and a given generation of capital goods gets more productive over time due to learning. The problem is turned into an optimal control model that distinguishes the vintages of capital goods, and where, unlike most of the recent contributions, it is possible to keep on investing in older technologies. It is shown 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 faster technological progress, (iii) under faster technological progress investments are more vulnerable to output price developments, and (iv), on average, machines are older during recessions. In deciding whether to invest in newer or older capital goods, also the lower productivity due to aging versus differences in cost of discounting and acquisition have to be taken into account.

Environmental policy, the Porter hypothesis and the composition of capital : Effects of learning and technological progress

In this paper, the effect of environmental policy on the composition of capital is investigated. By allowing for non-linearities, it generalizes Xepapadeas and De Zeeuw (Journal of Environmental Economics and Management, 1999) and determines scenarios in which their results do not carry over. In particular, we show that the way acquisition cost of investment decreases with the age of the capital stock is of crucial importance. Also, it is obtained that environmental policy has opposite effects on the average age of the capital stock in the case of either deterioration or depreciation. We also focus more explicitly on learning and technological progress. Among others, we obtain that in the presence of learning, implementing a stricter environmental policy with the aim to reach a certain target of emissions reduction has a stronger negative effect on industry profits, which implies quite the opposite as to what is described by the Porter hypothesis.

Uniform Convergence and Mesh Independence of Newton's Method for Discretized Variational Problems

In an abstract framework, we study local convergence properties of Newtons method for a sequence of generalized equations which models a discretized variational inequality. We identify conditions under which the method is locally quadratically convergent, uniformly in the discretization. Moreover, we show that the distance between the Newton sequence for the continuous problem and the Newton sequence for the discretized problem is bounded by the norm of a residual. As an application, we present mesh-independence results for an optimal control problem with control constraints.

Lipschitz continuity of the value function in optimal control

AbstractFor optimal control problems in

Second-order discrete approximation to linear differential inclusions

\mathbb{R}^n

On the discretization of switched linear systems

with given target and free final time, we obtain a necessary and sufficient condition for local Lipschitz continuity of the optimal value as a function of the initial position. The target can be an arbitrary closed set, and the dynamics can depend in a measurable way on the time. As a limit case of this condition, we obtain a characterization of the viability property of the target, in terms of perpendiculars to the target instead of tangent cones. As an application, we analyze the convergence of certain discretization schemes for time-optimal problems.

Needle variations in infinite-horizon optimal control

This note presents a necessary and sufficient condition for small time controllability of a linear switching system (that is, a collection of linear time-invariant control systems, where a trajectory is any concatenation of trajectories of the individual systems). This result extends the controllability condition recently obtained for unconstrained linear switching systems to the case of control which is constrained in a cone.