The genuine savings criterion and the value of population

Summary. In any dynamic model of the economy with changing population, the latter should properly be one of the state variables of the system. It enters both in the maximand, at least under total utilitarianism, and into the production function in one way or another. If population growth is exponential and constant returns prevails, then a simple transformation to per capita variables can be used to eliminate one state variable, but this ceases to be true if growth is not exponential, as it obviously is not and cannot be. If the growth of population is exogenous, then introducing it into the system does not affect the optimal policy. However, if one asks whether the system is sustainable, in the sense of at least maintaining total welfare (integral of discounted utilities), then the criterion is that that the value of the rates of change of the state variables is non-negative, so that the shadow price of population becomes relevant. In this paper, we derive explicit formulas in a simple model, showing that the rate of growth of per capita capital is not the correct formula but must have another terms added to it. We also study the question under an alternative criterion of long-run average utilitarianism. Received: June 1, 2002; revised version: September 27, 2002 RID="*" ID="*"Research support was provided by the William and Flora Hewlett Foundation. An earlier version of this paper was presented at a celebration of Mordecai Kurz's 66th birthday at Stanford University, 1–3 August 2002. Correspondence to: K.J. Arrow     

On some alternative criteria for justice between generations

This paper is concerned with Rawls' principle of just savings. Both the intergenerational maxi–min solution and the Nash equilibrium are analyzed in the context of a simple growth model and a specific preference structure. The results are compared to the Utilitarian solution. The maxi–min solution is intertemporally inconsistent and all the Nash equilibria are Pareto inefficient. The latter part of the paper analyzes intergenarational strong equilibria, the α-core and the β-core. It is shown that for the model in question the set of strong equilibria is empty, and that both the α- and β-cores are roughly speaking equal to the set of all Pareto efficient programmes of accumulation.     

An epidemiological study of injury in mines: implications for safety promotion

The role of various factors in coal mine-related injuries was investigated using a case-control design. The study setting was two neighbouring underground coal mines in India. Cases comprised mine workers (n = 150) who had sustained a prior mine-related injury from a population of 1000 underground workers. Controls were selected from those mineworkers with no history of a prior mine-related injury using frequency matching (n = 150) from the same source population. Data were collected from the cases and controls using a structured survey questionnaire. Based on the responses of the participants, each factor was grouped into three categories. High-low plots and Chi-square tests were conducted to explore the differences between the cases and controls. Bivariate logistic regression was run to estimate the crude odds of injuries, while multivariate logistic regression estimated the adjusted odds of injuries to the workers for the various variable categories. High-low plots and the Chi-square test clearly revealed that the cases and controls significantly differed in their responses for the variables studied. Accident-involved workers take more risks, are negatively affected, job dissatisfied, feel more production pressure, job stress, work hazards and are less job involved and are more dissatisfied with safety environment and social climate of the mines compared to the controls. The multivariate odds of injuries to high risk taking, negatively affected and job dissatisfied workers are 1.21, 9.34 and 2.00 times more compared to their lowest counterparts. Similarly, workers satisfied with the overall safety practice and safety equipment availability and maintenance are 1.5 and 3.12 times less likely to be injured than the workers with little or no satisfaction with the above factors. It is therefore concluded that negative affectivity and job dissatisfaction are the two major personal level factors that contribute more towards accident/injury in the mines studied. Identification and elimination/reduction of negative attitudes are of utmost importance.     

Optimal and competitive programs in reachable multi sector models

Summary. We show that in multi-sector optimal growth models, where the technology satisfies a simple reachability condition, infinite horizon programs which satisfy the competitive conditions are optimal. We provide examples of a variety of production models where the reachability condition is satisfied. An example is also provided where the reachability condition is not satisfied and there are competitive programs which are not optimal. The results of the paper are of interest from the standpoint of decentralization in intertemporal economies. Received: March 24, 1994; revised version: October 10, 1998