One-machine scheduling to minimize mean tardiness with minimum number tardy

In this paper the one-machine scheduling problem with the objective of minimizing the mean tardiness subject to maintaining a prescribed number of tardy jobs is analysed. An algorithm for solving this problem is presented. It is proved that the schedule generated by the proposed algorithm is indeed optimal.     

Assessing Parfit’s Repugnant Conclusion within a canonical endogenous growth set-up

Parfit’s Repugnant Conclusion stipulates that under total utilitarianism, it might be optimal to choose increasing population size while consumption per capita goes to zero. We evaluate this claim within a canonical AK model with endogenous population size and a reduced form relationship between demographic and economic growth. First we characterize the optimal solution paths for any capital dilution function. Second, we prove that while the Repugnant Conclusion can never occur for realistic values of intertemporal substitution in the traditional linear dilution model, it does occur when population growth is linked to economic growth via an inverted U-shaped relationship.     

Empiricial Comparison between Some Model Selection Criteria

Model selection aims to find the best model. Most of the usual criteria are based on goodness of fit and parsimony and aim to maximize a transformed version of likelihood. The situation is less clear when two models are equivalent: are they close to the unknown true model or are they far from it? Based on simulations, we study the results of Vuong's test, Cox's test, AIC and BIC and the ability of these four tests to discriminate between models.     

EARLY LITERACY ACHIEVEMENTS,POPULATION DENSITY,AND THE TRANSITION TO MODERN GROWTH

The transition from economic stagnation to sustained growth is often modeled thanks to “population‐induced” productivity improvements, which are assumed rather than derived from primary assumptions. In this paper the effect of population on productivity is derived from optimal behavior. More precisely, both the number and location of education facilities are chosen optimally by municipalities. Individuals determine their education investment depending on the distance to the nearest school, and also on technical progress and longevity. In this setting, higher population density enables the set‐up costs of additional schools to be covered, opening the possibility to reach higher educational levels. Using counterfactual experiments we find that one‐third of the rise in literacy can be directly attributed to the effect of density, and one‐sixth is linked to higher longevity. Moreover, the effect of population density in the model is consistent with the available evidence for England, where it is shown that schools were established at a high rate over the period 1540–1620. (JEL: O41, I21, R12, J11)