Strategic capital budgeting: asset replacement under market uncertainty

In this paper the impact of product market uncertainty on the optimal replacement timing of a production facility is studied. The existing production facility can be replaced by a technologically more advanced and thus more cost-effective one. We take into account strategic interactions among the firms competing in the product market by analyzing the problem in a duopolistic setting. We calculate the value of each firm and show that i) a preemptive (simultaneous) replacement occurs when the associated sunk cost is low (high), ii) despite the preemption effect uncertainty always raises the expected time to replace, and iii) the relationship between the probability of optimal replacement within a given time interval and uncertainty is decreasing for long time intervals and humped for short time intervals. Furthermore it is shown that result ii) carries over to the case where firms have to decide about starting production rather than about replacing existing facilities

Analysis of Current Penalty Schemes for Violations of Antitrust Laws

The main feature of the penalty schemes described in current sentencing guidelines is that the fine is based on the accumulated gains from cartel activities or price-fixing activities for the firm. The regulations suggest modeling the penalty as an increasing function of the accumulated illegal gains from price fixing to the firm, so that the history of the violation is taken into account. We incorporate these features of the penalty scheme into an optimal control model of a profit-maximizing firm under antitrust enforcement. To determine the effect of taking into account the history of the violation, we compare the outcome of this model with a model where the penalty is fixed. The analysis of the latter model implies that complete deterrence can be achieved only at the cost of shutting down the firm. The proportional scheme improves upon the fixed penalty, since it can ensure complete deterrence in the long run, even when penalties are moderate. Phase-diagram analysis shows that, the higher the probability and severity of punishment, the sooner cartel formation is blocked. Further, a sensitivity analysis is provided to show which strategies are most successful in reducing the degree of price fixing. It turns out that, when the penalties are already high, the antitrust policy aiming at a further increase in the severity of punishment is less efficient than the policy that increases the probability of punishment.Optimal Control; Dynamic Analysis; Antitrust Policy; Antitrust Laws

Uncertainty and stepwise investment

We analyze the optimal investment strategy of a firm that can complete a project either in one stage at a single freely chosen time point or in incremental steps at distinct time points. The presence of economies of scale gives rise to the following trade-off: lumpy investment has a lower total cost, but stepwise investment gives more flexibility by letting the firm choose the timing individually for each stage. Our main question is how uncertainty in market development affects this trade-off. The answer is unambiguous and in contrast with a conventional real-options intuition: higher uncertainty makes the single-stage investment more attractive relative to the more flexible stepwise investment strategy

The Deterministic Impulse Control Maximum Principle in Operations Research: Necessary and Sufficient Optimality Conditions (replaces CentER DP 2011-052)

This paper considers a class of optimal control problems that allows jumps in the state variable. We present the necessary optimality conditions of the Impulse Control Maximum Principle based on the current value formulation. By reviewing the existing impulse control models in the literature, we point out that meaningful problems do not satisfy the sufficiency conditions. In particular, such problems either have a concave cost function, contain a fixed cost, or have a control-state interaction, which have in common that they each violate the concavity hypotheses used in the sufficiency theorem. The implication is that the corresponding problem in principle has multiple solutions that satisfy the necessary optimality conditions. Moreover, we argue that problems with fixed cost do not satisfy the conditions under which the necessary optimality conditions can be applied. However, we design a transformation, which ensures that the application of the Impulse Control Maximum Principle still provides the optimal solution. Finally, we show for the first time that for some existing models in the literature no optimal solution exists.Impulse Control Maximum Principle;Optimal Control;discrete continuous system;state-jumps;present value formulation.

Optimal dynamic environmental policies of a profit maximizing firm

Marketing;Game Theory;Pollution;environmental economics

Innovation Strategies in a Competitive Dynamic Setting

This paper presents a dynamic model of a competitive R&D and production duopoly subject to knowledge spillovers. Two asymmetric firms operate for a limited period of time and dispose their knowledge capital in the end. Both firms and the social planner prefer the R&D-cooperative strategy over the competitive one regardless of the intensity of knowledge spillovers. Accumulation of knowledge capital results allows the monopolist to have lower marginal cost of production and charge a lower market price than a fully competitive duopoly. Being able to define the degree of knowledge exchange when creating a research joint venture, the firms do not necessary choose the highest degree of cooperation available.innovation, R&D, spillovers, cooperation