A Dynamic Leontief Model with Non-renewable Resources

In this paper we study a generalization of the dynamic Leontief input–output model. We extend the standard dynamic Leontief model with the balance equation of non-renewable resources. Obviously, the non-renewable stocks will decrease, exploiting primary resources. In this study we examine the controllability of this extended model by taking the consumption as the control parameter. Assuming balanced growth for both consumption and production, we investigate how long these scarce resources will cover the input needs of production and how the lifetime of the system depends on the balanced growth rate and on the consumption. In doing so, we apply classic results from control theory and on eigenvalue problems in linear algebra.     

Luenberger Productivity Indicators: Aggregation Across Firms

Two methods of aggregating Luenberger productivity indicators across firms are considered. One method makes use of some rather implausible allocative efficiency assumptions. The second method, a superlative index number approach, relies on more palatable assumptions and is judged to be the more promising of the two methods.     

Analyzing the Relationships between Individual Criminal Behavior and the Severity and Probability of Punishment

This paper deals with problems encountered in analyzing how an individual is deterred from committing a crime by the severity and probability of punishment. It is argued that it might be advantageous to base such an analysis on a model of maximization of expected utility. According to this model, the attractiveness of committing a crime is strongly affected by the product of the relative utility of committing the crime and being punished as compared with the utility of not committing the crime times the probability of the punishment. This implies that the bivariate linear relationships of choices to commit or not to commit crime and the severity and probability factors are dependent on the variations in both these factors and their mean values. In this paper, these bivariate relationships are analyzed in two ways – formally-algebraically and by numerical examples.