Non-renewable resources and growth, the case of the oil: a simple endogenous model

We present a growth model in which a non-renewable resource enters in the production function. The non-renewable resource is supposed to be sold by an external monopolistic that maximizes his intertemporal discounted cash flow. This approach allows to endogenize the price of the resource. We use the historical data of the oil price and of the oil production to calibrate the model. The forecasts of the model about the evolution of the GDP growth rate, the price and amount of the production of the oil are described. The formulation of the model is quite easy but it hallows to obtain a good fit with the recent data and especially with the behavior of the three main quantities considered (oil price, oil supply and GDP growth rate) in the last years. Indeed the recent data suggest a new scenario and probably a progressive reduction of the world oil supply (and an indefinite growth of the prices). The model suggests that such a behavior is not due to the imminent physical end of the oil but has a clear economic explanation.Non-renewable resources, Oil, Endogenous Growth

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

Parfit's Repugnant Conclusion stipulates that under total utilitar- ianism, 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 fertility and a reduced form re- lationship between demographic growth and economic growth. While in the traditional linear dilution model, the Parfit Repugnant Conclu- sion can never occur for realistic values of intertemporal substitution, we show that it occurs when population growth is linked to economic growth via an inverted U-shaped relationship. Finally, we find moving from the Benthamite to the Millian social welfare function may not only cause optimal population size to go up and consumption to go down, it may also favor the realization of the Repugnant Conclusion.Parfit's Repugnant Conclusion, AK models, endogenous fertility, intertemporal altruism

Assessing the 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 fertility and a reduced form relationship between demographic growth and economic growth. While in the traditional linear dilution model, the Parfit Repugnant Conclusion can never occur for realistic values of intertemporal substitution, we show that it occurs when population growth is linked to economic growth via an inverted U-shaped relationship. Finally, we find moving from the Benthamite to the Millian social welfare function may not only cause optimal population size to go up and consumption to go down, it may also favor the realization of the Repugnant Conclusion.Parfit's Repugnant Conclusion, AK models, endogenous fertility, intertemporal altruism

Dynamic Programming, Maximum Principle and Vintage Capital

We present an application of the Dynamic Programming (DP) and of the Maximum Principle (MP) to solve an optimization over time when the production function is linear in the stock of capital (Ak model). Two views of capital are considered. In one, which is embraced by the great majority of macroeconomic models, capital is homogeneous and depreciates at a constant exogenous rate. In the other view each piece of capital has its own finite productive life cycle (vintage capital). The interpretation of the time patterns of macroaggregates is quite different between the two cases. A technological shock generates an oscillatory movement in the time pattern of per capita output when capital has a vintage structure; conversely an instantaneous adjustment with no transitional dynamics occurs when capital is homogeneous. From a methodological point of view it emerges that the DP approach delivers sharper results than the MP approach (for instance it delivers a closed form solution for the optimal investment strategy) under slacker parameter restrictions. Cross-time and cross-country data on investments, income, and consumption drawn from the Penn World Table version 6.2 are used to evaluate the vintage and standard Ak model.Vintage Capital; Penn World Table; Maximum Principle; Hilbert Space

Consumer boycott, household heterogeneity and child labour

Consumer boycott campaigns against goods produced using child labour are becoming increasingly popular. Notwithstanding, there is no consensus on which are the effects of such type of activism on child labour. If some agreement is to be found in the recent economic literature, it is that the boycott does not reduce child labour. We contribute to this debate presenting a simple model which shows, instead, that there are conditions under which a consumer product boycott does reduce child labour. We consider a small country two-factor economy populated by heterogeneous households. The boycott affects both the adult and the child labour markets. The income distribution determines how these changes affect child labour at the household level. We derive the conditions under which the consumer boycott reduces child labour also for some of the households whose' income is - before the boycott - under the subsistence level.Consumer product boycott, child labour, household heterogeneity, income distribution

International Borrowing Without Commitment and Informational Lags: Choice under Uncertainty

