Factor intensity and order of resource extraction

This paper characterizes the optimal time paths of extraction of several nonrenewable resource deposits with different costs of extraction when the extracted resource can be converted into productive capital and the extraction process, as well as the production of the substitute, requires two primary factors of production. Under a technological assumption granting that the time paths of primary factor prices are monotonic, we show that, for each pair (lower cost/higher cost) of deposits, an intensity condition is necessary in order to have discontinuous extraction of the lower cost deposit. We also show that the same condition is sufficient for discontinuous extraction of the lower cost deposit, provided the stock of the lower cost deposit is sufficiently large and the stocks of all other deposits are sufficiently small.Exhaustible resources; Optimal control; Order of extraction

Existence of optimal strategies in linear multisector models with several consumption goods

In this paper we give a sufficient and almost necessary condition for the existence of optimal strategies in linear multisector models when time is continuous and the the instantaneous utility function of the representative agent has two properties: (a) the intertemporal elasticity of substitution is constant over time and (b) preferences are concave and homothetic.In this paper we give a sufficient and almost necessary condition for the existence of optimal strategies in linear multisector models when time is continuous and the the instantaneous utility function of the representative agent has two properties: (a) the intertemporal elasticity of substitution is constant over time and (b) preferences are concave and homothetic.Non-Refereed Working Papers / of national relevance onl

Factor intensity and order of resource extraction

This paper characterizes the optimal time paths of extraction of several nonrenewable resource deposits with different costs of extraction when the extracted resource can be converted into productive capital and the extraction process, as well as the production of the substitute, requires two primary factors of production. Under a technological assumption granting that the time paths of primary factor prices are monotonic, we show that, for each pair (lower cost/higher cost) of deposits, an intensity condition is necessary in order to have discontinuous extraction of the lower cost deposit. We also show that the same condition is sufficient for discontinuous extraction of the lower cost deposit, provided the stock of the lower cost deposit is sufficiently large and the stocks of all other deposits are sufficiently small

On competition for spatially distributed resources on networks

Ranking questions regarding settings where a network of flows connects the resource extraction sites have been central in the network literature, however, they have received scant attention in the metapopulation literature. This study examines the dynamics of the exploitation of a natural resource distributed among and flowing between several nodes connected via a weighted, directed network. The network represents the locations and interactions of the resource nodes. A regulator decides to designate some of the nodes as natural reserves where no exploitation is allowed. The remaining nodes are assigned (one-to-one) to players, who exploit the resource at the node. The present study demonstrates how the equilibrium exploitation and resource stocks depend on the productivity of the resource sites, the structure of the connections between the sites, and the number and preferences of the agents. The best locations to host nature reserves are identified per the model’s parameters and correspond to the most central (in the sense of eigenvector centrality) nodes of a suitably redefined network that considers the nodes’ productivity. The technique proposed in the present study may have applications in decisions regarding the formation of teams when candidate members are heterogeneous in their productivities and connections

Factor intensity and order of resource extraction

This paper characterizes the optimal time paths of extraction of several nonrenewable resource deposits with different costs of extraction when the extracted resource can be converted into productive capital and the extraction process, as well as the production of the substitute, requires two primary factors of production. Under a technological assumption granting that the time paths of primary factor prices are monotonic, we show that, for each pair (lower cost/higher cost) of deposits, an intensity condition is necessary in order to have discontinuous extraction of the lower cost deposit. We also show that the same condition is sufficient for discontinuous extraction of the lower cost deposit, provided the stock of the lower cost deposit is sufficiently large and the stocks of all other deposits are sufficiently small

On competition for spatially distributed resources in networks: an extended version

We study the dynamics of the exploitation of a natural resource distributed among and flowing between several nodes connected via a weighted, directed network. The network represents both the locations and the interactions of the resource nodes. A regulator decides to designate some of the nodes as natural reserves where no exploitation is allowed. The remaining nodes are assigned (one-to-one) to players, who will exploit the resource at the node. We show how the equilibrium exploitation and the resource stocks depend on the productivity of the resource sites, on the structure of the connections between the sites, and on the number and the preferences of the agents. The best locations to host nature reserves are identified according to the model’s parameters, and we find that they correspond to the most central (in the sense of eigenvector centrality) nodes of a suitably redefined network that considers the nodes’ productivity

Back to the Sixties: A Note on Multi-Primary-Factor Linear Models with Homogeneous Capital

This paper extends Bruno's (1967) one capital good two-sector growth model with discrete technology by allowing multiple primary factors of production. While the existence of an optimal steady state is established for any positive rate of discount, an example in which three "modified golden rules" exist shows that the optimal steady state is non necessarily unique. The extended model provides a simple exemplification of the more general principle that the presence of multiple primary factors of production into homogeneous capital models can definitively result into the same complications that arise when there is joint production

Growth Models with Externalities on Networks

This study examines the dynamics of capital stocks distributed among several nodes, representing different sites of production and connected via a weighted, directed network. The network represents the externalities or spillovers that the production in each node generates on the capital stock of other nodes. A regulator decides to designate some of the nodes for the production of a consumption good to maximise a cumulative utility from consumption. It is demonstrated how the optimal strategies and stocks depend on the productivity of the resource sites and the structure of the connections between the sites. The best locations to host production of the consumption good are identified per the model's parameters and correspond to the least central (in the sense of eigenvector centrality) nodes of a suitably redefined network that combines both flows between nodes and the nodes' productivity

On Competition for Spatially Distributed Resources in Networks

We study the dynamics of the exploitation of a natural resource, distributed in space and mobile, where spatial diversification is introduced by a network structure. Players are assigned to different nodes by a regulator, after he/she decides at which nodes natural reserves are established. The game solution shows how the dynamics of spatial distribution depends on the productivity of the various sites, on the structure of the connections between the various locations, and on the preferences of the agents. At the same time, the best locations to host a nature reserve are identified in terms of the parameters of the model, and it turns out they correspond to the most central (in the sense of eigenvector centrality) nodes of a suitably redefined network which takes into account the nodes productivities

A Ricardian Model of Forestry

This paper provides a continuous-time “Ricardian” model of forestry where, in response to an increase in timber demand, forest cultivation is progressively intensified on the most fertile lands and/or extended to less fertile qualities of lands. It is shown that, at a given level of the rate of interest, a set of “break-through timber prices” gives the order of fertility (i.e., the order in which the different qualities of land are taken into cultivation) and that, for each land, prices of standing trees are positive above a “threshold timber price”. Since, for each land, the break-through price is higher than the threshold price, Ricardo is shown to be right: a higher demand for timber could simply raise those components of the landlord compensation which are not rent