Hartwick's rule and maximin paths when the exhaustible resource has an amenity value

This paper studies the maximin paths of the canonical Dasgupta-Heal-Solow model when the stock of natural capital is a direct argument of well-being, besides consumption. Hartwick's rule then appears as an efficient tool to characterize solutions in a variety of settings. We start with the case without technical progress. We obtain an explicit solution of the mmaximin problem in the case where production and utility are Cobb-Douglas. When the utility function is CES with a low elasticity of substitution between consumption and natural capital, we show taht it is optimal to preserve forever a critical level of natural capital, determined endogeneously. We then study how technical progress affects the optimal maximin paths, in the Cobb-Douglas utility case. On the long run path of the economy capital, production and consumption grow at a common constant rate, while the resource stock decreases at a constant rate and is therefore completely depleted in the very long run. A higher amenity value of the resource stock leads to faster economic growth, but to a lower long run rate of depletion. We then develop a complete analysis of the dynamics of the maximin problem when the sole source of well-being is consumption, and provide a numerical resoultion of the model with resource amenity. The economy consumes, produces and invests less in the short run if the resource has an amenity value than if doesn't whereas it is the contrary in the medium and long runs. However, and without surprise, the resource stock remains for ever higher with resource amenity than without.Exhaustible resources, sustainability, Hartwick's rule.

Social Capital in the creation of Human Capital and Economic Growth: A Productive Consumption Approach

Social capital is a broad term containing the social networks and norms that generate shared understandings, trust and reciprocity, which underpin cooperation and collective action for mutual benefits, and creates the base for economic prosperity. This study deals with the formation of social capital through development of human capital that is created from productive consumption. This paper attempts to formalize incorporation of social capital (SK). This paper sets up a one-sector growth model, where the engine of growth is capital accumulation. The production function for final output is of the AK – type, which uses aggregate capital as single input. Aggregate capital is represented by a Cobb-Douglas index comprising three types capital. Human capital accumulation results from productive consumption and an increase in social capital is driven by the existence of human capital. The optimal growth rate of consumption is derived and it is shown that both human capital and social capital accumulation affect the equilibrium growth rate. Finally, paper presents some empirical evidence on social capital and economic growth

Social Capital in the creation of Human Capital and Economic Growth: A Productive Consumption Approach

Social capital is a broad term containing the social networks and norms that generate shared understandings, trust and reciprocity, which underpin cooperation and collective action for mutual benefits, and creates the base for economic prosperity. This study deals with the formation of social capital through development of human capital that is created from productive consumption. This paper attempts to formalize incorporation of social capital (SK). This paper sets up a one-sector growth model, where the engine of growth is capital accumulation. The production function for final output is of the AK – type, which uses aggregate capital as single input. Aggregate capital is represented by a Cobb-Douglas index comprising three types capital. Human capital accumulation results from productive consumption and an increase in social capital is driven by the existence of human capital. The optimal growth rate of consumption is derived and it is shown that both human capital and social capital accumulation affect the equilibrium growth rate. Finally, paper presents some empirical evidence on social capital and economic growth

A two-dimensional non-equilibrium dynamic model

This paper develops a non-equilibrium dynamic model (NEDyM) with Keynesian features (it allows for a disequilibrium between output and demand and it considers a constant marginal propensity to consume), but where production is undertaken under plain neoclassical conditions (a constant returns to scale production function, with the stocks of capital and labor fully employed, is assumed). The model involves only two endogenous / prognostic variables: the stock of physical capital per unit of labor and a goods inventory measure. The two-dimensional system allows for a careful analysis of local and global dynamics. Points of bifurcation and long-term cyclical motion are identified. The main conclusion is that the disequilibrium hypothesis leads to persistent fluctuations generated by intrinsic deterministic factors

Zero discounting and optimal paths of depletion of an exhaustible resource with an amenity value

This paper studies the undiscounted utilitarian optimal paths of the canonical Dasgupta-Heal-Solow model when the stock of natural capital is a direct argument of well-being, besides consumption. We use a Keynes-Ramsey rule wich yields a generalization of Hartwick's rule : if society has a zero discount rate but is ready to accept intertemporal substitution, net investment should not be zero as in the maximin case but should be positive, its level depending on the distance between the current and the long run bliss level of utility. We characterize solutions in the Cobb-Douglas utility and production case, and analyse the influence of the intertemporal elasticity of substitution on the time profile of the optimal paths. We show that, in the Cobb-Douglas case, the ratio of the values of the resource and capital stocks remains constant along the optimal path, and is independent of initial conditions.Exhaustible resources ; Hartwick's rule ; intertemporal substitution

The Fundamental Duality Theorem of Balanced Growth

In this paper we demonstrate that a simple duality relation underlies balanced growth models with non-joint production. Included in this class of models is the standard neoclassical growth model and endogenous growth models that admit balanced growth paths. In all of these models, the optimal transformation frontier and the factor price frontier take precisely the same mathematical formulation. Studying these identical frontiers in the context of the different models provides new insights into the relative structures of these models, the role of savings, and the nature of dynamic efficiency in each.

Biased Technical Change, Intermediate Goods and Total Factor Productivity

Biased technical change can be defined as changes that affect the elasticity of output with respect to inputs. In this paper, I analyze the effect of biased technical change on total factor productivity (TFP). I construct an input-output economy in which firms produce gross output using capital, labor and intermediate goods. In equilibrium, biased technical change appears as an explicit part of TFP in the value added aggregate production function, where the latter is obtained through the aggregation of individual firms optimal decisions. A larger elasticity of gross output with respect to intermediates implies a smaller TFP level. I use the model to quantify the impact of biased technical change for measured TFP growth in Italy. The exercise shows that biased technical change can account for the productivity slowdown observed in Italy from 1994 to 2004

The Environmental Kuznets Curve from Multiple Perspectives

The analysis finds that in addition to U-shaped paths of environmental quality arising for growth in income per capita, growth in population can also produce socially efficient patterns that are U-shaped. Sufficient conditions for both types of paths are identified for a range of models and parameters, including symmetrical models with homothetic, constant-returns functions such as with CES functions. Similar results are also shown to arise in decentralized economies under either homogeneous or heterogeneous income levels.Environmental Kuznets Curve, Economic Growth, Environmental Quality