Ce working paper a fait l'objet d'une publication dans : Journal of Mathematical Economics, 68:103-114, 2017A series of recent studies in economic growth theory have considered a class of models of international borrowing where, in the absence of a perfect investment commitment , the borrowing constraint depends on the historical performances of the country. Thus, a better level of past economic activity gives a higher reputation, thereby increasing the possibility of accessing the international credit market. This note considers this problem in a stochastic setting based on the volatility of the internal net capital. We study how the optimal consumption level and the maximal expected welfare depend on the combined influence of the trajectory of past economic variables and the volatile environment. In particular, we show how the strength of the history effect and the relative weight of the historical performance depend on the degree of risk

On the Dynamic Programming approach to economic models governed by DDE's

In this paper a family of optimal control problems for economic models is considered, whose state variables are driven by Delay Differential Equations (DDE's). Two main examples are illustrated: an AK model with vintage capital and an advertising model with delay e ect. These problems are very di cult to treat for three main reasons: the presence of the DDE's, that makes them ifinite dimensional; the presence of state constraints; the presence of delay in the control. The purpose here is to develop, at a first stage, the Dynamic Programming approach for this family of problems. The Dynamic Programming approach has been already used for similar problems in cases when it is possible to write explicitly the value function V (Fabbri and Gozzi, 2006). The cases when the explicit form of V cannot be found, as most often occurs, are those treated here. The basic setting is carefully described and some first results on the solution of the Hamilton-Jacobi-Bellman (HJB) equation are given, regarding them as a first step to nd optimal strategies in closed loop form.

Years of Schooling, Human Capital and the Body Mass Index of European Females

We use the compulsory school reforms implemented in European countries after the II World War to investigate the causal effect of education on the Body Mass Index (BMI) and the incidence of overweight and obesity among European females. Our IV estimates suggest that years of schooling have a protective effect on BMI. The size of the estimated effect is not negligible but smaller than the one found in comparable recent work for the US. We depart from the current empirical literature in three main directions. First, we use a multi-country approach. Second, we complement the standard analysis of the causal impact of years of schooling on BMI with one relying on a broader measure of education, i.e. individual standardized cognitive tests, and show that the current focus in the literature on years of schooling as the measure of education is not misplaced. Last, we evaluate whether the current focus on conditional mean effects should be integrated with an approach which allows for heterogeneous responses to changes in compulsory education. Although our evidence based on quantile regressions is mixed, there is some indication that the protective effect of schooling does not increase monotonically from the lower to the upper quantile of the distribution of BMI. Rather, the marginal effect is stronger among overweight (but not obese) females than among females with BMI above 30.obesity, human capital, Europe

Life span and the problem of optimal population size

We reconsider the optimal population size problem in a continuous time economy populated by homogenous cohorts with a fixed life span. Linear production functions in the labor input and standard rearing costs are also considered. First, we study under which conditions the successive cohorts will be given the same consumption per capita. We show that this egalitarian rule is optimal whatever the degree of altruism when life spans are infinite. However, when life spans are finite, this rule can only be optimal in the Benthamite case, i.e. when the degree of altruism is maximal. Second, we prove that under finite life spans the Millian welfare function leads to optimal extinction at finite time whatever the lifetime. In contrast, the Benthamite case is much more involved: for isoelastic utility functions, it gives rise to two threshold lifetime values, say T0Optimal population size, Benthamite Vs Millian criterion, finite lives, optimal extinction

Revisiting the optimal population size problem under endogenous growth: minimal utility level and finite lives

In this paper, we devise a social criterion in the spirit of the critical utility level of Blackorby-Donaldson (1984) to study an optimal population size problem in an endogenously growing economy populated by workers living a fixed amount of time and without capital accumulation. Population growth is endogenous. The problem is analytically solved, yielding closed-form solutions to optimal demographic and economic dynamics. It is shown that provided the economy is not driven to optimal finite time extinction, the optimal solution is egalitarian for appropriate choices of the critical utility levels: all individuals of any cohort are given the same consumption. The results obtained do not require any priori restriction of the values of the elasticity of intertemporal substitution unlike in several related papers.Optimal population size; finite life span; critical utility value; optimal extinction; balanced growth paths