SUSTAINABLE CONSTANT CONSUMPTION IN A SEMI‐OPEN ECONOMY WITH EXHAUSTIBLE RESOURCES*

To sustain constant consumption, Hartwick's rule prescribes reinvesting all resource rents in reproducible capital. However, Hartwick's rule is not necessarily the result of optimization. In this paper, we address this insufficiency by deriving a constant consumption path endogenously in a semi‐open economy with an exhaustible resource, which has full access to world goods and capital markets, while the resource flows are not internationally tradable. Our findings show that, due to the essentiality of both capital and resource to the production process, the economy transforms its domestic assets into foreign ones, consuming a constant interest flow from the latter.     

Sustainable development,the Hartwick rule and optimal growth

Defining sustainable development as non-declining utility, the consistency of this concept with the Hartwick rule and optimal growth is explored when resources are exhaustible. A simple proof that a generalized Hartwick rule is necessary and sufficient for constant consumption is derived. The existence of a maximal constant consumption path is shown to depend critically on the elasticity of substitution; if this is less than 1, consumption declines; if it is greater than 1 then consumption is not maximal; if it is equal to 1 (the Cobb-Douglas case) then existence is proved. Consumption can increase along an optimal path if the pure rate of time preference is 0; if it is non-zero then consumption declines.     

Hotelling and recycling

We study the exploitation of recyclable exhaustible resources such as metals that are crucial for the energy transition or phosphorus that is crucial for agricultural production. We use a standard Hotelling model of resource exploitation that includes a primary sector and a recycling sector. We study two polar cases: competitive and monopolistic extraction. We show that, when the primary sector is competitive, the Hotelling’s rule holds and the price of the recyclable resource increases over time. We then show a new reason why the price of an exhaustible resource may decrease: when the primary sector is monopolistic, the primary producer has incentives to delay its production activities in order to delay recycling. As a consequence, the price path of the recyclable resource may be U-shaped. Numerical simulations reveal that the monopolist has an incentive to delay extraction when the recoverability rate is high (because more recycled goods are produced) or when the recoverability rate is low (when fewer recycled goods are expected to be produced in the future). As a consequence, the date of exhaustion of the virgin resource is further away in time for high and low levels of recoverability than for intermediate levels.     

International trade, exhaustible-resource abundance and economic growth

Countries with oil and other natural resources have grown less rapidly than those countries without. This phenomenon is known as the “natural resource curse”. We develop an infinite-horizon, two-country model of trade in which countries are identical, except that one country is endowed with deposits of an exhaustible resource and the other is not. Within the context of the model, we show that this phenomenon can be explained in part by an inelastic demand for the exhaustible resource that increases growth in trade revenues and induces the resource-abundant country to invest relatively less than the country lacking in exhaustible resources. These results are derived analytically and illustrated by an empirical analysis based on plausible parameters obtained from data.     

Capital Accumulation and Resource Depletion: A Hartwick Rule Counterfactual

How much produced capital would resource-abundant countries have today if they had actually followed the Hartwick Rule (invest resource rents in other assets) over the last 30 years? We employ time series data on investment and rents on exhaustible resource extraction for 70 countries to answer this question. The results are striking: Venezuela, Trinidad and Tobago, and Gabon would all have as much produced capital as South Korea, while Nigeria would have five times its current level. A specific rule for sustainability – maintain positive constant genuine investment – is shown to lead to unbounded consumption.     

Savings growth and the path of utility

Abstract.  We derive an expression relating the change in instantaneous utility to the growth of net (genuine) saving in an economy with multiple stocks and externalities that maximizes welfare in the utilitarian sense. This result is then shown to hold for decentralized competitive efficient economies as well, to yield an extension of the Hartwick rule: instantaneous utility is non-declining along a development path if genuine saving is decreasing. By way of example the rule is applied as a constant genuine saving rate rule in a simple Dasgupta-Heal-Solow-Stiglitz economy. The rule yields a path with unbounded consumption and higher wealth than on the standard Hartwick constant consumption path.     

Intertemporal Equity and Efficient Allocation of Resources

Competitive paths which are efficient are shown to satisfy a terminal cost minimization condition, thereby providing a continuous-time counterpart to the discrete-time result due to Malinvaud. Using this result, competitive paths which are equitable and efficient are shown to satisfy Hartwick's investment rule, which states that the value of net investment is zero at each date. Our result indicates that Hartwick's rule can help to signal inefficiency of competitive equitable paths. Journal of Economic Literature Classification Numbers: C61, D90, O41.     

