Peter M. Kort

Optimal timing of technology adoption

Abstract In a dynamic programming framework, this paper investigates the optimal timing of technology adoption by a competitive firm when technology choice is irreversible and the firm faces a stochastic innovation process with uncertainties about both the speed of the arrival and the degree of improvement of new technologies. A numerical example illustrates how the optimal timing decision is affected by changes in parameter values reflecting market conditions, the firms initial technological attributes, and the characteristics of the stochastic innovation process. Some of these effects turn out to be in sharp contrast to common intuition. Contrasting the optimal decision rule derived here with the rule obtained under the net present value shows that the former implies a slower pace of adoption than implied by the latter. The optimal decision rule is generalized for the case of multiple technology switches and it is shown that for all the switching decisions except the last one , the optimal rule satisfies the net present value criterion.

Strategic Technology Adoption Taking Into Account Future Technological Improvements: A Real Options Approach

This paper studies a dynamic duopoly in which firms compete in the adoption of new technologies. The innovation process is exogenous to the firms. Both firms have the possibility to adopt a current technology or to wait for a better technology that arrives at an unknown point of time in the future. At the moment that a firm invests it enters a new market with a profit flow that follows a stochastic Brownian motion process. Results turn out to largely depend on the probability that a new technology arrives in the immediate future. If this probability is low, firms only take the current technology into account, which results in the usual preemption game. Increasing this probability gradually changes the outcome from a preemption game where both firms adopt the current technology, to a preemption game where the follower will adopt the new technology. Increasing the probability of arrival of the new technology further, turns the preemption game into a war of attrition where the follower adopting the new technology is better of than the leader. Finally, when the probability of arrival of a new technology is really large, both firms will adopt the new technology.

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.

Strategic investment in technological innovations

Abstract The aim of this paper is to determine the optimal timing of technology investment of a single firm in a duopoly framework. As time passes different technologies are invented which after sometime become available for the firm to adopt. The question here is not only when a firm should invest but also which technology should be adopted. For different scenarios the optimal technology investment decision is determined. Outcomes range from pre-emption equilibria to equilibria with second mover advantages.

Production, inventory, and pricing under cost and demand learning effects

Abstract The paper considers a monopolist firm that plans its production, inventory, and pricing policy over a fixed and finite horizon. The problem is represented by an optimal control model which combines elements from three streams of literature. The first of these is a classical OR area and deals with optimal production and inventory under exogenously given demand conditions. The second is an area of marketing science which studies dynamic pricing under demand learning effects. Demand learning refers to the situation where current demand for a product is influenced by past demand. The third area belongs to microeconomics and industrial organization and is concerned with the effects of learning-by-doing in a firms production process. Learning is reflected in a unit production cost that decreases with cumulative production. Using a path-synthezising procedure we obtain closed-form characterizations of optimal production, pricing, and inventory policies.

Brand image and brand dilution in the fashion industry

We develop a dynamic optimal control model of a fashion designers challenge of maintaining brand image in the face of short-term profit opportunities through expanded sales that risk brand dilution in the longer-run. The key state variable is the brands reputation, and the key decision is sales volume. Depending on the brands capacity to command higher prices, one of two regimes is observed. If the price markups relative to production costs are modest, then the optimal solution may simply be to exploit whatever value can be derived from the brand in the short-run and retire the brand when that capacity is fully diluted. However, if the price markups are more substantial, then an existing brand should be preserved. It may even be worth incurring short-term losses while increasing the brands reputation, even if starting a new brand name from scratch is not optimal.

INVESTMENT IN OLIGOPOLY UNDER UNCERTAINTY: THE ACCORDION EFFECT

This paper studies investments in new markets where more than two (anticipated) identical competitors are present. In case of three firms an accordion effect is detected: an exogenous demand shock results in a change of the wedge between investment thresholds of the first and second investor that is qualitatively different from the change of the wedge between the second and third investment threshold. Furthermore, it turns out that in the three-firm case the investment timing of the first investor lies in between the one and the two-firm case. These results are numerically extended to the n-firm case.

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.

Optimal Pricing and Inventory Policies: Centralized and Decentralized Decision Making

Abstract The paper studies an optimal control problem of pricing and inventory replenishment in a system with serial inventories. Consumer demand for a specific product at a retail outlet depends on price as well as the in-store stock of the product. The hypothesis is that for certain consumer products, a large volume of displayed goods leads consumers to buy more than if the stock is small. In addition to the stock that is on display in the store, there is an inventory of the product in a central warehouse. First we consider a setup in which management of the two stocks is decentralized such that pricing decisions are made by the store manager who also decides on the level of in-store inventory. The warehouse manager makes the replenishment decisions concerning the stock in the warehouse. Next we study the problem where stock management and pricing decisions are centralized. Optimal trajectories for inventories, replenishment rates, and retail price are derived by using phase diagrams and a formal synthesizing procedure.