Duopoly models with a joint capacity constraint

The paper proposes a two-stage mixed duopoly model of exhaustible resource market where at the first stage the government decides on the degree of privatization of public firm and at the second stage the public and private firms decide simultaneously on the two-period extraction paths. It is demonstrated that if the two firms have symmetric technologies with increasing marginal extraction costs and the same resource stocks, then neither full nationalization of any of the two firms nor full privatization will be socially desirable. It is shown that the presence of a semi-public firm improves intertemporal allocation of the fixed resource stock. Thus, partial privatization is optimal even under exogenously fixed total outputs of each firm. For asymmetric cost case, when the public firm is less efficient than the private firm, we derive the conditions under which full nationalization or full privatization is optimal.     

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.     

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.     

Uncertain Climate Change in an Intergenerational Planning Model

A three-generation planning model incorporating uncertain climate change is developed. Each generation features a production activity based on capital and an exhaustible resource. An irreversible climate change may occur in period two or three, reducing the productivity for this and the remaining generation. The model is solved by stochastic dynamic programming. If the climate impact and climate change probability is constant, the optimal period one (and two) resource extraction is larger than for the reference case of climate stability. If, however, climate impact and climate change probability increases with increased aggregate resource use, this result is reversed.     

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.     

Exhaustibility and Risk as Asset Class Dimensions: A Social Investor Approach to Capital-Resource Economies

This paper develops a framework in which asset class dimensions are extended to include both risk and exhaustibility for explaining the evolution of shadow prices of marginal units of exhaustible natural resources in capital-resource economies. It is shown that the pricing kernel function required for socially valuing marginal units of exhaustible resource, hereafter called the Exhaustion-Stochastic Discount Factor, combines a factor that discounts for risk and another factor that discounts for resource exhaustion over time. The social rate of return on the marginal unit of resource stock adds to the risk-premium an exhaustion premium that accounts for the resource depletion over time. In this setting, the principle of no-arbitrage holds by extending asset-class dimensions to include not only a risk dimension but also an exhaustibility dimension.     

A Pre-purchase Product Trial of a Monopolist with Multiple Products

For the heterogeneous consumers who do not know their individual utilities from a new product, a pre-purchase product trial would be helpful. We found out that a monopoly firm with two similar products would have a strong incentive not to allow a pre-purchase product trial, even though it is socially optimal to allow it. Furthermore, it is more likely for a monopoly firm with a pre-purchase product trial policy to introduce a new product to the market when introducing a new product is socially optimal.     

新能源成本不确定下能源最优开采研究

随着全球气候变暖和环境的恶化,低污染高效率的新能源成为各国能源政策的主要发展对象,因此新能源取代传统能源是大势所趋。针对未来新能源对传统能源的替代趋势,本文通过建立基于社会和企业总效益最大化的能源最优开采的动态模型,分析了新能源成本不确定性和社会风险偏好的差异对能源耗竭速度的影响,并提出了提高社会总收益的合理方案。分析表明：在替代品出现之前能源的开采量随着新能源替代品成本不确定性的增加而增加;而社会风险厌恶倾向于减少社会的最优开采,但是会增加竞争性企业的的开采量;对T时刻之前的能源开采征收额外的税收可以减缓能源耗竭速度,增加社会总收益。最后,本文提出了T时刻之前的能源开采征收额外的税收,或者是对T时刻之后的能源开采进行补贴来实现我国能源最优开采,提高能源利用效率的建议。     

Climate change,fossil fuel prices and depletion: The rationale for a falling export tax

This paper examines how world prices affect depletion of exhaustible fossil fuels for export and the role of an export revenue tax in curbing depletion. Both effects are studied for a small open economy affected by climate change. We find that setting an export revenue tax rate to fall over time at the marginal social cost of depletion due to lower productivity from climate change encourages a resource exporter to leave an optimal stock in the ground – unextracted and unburnable. Growing prices during the past decade similarly curb depletion. Falling prices bring forward extraction. Because production is independent of consumption, the marginal social cost is independent of utility parameters which are difficult to estimate. Slowing fossil fuel extraction and the effective export of emissions is a contemporary challenge for climate policy. Our findings identify both why an export revenue tax should decline over time and an estimable target rate of decline to help meet this challenge amid changing world prices.     

