Workshop on "Age-structured models in population dynamics and economics at the Vienna Institute of Demography, October 27-28, 2003

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Age-structured optimal control in population economics

This paper brings both intertemporal and age-dependent features to a theory of population policy at the macro-level. A Lotkatype renewal model of population dynamics is combined with a Solow/Ramsey economy. By using a new maximum principle for distributed parameter control we derive meaningful qualitative results for the optimal migration path and the optimal saving rate.

Keeping a learned society young

Aging organizations - regardless of whether they are firms, faculties, societies, political bodies, teams, or national academies - seek ways to rejuvenate. This paper demonstrates that the best way to keep an organization young is through a mixed strategy of recruiting both young and old, and that, contrary to intuition, recruiting those of middle age is the least effective strategy for maintaining a younger age structure. The aging of learned societies is a problem in many national academies. Faced with rising life expectancy, particularly for older persons, the average age of academy members is increasing. Another reason for "overaging" is an increase in the age at election. In an organization with a fixed size, the annual intake is strictly determined by the number of deaths and the statutory retirement age. This can, among many learned societies, lead to a fundamental dilemma: the desire to maintain a young age structure, while still guaranteeing a high recruitment rate. We derive an optimal recruitment policy which is bimodal, i.e., it entails shifting recruitment partly to younger ages and partly to older ages, while decreasing the recruitment of middle-aged candidates. Although the optimization problem explicitly involves only the average age and the recruitment rate as objectives, the methodology implicitly allows us to take into consideration all other objectives (formal or informal) used in the actual election practice.age-specific recruitment policy, fixed-size population, optimal control

The reproductive value as part of the shadow price of population

The reproductive value (see Fisher [10]) arises as part of the shadow price of the population in a large class of age-structured optimal control models.life history, reproductive value

Externalities in a Life-Cycle Model with Endogenous Survival

We study socially vs. individually optimal lifecycle allocations of consumption and health care, when individual health expenditure curbs own mortality but also has a spillover effect on other persons' survival. Such spillovers arise, for instance, when health care activity at aggregate level triggers improvements in treatment through learningbydoing (positive externality) or a deterioration in the quality of care through congestion (negative externality). We combine an agestructured optimal control model at population level with a conventional lifecycle model to derive the social and private value of life. We then examine how individual incentives deviate from social incentives and how they can be aligned by way of a transfer scheme. The agepatterns of socially and individually optimal health expenditure and the transfer rate are derived. Numerical analysis illustrates the workings of our model.Demand for health, externality, life-cycle-model, optimal control, tax-subsidy, value of life.

The Reproductive Value in Distributed Optimal Control Models

We show that in a large class of distributed optimal control models (DOCM), where population is described by a McKendrick type equation with an endogenous number of newborns, the reproductive value of Fisher shows up as part of the shadow price of the population. Depending on the objective function, the reproductive value may be negative. Moreover, we show results of the reproductive value for changing vital rates. To motivate and demonstrate the general framework, we provide examples in health economics, epidemiology, and population biology.Reproductive value, distributed optimal control theory, McKendrick, shadow price, indirect effect, health economics, epidemiology, population biology.

The Reproductive Value as Part of the Shadow Price of Population

The reproductive value (see Fisher 1930) arises as part of the shadow price of the population in a large class of age-structured optimal control models.Reproductive value, distributed optimal control theory, McKendrick equation, shadow price, indirect effect.

Cyclical Consumption Patterns and Rational Addiction

Series: Department of Economics Working Paper Serie

On the age dynamics of learned societies - taking the example of the Austrian Academy Sciences

In a hierarchical organisation of stable size the annual intake is strictly determined by the number of deaths and a statutory retirement age (if there is one). In this paper we reconstruct the population of the Austrian Academy of Sciences from 1847 to 2005. For the Austrian Academy of Sciences we observe a shift of its age distribution towards older ages, which on the one hand is due to rising life expectancy, i.e., a rising age at death, as well as to an increased age at entry on the other hand. Therefore the number of new entrants has been fluctuating considerably - especially reflecting several statutory changes - and the length of tenure before reaching the age limit has declined during the second half of the last century. Based on alternative scenarios of the age distribution of incoming members - including a young, an old, the 'current' and a mixed-age model - we then project the population of the Austrian Academy and its ageing forward in time. Our results indicate that the 'optimum policy' would be to elect either young or old aged new members.

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.Extortion, Differential Games, Capital Accumulation