Adverse selection,commitment and exhaustible resource taxation

This paper studies the contractual relationship between a government and a firm in charge of the extraction of an exhaustible resource. Governments design taxation scheme to capture resource rent and they usually propose contracts with limited duration and possess less information on resources than the extractive firms do. This article investigates how information asymmetry on costs and an inability to commit to long-term contracts affect tax revenue and the extraction path. This study gives several unconventional results. First, when information asymmetry exists, the inability to commit does not necessarily lower tax revenues. Second, under asymmetric information without commitment, an efficient firm may produce during the first period more or less than under symmetric information. Hence, the inability to commit has an ambiguous effect on the exhaustion date. Third, the modified Hotelling's rule is such that an increase in the discount factor does not necessarily reduce the first-period extraction.     

Exhaustible resources,technology choice and industrialization of developing countries

How should the world economy adapt to the increased demand for exhaustible resources from countries like China and India? To address that issue, this paper presents a dynamic model of the world economy with two technologies for production; a resource technology, which uses an exhaustible resource as an input and an alternative technology, which does not. I find that both the time path of resource extraction and the adoption of the alternative technology depend on the optimal allocation of capital across the technologies, and on the size of the capital stock in relation to the resource stock. In particular, if the capital stock is low, only the resource technology is used initially and the alternative technology is adopted with a delay. Next, I use the model to analyze the effects of industrialization of developing countries on the extraction of oil and technology choice for energy production. As a result of industrialization, the alternative technology for energy production is adopted earlier.     

ACCOUNTING FOR EXHAUSTIBLE RESOURCES IN THE CANADIAN SYSTEM OF NATIONAL ACCOUNTS: FLOWS, STOCKS AND PRODUCTIVITY MEASURES

The paper shows that the Canadian System of National Accounts includes exhaustible resources but treats them as if they were produced goods. Thus, the claim that conventional accounts ignore the contribution of exhaustible natural resources is partly true. To fully account for exhaustible resources, we present an alternative national accounting framework that incorporates natural resource flows and stocks. The framework modifies the measure of the net domestic product by a factor that differs from the Hartwick-Solow-Weitzman rule and leads to different estimates of GDP, national wealth, and productivity growth. An application to the Canadian oil and gas industry shows order-of-magnitude effects.     

Nonconvexity,efficiency and equilibrium in exhaustible resource depletion

We consider the problem of efficiency and existence of a competitive equilibrium in exhaustible resource markets where extraction costs are nonconvex. Nonconvexity is shown to imply that (1) (efficient) extraction ceases to the left of the minimum efficient scale, i.e., where average costs exceed marginal costs; and (2) a competitive equilibrium does not exist. Introduction of a backstop technology (which induces a flat portion of the industry demand curve) restores both existence and efficiency, provided that the backstop price is sufficiently low. If firms face even a small amount of uncertainty regarding their rivals' stocks, a backstop technology is sufficient to restore existence of competitive equilibrium, even if the backstop price is very high. In this case, however, the competitive equilibrium is not efficient.     

Intergenerational transfers and the social discount rate

This paper investigates the relationship between intergenerational asset transfers and the choice of the discount rate for use in cost-benefit analysis in a model of a competitive overlapping generations economy constrained by a socially managed exhaustible resource. Provided that there are no distortions in capital markets and that all agents hold perfect foresight, cost-benefit techniques will result in a Pareto efficient resource allocation if the discount rate is set equal to the market rate of interest. But since the path of the interest rate depends on the level of intergenerational transfers, cost-benefit techniques do not ensure a socially desirable distribution of welfare between generations; a social optimum will result only if intergenerational transfers are properly chosen and enforced. Decentralized private altruism may result in intergenerational transfers that both present and future individuals would agree are too small if members of the present generation attach positive weight to the general welfare of future generations, not simply their personal descendants. In a world where intergenerational transfers are non-optimal, second-best policy-making may imply a constrained optimum that is inefficient. Together, these findings suggest that cost-benefit analysis is at best a partial criterion to policy formulation that should be used only in conjunction with ethical principles that define the proper distribution of welfare between present and future generations.     