Contracts payments for ecosystem services: the case of bio-pospecting

We examine the economics of royalties in bioprospecting contracts between a pharmaceutical and genetic resource supplier (local), with an eye to understanding the relative advantages of indexing royalty payments to gross revenue or net revenue. We show a risk-averse firm facing only production or only cost risks will index royalties to net revenue. When facing both types of risk, the choice of royalty type depends on the relative magnitudes of the production and cost risk. In each case, the risk-averse firm chooses the royalty type that shifts as much risk as possible to the local. When the local is risk neutral, the pharmaceutical's and local's preferences are compatible. If the local is risk averse and there is only one type of risk, it will prefer a gross revenue royalty, and shift as much risk as possible to the firm: here the local and firm preferences are compatible only if the firm is risk-neutral, Lastly, we show if the firm sets the terms of the contract, and both agents are risk averse, the firm will not likely volunteer to implement the socially optimal royalty arrangement as it prefers to shift as much risk to the local, who now also prefers a more certain return. This last outcome is at the heart of the benefit sharing discussion and suggests if risk sharing and equity are a concern in benefit sharing, then the choice of royalty type can be an important part of negotiations between pharmaceuticals and locals for the phytochemical from nature for new drug discovery.     

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     

Resource and Waste Taxation in the Theory of the Firm with Recycling Activities

The management of solid waste has become an urgent problem in nations with a great population density. Accordingly, waste reduction through source reduction and recycling has become increasingly important. Our purpose is to show how prevention, recycling and disposal of waste could be part of a theory of the firm. We first derive efficient production functions from production processes with waste as a by-product. Waste obtained as new scrap can partially be recycled by using additional inputs in order to cut back the purchase of virgin material. Waste not completely recyclable will leave the firm as disposal which also entails cost to the firm. We use the dual cost function approach to develop a theory of the firm under solid residual management.Since the producer does not bear the full cost of disposal, there will be a bias toward virgin materials and away from recycling. The goal of the government is to stimulate the firms to recycle with respect to the preservation of exhaustible resources. An incentive to recycle is a tax on resources or on waste. In order to determine the tax levels the government maximizes welfare subject to the dynamic constraint for decumulation of land fill for waste deposits. This gives the user cost and its time profile for taxing waste disposal or virgin material.In a comparative statics analysis we compare the effect of taxes on waste vs. virgin material on effort to produce in a resource saving manner, on the quantity of recycled material, on output, and on the reduction of waste. Since the impact of environmental regulation on employment is important, our model detects seven effects on labor demand as part of resource conservation policy. We finally carry out a comparative statics analysis of waste intensive firms operating in different market structures. Of interest is the impact of a resource or waste taxation on market volume, on the number of firms, on resource saving effort, and on profit.     

OPTIMALITY OF PRE-EMPTING REGULATIONS ON NATURAL RESOURCE USE

Firms are often confronted with regulations on their productive and commercial activities. In many instances a firm can take various actions to pre-empt regulations. This article determines the optimality of pre-emptive action for a firm subject to natural resource regulation. The regulation may be either fixed or relative to the production history. Dependent on the type of regulation, a firm can pre-empt by terminating its current use of resources and converting to other use or by building up the input use or output history in the period prior to regulation. It is shown that the optimal pre-emption decision depends on the extent and perceived probability of regulation, on the rate of discount and on technological characteristics of the production process including the alternative use of the resource.     

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.     

Sustainability of an economy with an exhaustible resource: A viable control approach

We examine the conditions for the sustainability of a production–consumption system based on the use of an exhaustible natural resource. Instead of studying the environmental and economic interactions in terms of optimal control, we focus on the viability of the system, defined by a set of constraints combining guaranteed consumption and a stock of resources to be preserved at all times, which refers to a Rawlsian intergenerational equity perspective. Using the mathematical concept of viability kernel, which makes it possible to deal with the consistency between constraints and controlled dynamics, we exhibit the sustainable technological configurations and, whenever possible, the policy options and environmental-economic states required to obtain a perennial system. We point out the flexibility of the sustainable “extraction–consumption” choices and we show how they are neither reduced to constant consumption paths nor to Hartwick’s rule. Numerical simulations illustrate the general results.     

