Josef L. Haunschmied

A DNS-curve in a two-state capital accumulation model: A numerical analysis

Abstract In this paper we study a capital accumulation model in an optimal control theoretic framework, where the capital stock and the investment rate are modelled as state variables and the change in the investment rate as control. Adjustment costs are introduced for investment rate and its change. Moreover, we model network externalities by a convex segment in the revenue function, which implies the existence of two long-run optimal steady-states, one with a low level and the other with a high level capital stock. It depends on the initial capital endowment and initial investment rate to which steady-state it is optimal to converge. We numerically compute a curve in the state plane, for which it holds that, when starting from a point on this curve, the decision maker is indifferent between going to either one of these steady-states, and identify this curve as the DNS-curve. The negative slope of the DNS-curve indicates that there is a trade-off between the initial capital endowment and initial investment rate.

A Resource-Constrained Optimal Control Model for Crackdown on Illicit Drug Markets

In this paper we present a budget-constrained optimal control model aimed at finding the optimal enforcement profile for a street-level, illicit drug crackdown operation. The objective is defined as minimizing the number of dealers dealing at the end of the crackdown operation, using this as a surrogate measure of residual criminal activity. Analytical results show that optimal enforcement policy will invariably use the budget resources completely. Numerical analysis using realistic estimates of parameters shows that crackdowns normally lead to significant results within a matter of a week, and if they do not, it is likely that they will be offering very limited success even if pursued for a much longer duration. We also show that a ramp-up enforcement policy will be most effective in collapsing a drug market if the drug dealers are risk-seeking, and the policy of using maximum enforcement as early as possible is usually optimal in the case when the dealers are risk averse or risk neutral. The work then goes on to argue that the underlying model has some general characteristics that are both reasonable and intuitive, allowing possible applications in focused, local enforcement operations on other similar illegal activities.

The Euler Method for Linear Control Systems Revisited

Although optimal control problems for linear systems have been profoundly investigated in the past more than 50 years, the issue of numerical approximations and precise error analyses remains challenging due the bang-bang structure of the optimal controls. Based on a recent paper by M. Quincampoix and V.M. Veliov on metric regularity of the optimality conditions for control problems of linear systems the paper presents new error estimates for the Euler discretization scheme applied to such problems. It turns out that the accuracy of the Euler method depends on the “controllability index” associated with the optimal solution, and a sharp error estimate is given in terms of this index. The result extends and strengthens in several directions some recently published ones.

Diversity of firm’s life cycle adapted from the firm’s technology investment decision

The stylized model presented is an optimal control model of technology investment decision of a single product firm. The firm’s technology investment does not have only a long-run positive effect but also a short-run adverse effect on its sales volume. We examine the case of high adverse investment effects where the firm finally leaves the market but we have observed different life cycles till this happens. Depending on the firm’s initial technology stock and sales volume, we compute different firm’s life cycles, which are driven by a trade-off between two strategies: technology versus sales focus strategy. Indifference curves, where managers are indifferent to apply initially technology or sales focus strategies, separate founding conditions of the firm to various classes distinguishable because of the firm’s life cycle.

Optimal firm investment in security

In this paper, we analyze the problem of an individual firm that has to deal with lossesfrom criminal activities. It is assumed that the firm can protect itself by investing in securityequipment. Two different models are considered. In the first model, the firm has the possibilityto spend money on production and on security investment. More production increasesrevenue but also criminal losses, while the latter can be decreased by investing in security.It turns out that the optimal production level increases with security equipment and is determinedsuch that marginal revenue, net from criminal losses, equals marginal cost. For theoptimal level of security investment it holds that, in the case of the existence of a long‐runsteady‐state equilibrium, the properly discounted future reductions in criminal losses, whichare due to an additional unit of security investment, exactly balances the initial outlaynecessary to acquire an extra unit of security investment. In the second model, we extendthis analysis by considering the effect that the firms reputation has in the criminal world. Ifthe firm has produced a lot in the past without having invested in security equipment, thisfirm is known to be a fruitful target for criminals. Therefore, more criminals will try to robthis firm, and this will increase future criminal losses.

Dynamic games in economics

Robust Markov Perfect Equilibria in a Dynamic Choice Model with Quasi-hyperbolic Discounting.- Stochastic Differential Games and Intricacy of Information Structures.- Policy Interactions in a Monetary Union: An Application of the OPTGAME Algorithm.- The Dynamics of Lobbying Under Uncertainty: On Political Liberalization in Arab Countries.- A Feedback Stackelberg Game of Cooperative Advertising in a Durable Goods Oligopoly.- Strategies of Foreign Direct Investment in the Presence of Technological Spillovers.- Differential Games and Environmental Economics.- Capacity Accumulation Games with Technology Constraints.- Dynamic Analysis of an Electoral Campaign.- Multi-Agent Optimal Control Problems and Variational Inequality Based Reformulations.- Time-consistent Equilibria in a Differential Game Model with Time Inconsistent Preferences and Partial Cooperation.- Interactions Between Fiscal and Monetary Authorities in a Three-Country New-Keynesian Model of a Monetary Union.- Subgame Consistent Cooperative Provision of Public Goods Under Accumulation and Payoff Uncertainties.