Technological breakthroughs and asset replacement.

INTRODUCTION

The article analyzes the impact of discontinuous technological change (TC) on the optimal replacement of assets (capital equipment, machines). The asset replacement under continuous TC has been intensively analyzed (see Bean et al. 1994; Bethuyne 1998; Grinyer 1973; Hartman 2000; Hritonenko and Yatsenko 2007, 2008b, 2008c; Regnier et al. 2004 and references therein). The case of discontinuous TC is less explored. At the same time, there is economic evidence that both TC types arc present in economic and engineering reality (Goolsbee 1998; Rogers and Hartman 2005).

This article is inspired by Rogers and Hartman (2005), who numerically analyzed the joint impact of the continuous TC and periodic technological breakthroughs on the constant asset lifetime. They show that the optimal lifetime of assets is always smaller under more intensive continuous TC and is usually smaller under more intensive discontinuous TC (with some exceptions). As shown by Hritonenko and Yatsenko (1996, 2005, 2007, 2008b) and Regnier et al. (2004), the optimal lifetime of assets can be variable even under continuous exponential TC. Obviously, the same is true for discontinuous TC. Compared to previous works of the authors and other researchers, the new contribution of this article is the optimization of the variable asset lifetime under continuous exponential TC and discontinuous TC in the form of nonperiodic technological breakthroughs. More exactly, the capital and maintenance costs are different exponents on different time intervals (with TC jumps between these intervals). So, we analyze a new combination of continuous and discontinuous TC that has not been considered in literature. We demonstrate that a technological breakthrough causes irregularities (anticipation echoes) in the optimal asset lifetime before the breakthrough. These echoes weaken fast, so the asset lifetime is close to the optimal trajectory without breakthrough at times distant from the breakthrough. The obtained results are new in asset replacement theory.

The article is organized as follows. The next section introduces a serial asset replacement model on the infinite horizon with the variable asset lifetime and describes necessary preliminary analytic results such as an extremum condition. Then we investigate the model under discontinuous TC with one and several breakthroughs analytically and numerically, the latter using real data about car replacement. We then demonstrate how the variable optimal asset lifetime is impacted by the technological breakthroughs. Concluding remarks are provided.

MODEL OF SERIAL ASSET REPLACEMENT UNDER TC

Let us suppose that a production shop (plant, enterprise) keeps one asset (machine) of a certain type. The shop periodically sells the old asset and buys a new replacement asset. We consider this replacement process in continuous time t using the following notation:

* [t.sub.0] = 0: the starting point of the planning horizon;