Optimal combination of pollution prevention and abatement policies: The case of agricultural drainage

The adoption of pollution prevention and abatement practices is examined in the context of a model of exhaustible resource use with a backstop technology. For the sake of concreteness, the paper focuses on the problem of water-logging caused by the subsurface accumulation of agricultural drainwater. In modelling this problem, a region's underground capacity to store drainwater is considered an exhaustible resource, while the installation of subsurface drainage is viewed as the corresponding backstop technology (or abatement practice). The exhaustible resource is typically over-exploited due to common access problems, which forces a suboptimally fast adoption of the abatement practice. Conservationist irrigation technologies, such as drip and sprinkler systems, tend to reduce drainwater generation, and their adoption could increase social welfare by delaying the abatement stage. Public policies are suggested to increase the adoption of such conservationist technologies. Data from California is used to illustrate the results and to demonstrate the efficacy of the model for policy purposes. While the setting used for the analysis in this paper is quite specific (i.e., water-logging), the same general modelling ideas may be applied to many other problems of environmental degradation.     

Characterizing the sustainability problem in an exhaustible resource model

We provide a general condition under which consumption can be sustained indefinitely bounded away from zero in the continuous time Dasgupta–Heal–Solow–Stiglitz model, by letting augmentable capital substitute for a non-renewable resource. The assumptions made on the production function are mild, thus generalizing previous work. By showing that Hartwick?s rule minimizes the required resource input per unit of capital accumulation, and integrating the required resource input with respect to capital, we obtain a complete technological characterization without reference to the time path. We also use the characterization result to establish general existence of a maximin path.     

When does the cost channel pose a challenge to inflation targeting central banks?

In a sticky-price model where firms finance their production inputs, there is both a lower and an upper bound on the central bank's inflation response necessary to rule out the possibility of self-fulfilling inflation expectations. This paper shows that real wage rigidities decrease this upper bound, but coefficients in the range of those on the Taylor rule place the economy well within the determinacy region. However, when there is time-variation in the share of firms who finance their inputs (i.e. Markov-switching) then inflation targeting interest rate rules frequently result in indeterminacy, even if the central bank also targets output. Adding a nominal growth target to the policy rule can often alleviate this indeterminacy and therefore anchor inflation expectations.     

Reciprocity Game

This paper shows that reciprocity comes from the desire to cooperate in finitely repeated prisoner's dilemma game. Before playing the finitely repeated prisoner's dilemma game, players choose the reciprocity level and commit to it, and the reciprocity level is public information. There are T equilibria if the prisoner's dilemma game is repeated for T periods, and each equilibrium is associated with different levels of cooperation. Further, if players choose their reciprocity levels sequentially, then the most cooperative equilibrium will be the unique equilibrium. However, reciprocity does not matter for the one‐period game and the infinitely repeated game.     

Rule changes and competitive balance in Formula One motor racing

This article provides an economic explanation of the frequent rule changes in the Formula One (F1) motor racing series. In a two-stage model, the FIA (the organizer of the F1) first decides whether to change the rules or not, and then the racing teams compete in a contest. It turns out that a rule change reduces the teams’ performances, but also improves competitive balance between the teams. The rule change is implemented, if the FIA's revenue gain from the latter effect overcompensates the FIA's revenue loss from the former effect. We provide empirical evidence from F1 seasons in the period 1950 to 2005, which supports the main implications of the model.     

Competition in Markets for Depletable Resources with Setup Costs

This paper analyzes the impact on exhaustible resource markets of setup costs, a sparsely analyzed category of nonconvex production technologies. This paper proves that, even under idealized circumstances for competition, a competitive equilibrium will fail to exist in the presence of setup costs, for any utility and cost functions such that a planner would exploit exhaustible resource pools sequentially.JEL classifications: Q3, C62     

A DYNAMIC ENTRY AND PRICE GAME WITH CAPACITY INDIVISIBILITY

Strategic market interaction is here modelled as a two‐stage game in which potential entrants choose capacities and next active firms compete in prices. Due to capital indivisibility, the capacity choice is made from a finite grid and there are economies of scale. In the simplest version of the model with a single production technique, the equilibrium turns out to depend on the ratio between the level of total output at the long‐run competitive equilibrium and the firm's minimum efficient scale: if that ratio is sufficiently large (the market is sufficiently ‘large’), then the competitive price emerges at a subgame‐perfect equilibrium of the capacity and price game; if not, then the firms randomize in prices on the equilibrium path. The role of the market size for the competitive outcome is shown to be even more important if there are several available production techniques.     

汇率变动、可耗竭资源和经济增长

本文基于贸易的视角,从理论和实证两方面分析了汇率变动、可耗竭资源与经济发展之间的关系.得出贸易传导机制下的"资源诅咒"在我国虽然存在不明显,这种局面到底能持续多久,在一定程度上依赖于我国资源的承受力和可持续性的结论.最后给出了从长远来看,人民币适度升值,可以化解"资源诅咒"的陷阱的建议.