The optimal depletion of exhaustible resources: A complete characterization

We provide the closed form solution to the Dasgupta–Heal–Solow–Stiglitz (DHSS) model. The DHSS model is based on the seminal articles Dasgupta and Heal, 1974, Solow, 1974 and Stiglitz (1974) and describes an economy with two assets, man-made capital and a nonrenewable resource stock. We explicitly characterize, for such an economy, the dynamics along the optimal trajectory of all the variables in the model and from all possible initial values of the stocks. We use the analytical solution to prove several properties of the optimal consumption path. In particular, we show that the initial consumption under a utilitarian criterion starts below the maximin rate of consumption if and only the resource is abundant enough and that under a utilitarian criterion, it is not necessarily the present generation that benefits most from a windfall of resources.     

Increasing returns,entrepreneurship and imperfect competition

We study a simple bilateral oligopoly model in which individual agents, who are initially endowed with capital, decide sequentially (1) whether they want to act as producers (entrepreneurs) or as capital lenders (rentiers) and, then (2) which quantity of capital they would like to borrow or lend, though exchange of capital units against units of the produced good. Production takes place under increasing returns to scale. We show the existence of “natural equilibria”, at which wealthier capital owners become entrepreneurs while the remaining ones decide to be rentiers. We also study the efficiency of equilibria which is shown to increase by replication of the economy, but sometimes to decrease as a consequence of wealth redistribution.We thank an anonymous referee for his insightful comments     

Technical progress,population growth and intergenerational equity in a model with many exhaustible and renewable resources

A condition ensuring intergenerational equity is derived using a neoclassical model of many exhaustible and renewable resources involving technical progress and population growth.     

Futures markets,price stabilization and efficient exploitation of exhaustible resources

Markets for natural resource futures contracts and cash forward contracts experience a rapid growth. According to theory, this should result in more efficient resource depletion, implying that price formation is more consistent with Hotelling's rule. The rationale of this stabilization effect is briefly discussed. Next, we analyze the impact of expanding futures markets on the behaviour of individual resource owners trading on the cash market. Using a simple pulse extraction model, we demonstrate that the expected time of depletion can shift to the present or the future, and that utility of exploitation can go up or down, as market prices are stabilized.     

Indefinitely sustained consumption despite exhaustible natural resources

Summary This paper analyzes the feasibility of sustaining uniformly positive consumption forever — even when flows of exhaustible resources are an indispensable input. The main result is a characterization of an economy's capability for sustaining such consumption — under quite general maintained assumptions on technology — in terms of a single, simple capital-resource substitution condition.This is a revised version of CARESS Working Paper #79-27. An even earlier preliminary paper by Mitra [1] contained the seminal idea developed more thoroughly here. Both of our research efforts were supported by the NSF, while much of Cass's participation took place during his tenure as a Sherman Fairchild Distinguished Scholar at Caltech. We thank both institutions for their support and encouragement.     

Comparing tests of the theory of exhaustible resources

The empirical relevance of Hotelling’s exhaustible resource theory has been tested with primarily negative results. Tests have been performed on various resources, at different levels of aggregation, with varying market structures, and over different time periods. Consequently, it is difficult to draw any general conclusions concerning the theory’s applicability in explaining producer behavior, given the assumptions and restrictions implicit in the data and tests. This paper compares test results when the implicit restrictions associated with the data are removed. Employing a single data set we compare the results for four published tests. Even with this uniform data set, two approaches reject the theory while two do not.     

Crossing Hubbert’s peak: Portfolio effects in a growth model with exhaustible resources

This paper elaborates a two-class growth model with an exhaustible resource (“oil”) and an alternative technique (“solar”). Bequest savers accumulate wealth, consisting of capital and oil, saving a constant fraction of their end-of-period wealth. The price of oil obeys Hotelling’s rule. Rising oil prices and the depletion of oil supplies create portfolio effects on the accumulation of capital. When growth is constrained by an exogenously increasing labor force, these wealth effects express themselves in changes in the distribution of income, which first shifts toward profits and then shifts back toward wages as the oil stocks approach depletion. When growth is constrained by capital (the labor force is endogenous), the portfolio effects express themselves in changes in the rate of capital accumulation, which first declines and then rises sharply as the oil stocks approach depletion.     

Increasing returns and cycles in fishing

We consider optimal fishery management under the assumption of increasing returns that is supported by previous empirical evidence. We improve the tractability and realism of the previous approaches by introducing flow adjustment costs on changes in harvest rate. Our framework is the first to provide a link between stable limit cycle policies and increasing returns in harvesting. The type of the harvest policy depends on flow adjustment costs: for relatively costly adjustments the usual steady state harvest policy is conceivable, whereas for relatively cheap adjustments the harvest policy is cyclical. We also show a connection between chattering control policies and limit cycles, which helps us to develop a clear economic meaning for cyclical harvesting.     

Increasing returns and the share economy

Under imperfect competition, profit maximization by firms results in the market price exceeding the marginal cost of production; Weitzman terms this “excess supply” Weitzman wishes to replicate in the cost function (in terms of labor) the properties of the revenue function (in terms of output), thus generating “excess demand” for labor. A revenue-sharing scheme will achieve this if and only if there are decreasing returns to scale. Hence increasing returns apparently play no role in Weitzman's analysis.     

On externalities related to the use of exhaustible resources

We are grateful to our colleague Friedel Bolle and two anonymous referees for useful comments on earlier versions of the paper. The usual disclaimer applies.     

A note on market structure and the search for exhaustible resources

This paper allows for country-specific and time-specific factors in the demand for international reserves by applying the error-components model. Forecasts based on the GLS parameter estimates are shown to be superior to those based on the OLS estimates.     

Increasing returns to savings and wealth inequality

In this paper I present an explanation to the fact that in the data wealth is substantially more concentrated than income. Starting from the observation that the composition of households' portfolios changes towards a larger share of high-yield assets as the level of net worth increases, I first use data on historical asset returns and portfolio composition by wealth level to construct an empirical return function. I then augment an Overlapping Generation version of the standard neoclassical growth model with idiosyncratic labor income risk and missing insurance markets to allow for returns on savings to be increasing in the level of accumulated assets. The quantitative properties of the model are examined and show that an empirically plausible difference between the return faced by poor and wealthy agents is able to generate a substantial increase in wealth inequality compared to the basic model, enough to match the Gini index and all but the top 1 percentile of the US distribution of wealth.     

Increasing returns to scale and productive systems

We consider an economy in which some producers may have nonconvex technologies, in particular they may operate under increasing returns to scale. These producers constitute the I-part of the economy. The prices of all goods and the target supply of the I-part are supposed to be given. Each producer in the I-part produces a certain output in a cost-minimizing way. There is a planning board which has to find decentralizing (gross) output levels for the producers in the I-part such that the net output equals target supply. The existence of such output levels is proven under a productivity assumption which includes the case of strongly increasing returns to scale as well as productive Leontief systems.