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 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

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.

Medical Progress, Demand for Health Care, and Economic Performance

We study medical progress within an economy of overlapping generations subject to endogenous mortality. We characterize the individual optimum and the general equilibrium of the economy and study the impact of improvements in the effectiveness of health care. We find that general equilibrium effects dampen strongly the increase in health care usage following medical innovation and that an increase in savings offsets the negative impact on GDP per capita of a decline in the support ratio.

Medical care within an OLG economy with realistic demography

We study the role of health care within a continuous time economy of overlapping generations subject to endogenous mortality. The economy consists of two sectors: final goods production and a health care sector, selling medical services to individuals. Individuals demand health care with a view to lowering mortality over their life-cycle. We derive the age-specific individual demand for health care based on the value of life as well as the resulting aggregate demand for health care across the population. We then characterize the general equilibrium allocation of this economy, providing both an analytical and a numerical representation. We study the allocational impact of a medical innovation both in the presence and absence of anticipation; and a temporary baby boom. We place particular emphasis on disentangling general equilibrium from partial equilibrium impacts and identifying the relevant transmission channels

Medical care within an OLG economy with realistic demography

We study the role of health care within a continuous time economy of overlapping generations subject to endogenous mortality. The economy consists of two sectors: final goods production and a health care sector, selling medical services to individuals. Individuals demand health care with a view to lowering mortality over their life-cycle. We derive the age-specific individual demand for health care based on the value of life as well as the resulting aggregate demand for health care across the population. We then characterize the general equilibrium allocation of this economy, providing both an analytical and a numerical representation. We study the allocational impact of a medical innovation both in the presence and absence of anticipation; and a temporary baby boom. We place particular emphasis on disentangling general equilibrium from partial equilibrium impacts and identifying the relevant transmission channels

Optimal Choice of Health and Retirement in a Life-Cycle Model

We examine within a life-cycle set-up the choice of health and retirement. Health care contributes to a reduction in both mortality, determining the need to accumulate retirement wealth, and in morbidity, determining the disutility of work. The retirement age affects health through the value of survival and the value of morbidity reductions. We compare the allocation for a first-best setting where the individual can transfer wealth freely within a perfect annuity market with a second-best set-up with an incentive incompatible (yet actuarially fair) retirement scheme and an imperfect annuity market and show how the inefficiencies shape the health-retirement nexus

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

R&D for green technologies in a dynamic oligopoly: Schumpeter, Arrow and inverted-U’s

We extend a well known differential oligopoly game to encompass the possibility for production to generate a negative environmental externality, regulated through Pigouvian taxation and price caps. We show that, if the price cap is set so as to fix the tolerable maximum amount of emissions, the resulting equilibrium investment in green R&D is indeed concave in the structure of the industry. Our analysis appears to indicate that inverted-U-shaped investment curves are generated by regulatory measures instead of being a "natural" feature of firms’ decisions