Andreas J. Novak

Limit cycles in intertemporal adjustment models: Theory and applications

This paper starts from well-behaved (i.e., concave) one-state-variable optimal control models. The crucial feature is that indigenous growth is present. The replacement of the control by an adjustment process and presumably penalizing these adjustments may convert stable (and only stable) fixed point equilibria into limit cycles. Indeed, given positive growth and proper externalities (such that discounting exceeds growth), one can generate stable limit cycles with ease, e.g., for a separable framework. Examples from such diverse fields as renewable resources, optimal saving and public choice highlight the economic applicability.

Capacity Allocation for Dynamic Process Improvement with Quality and Demand Considerations

Management of process improvement activities is an essential part of the manufacturing strategy of a firm to remain globally competitive in the long run. This paper considers a manufacturing environment where process improvement activities require use of the productive capacity of the firm in addition to other investments. Thus the firm must allocate its productive capacity between production activities and improvement activities. The output of production activities is used to meet customer demand. Process improvement activities improve the quality of the output, which in turn leads to lower quality related costs both internal and external and possibly lower per-unit production cost. It is assumed that the demand function is downward sloping and that revenue is a concave function of output. A continuous-time, finite-horizon, profit maximization, resource allocation model is developed to find an optimal time path for process improvement activities and production activities. Computational results are provided to study the effect of various problem parameters on the optimal decisions.

Increasing Returns and Cycles in Fishing

We consider optimal fishery management under the assumption of increasing returns that is supported by previous empirical evidence. We improve the tractability and realism of the previous approaches by introducing flow adjustment costs on changes in harvest rate. Our framework is the first to provide a link between stable limit cycle policies and increasing returns in harvesting. The type of the harvest policy depends on flow adjustment costs: for relatively costly adjustments the usual steady state harvest policy is conceivable, whereas for relatively cheap adjustments the harvest policy is cyclical. We also show a connection between chattering control policies and limit cycles, which helps us to develop a clear economic meaning for cyclical harvesting.(This abstract was borrowed from another version of this item.)(This abstract was borrowed from another version of this item.)

The distribution of estimators after model selection:large and small sample results

Frequently, parameter estimation is preceded by a data-driven model selection procedure. In such a case traditional distribution theory based on the assumption of an a priori given model is no longer valid. In Potscher (1991) the asymptotic distribution of estimators that are preceded by model selection has been studied. In this paper we study the small sample distribution and, in particular, evaluate the accuracy of the approximation provided by the asymptotic distribution in small samples. We also show, how one of the assumptions in Potscher (1991) can be weakened substantially.

Cycles of fear: periodic bloodsucking rates for vampires

In this paper, we present a new approach for modelling the dynamic intertemporal confrontation between vampires and humans. It is assumed that the change of the vampiristic consumption rate induces costs and that the vampire community also derives some utility from possessing humans and not only from consuming them. Using the Hopf bifurcation theorem, it can be shown that cyclical bloodsucking strategies are optimal. These results are in accordance with empirical evidence.

Petrarch's canzoniere: Rational addiction and amorous cycles

The paper is concerned with a celebrated collection of love poems, the 14th century Italian poet Francis Petrarchs Canzoniere. A striking feature of these poems is the emotional ups and downs experienced by Petrarch and his platonic mistress Laura. Recently, attempts have been made to model these emotional swings by catastrophe theory or nonlinear differential equations. This paper takes a different approach. Starting with a pair of differential equations that model the dynamics of the emotions of the two individuals, we formulate an optimal control problem. A key hypothesis of this problem is that Petrarch was a rational addict of his desire for Laura. With specific functional forms and parameter values we identify a stable limit cycle that gives a representation of the oscillating emotions of Laura and Petrarch.

Leading bureaucracies to the tipping point: An alternative model of multiple stable equilibrium levels of corruption

Highlights ► We model an alternative explanation for tipping points in societal-level corruption. ► The bureaucracy’s culture of corruption is influenced by an executive’s actions. ► The nonlinear dynamical formulation is solved with Pontryagin’s Principle. ► The solution exhibits state-dependence and so-called Skiba points. ► Policy interpretations are somewhat more optimistic than in Schelling’s (1978) classic model.

Extortion as an obstacle to economic growth: a dynamic game analysis

In this paper we use a differential game analysis to study the dynamic strategic interaction between a criminal gang extorting money from local shop-owners and the local police force. In particular, we are interested in characterizing which factors are important in determining whether the capital stock of local shop-owners keeps growing in spite of extortion or the criminal activity leads to a phase of stagnation of the local economy. A Markov perfect equilibrium of the game is characterized in order to address this question and several policy implications are derived to facilitate growth in regions affected by extortion.

Differential game model of the dynastic cycle: 3D-canonical system with a stable limit cycle

Ancient Chinese history reveals many examples of a cyclical pattern of social development connected with the rise and the decline of dynasties. In this paper, a possible explanation of the periodic alternation between despotism and anarchy by a dynamic game between the rulers and the bandits is offered. The third part of the society, the farmers, are dealt with as a renewable resource which is exploited by both players in a different manner. It is shown that the Nash solution of this one-state differential game may be a persistent cycle. Although we restrict the analysis to open-loop solutions, this result is of interest for at least two reasons. First, it provides one of the few existing dynamic economic games with periodic solutions. Second, and more important, the model is an example of a three-dimensional canonical system (one state, two costates) with a stable limit cycle as solution. As far as we see, our model provides up to now the simplest (i.e., lowest dimensional) case of a persistent periodic solution of an intertemporal decision problem.

Paradigm Depletion, Knowledge Production and Research Effort: Considering Thomas Kuhn's Ideas

This paper deals in a Stackelberg differential game with Kuhn (1962) ideas of paradigm depletion and resiliency. Paradigm is considered as potential knowledge, as a stock of ideas that can be harvested to produce science. The results are: (i) paradigm depletion can be optimal, (ii) the optimal editors shadow price of potential knowledge must be non‐positive, if it is positive, the editor is a keeper of the orthodoxy rather than a scientist, (iii) editors and/or researchers impatience is bad for science, and (iv) in equilibrium editors behavior does not matter for research effort, while only editors behavior matter for the paradigm.