Endogenous Market Structure and Technology Licensing

This paper analyses the optimal licensing strategy of a licensor firm that competes with potential licensee firms in an industry with endogenous entry. The optimal licensing strategy of the licensor firm is to have zero royalty and positive fixed fees, which is a result that sharply contrasts with the existing literature whereby licensor firms tend to charge positive royalties to their rival licensees. Under the optimal licensing strategy, the licensor firm and the licensee firms are active in the market, but not the non‐licensed firms. This equilibrium market structure is socially desirable if the fixed production cost is not too small.     

Jurisdictional Tax Competition and the Division of Nonrenewable Resource Rents

This paper presents a model of nonrenewable resource extraction across multiple jurisdictions which engage in strategic tax competition. The model incorporates rents due to both resource scarcity and capital scarcity as well as intra-region Ricardian rents. Regions set taxes on nonrenewable resource production strategically to balance tax revenues and local benefits from investment conditional on other regions’ tax rates. A representative extraction firm then allocates production capital across regions and time to maximize the present value of profits. Generally, we find that the division of resource rent between firms and regional governments ultimately depends on the relative scarcity of natural and production capital, relative costs across space, and the value regional governments place on economic activity. This theoretical result provides policymakers with information on the determinants of optimal tax rates and motivates future empirical research on the factors influencing the division of resource rent in practice.     

Mining the soil: Agricultural production system on peatland

Soil is usually considered as a renewable resource for dynamic crop and production management decision problems. For peatland, however, soil should be regarded as an exhaustible resource. This paper determines the optimal utilization of peatland for agricultural production within a dynamic context and it also presents an empirical study where the quasirent function is convex in the input and not concave as assumed in many economic studies. As a result of this convexity a corner solution is obtained. Moreover, the study demonstrates that there is only a slight difference between short- and farsighted behavior, and that both lead ultimately to an accelerated exhaustion of the resource. Private optimization leads to intensive use of the peat in the production of high value crops, which depletes the peat in a relatively short period of time. However, peatland also possesses a value as an environmental asset. The study provides a benchmark for the decision as to whether to convert peatland into productive agricultural land or to conserve it.The financial support of the Department of Environment, Forest and Landscape of Switzerland is gratefully acknowledged. The authors are also grateful to Michael Caputo for helpful suggestions.     

Natural resource economics under the rule of Hotelling

Abstract.  Natural resource stocks held in situ are physical assets. Equilibrium in the assets market requires that their rates of return be such that their owners are just willing to hold on to them rather than invest elsewhere. I discuss a number of factors relating to the evolution of extraction costs, to the durability of the resource, to market structure, and to uncertainty, that are important in correctly characterizing the rate of return on holding exhaustible natural resource stocks. The emphasis is put on how those factors can potentially help bridge the gap between the basic Hotelling's rule of natural resource exploitation and the historical behaviour of the flow price of a number of resources. I also highlight some theoretical and empirical issues that need further attention.     

Socially responsible firms and endogenous choice of strategic incentives

In this paper we are analyzing a mixed quantity-setting duopoly consisting of a socially concerned firm and a profit-maximizing firm. The socially concerned firm considers one group of stakeholders in its objective function and maximizes its profit plus a share of consumer surplus. Both firms have the option to hire a manager who determines the production quantity on behalf of the firm's owner. We find that in the subgame-perfect equilibrium of this game both firms hire a manager and delegate the production choice. If the unit production costs of the firms are similar, then the socially concerned firm has a higher market share and even higher profit. Interestingly, we observe that the relationship between the share of consumer surplus taken into account by the socially concerned firm and its profit is non-monotonic. As the share increases, the socially concerned firm's profit first increases and then decreases. The conclusion is that it pays off to take stakeholder interests into account, but not too much.