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.     

Optimal Extraction of a Polluting Nonrenewable Resource with R&D toward a Clean Backstop Technology

We study the optimal extraction of a polluting nonrenewable resource within the following framework: environmental regulation is imposed in the form of a ceiling on the stock of pollution and a clean unlimited backstop technology can be developed by research and development. More specifically, the time taken to develop a new technology depends on the amount spent on R&D. A surprising result is that the stringency of the ceiling and the size of the initial stock of the polluting nonrenewable resource have a bearing on whether environmental regulation speeds up the optimal arrival date of this new technology. Compared to a scenario with no environmental externalities, stringent environmental regulation drives up the optimal R&D investment and brings forward the optimal backstop arrival date only in the case of a large initial resource stock. Otherwise, if the initial resource stock is small, regulation reduces optimal R&D and postpones the optimal backstop arrival date. These results are explained by the two roles played by the backstop technology. First, the backstop serves to replace oil once it has been exhausted. As extraction is slowed down by regulation, the exhaustion of the nonrenewable resource is postponed and the long‐run gains of innovation are lowered. Second, environmental regulation raises the short‐run gains of innovation by increasing the cost of consuming just oil.     

Costly structural change and optimal growth

Summary This paper studies the optimal growth of a developing economy that has a choice to expend a fixed amount of resource for a structural change that advances its production technology. It is shown that structural change is undertaken if capital stock is above a critical level. Economies undertaking structural change converge to a larger steady state and economies not undertaking structural change converge to a smaller steady state. The optimal policy correspondences and growth paths are characterized. The social optimum is shown implementable by a competitive equilibrium with lump-sum taxation.We are grateful to Francis Cheung, Carmen Menezes, Peter Mueser, Don Schilling, two anonymous referees and an associate editor for their valuable suggestions.     

Trade using assets divisible at a cost

The consequences of costly divisibility of assets are studied using a model with the following features. The demand for assets is generated from an overlapping generations model with a continuum of agents in each generation and with intrageneration trade (intermediation) ruled out. There is a once-for-all supply of a stock of nonnegative-dividend assets in a large size, and there is a costly technology for dividing them into smaller sizes. Stationary equilibria are shown to exist. In contrast with similar models with costless divisibility of assets, competitive equilibria are not necessarily desirable; there can be Pareto-ordered equilibria.     

(Monopolistic) resource extraction and limit pricing: The market penetration of competitively produced synfuels

This paper analyzes the market penetration of a competitively produced synfuel, e.g., solar energy, in a market that is initially dominated by a resource extracting monopoly. The availability of the renewable substitute depends not only on the price/cost ratio but also on the installed capacities, which reflect historical investments. As a consequence, the resource monopoly faces a discontinuous residual demand schedule. The dynamic interactions between the resource cartel and the synfuel industry are modelled as a differential game; the (open loop) Nash equilibrium is applied to this game. It will be shown that the commodity price will exceed the production costs of the backstop and that the transition from the periods of resource dependence to the backstop technology will be gradual.     

Climate change mitigation options and directed technical change: A decentralized equilibrium analysis

The paper considers an endogenous growth model with climate change as well as three R&D sectors dedicated to energy, CCS (Carbon Capture and Storage) and backstop efficiency. First, we characterize the set of decentralized equilibria: a particular equilibrium is associated with any vector of policy instruments including a carbon tax and a subsidy to each R&D sector. Second, we show that it is possible to express any equilibrium as the solution of a maximization program. Third, we solve the first-best optimum problem and thereby deriving the optimal instruments. Finally, we illustrate the theoretical model using calibrated functional specifications. In particular, we investigate the effects of various combinations of policy instruments (including the optimal ones) by determining the deviation of each corresponding equilibrium from the “laisser-faire” benchmark. We find notably that introducing an R&D subsidy hardly affects emissions when a carbon tax is already implemented, thus revealing a complementary effect between these two policy instruments.     

Proactive planning and valuation of transmission investments in restructured electricity markets

Traditional methods of evaluating transmission expansions focus on the social impact of the investments based on the current generation stock which may include firm generation expansion plans. In this paper, we evaluate the social welfare implications of transmission investments based on equilibrium models characterizing the competitive interaction among generation firms whose decisions in generation capacity investments and production are affected by both the transmission investments and the congestion management protocols of the transmission system operator. Our analysis shows that both the magnitude of the welfare gains associated with transmission investments and the location of the best transmission expansions may change when the generation expansion response is taken into consideration. We illustrate our results using a 30-bus network example. An erratum to this article can be found at     

Indeterminate Balanced Growth under Habit Persistence and Fiscal Policies

This paper studies a dynamic general equilibrium model with habit persistence in preferences and fiscal policies of taxation and expenditures. Preference takes a subtractive form of habits (the marginal rate of substitution between the agent's own consumption and habit stocks is constant), and technology is linear in aggregate capital (the economy grows without a limit in the long run). We find a continuum of competitive equilibrium paths in conjunction with a unique balanced growth path in the growing economy, in which habits represent both envy/jealousy and altruism/admiration. In addition, in the social optimum under second-best fiscal policies, we show the existence of indeterminacy in transitional allocations along with a unique balanced growth path. Thus, we find that the introduction of habits influences the patterns of the transitional paths but has no impact on the balanced growth path in either competitive or social optimum allocations. The second-best fiscal policy, therefore, restores the socially optimal balanced growth rate but fails to select the unique transitional path among multiple competitive equilibrium paths in the imperfectly competitive economy.     

Effect of social security on fertility and savings: an overlapping generations model

Old-age pension schemes do not exist in most developing countries, so adults bear children as security investments for the future. This phenomenon leads to unduly high rates of population growth. It has been hypothesized that introducing social security programs in such countries would increase savings rates and reduce the number of children born over the long term. The author studies the general equilibrium effects of some social security programs on rates of population growth and capital accumulation within an overlapping generations framework with endogenous fertility and savings. Specifically, Raul's overlapping generations growth model is extended to study the general equilibrium effects of payroll-tax-financed and child-tax-financed social security programs. It is shown that if the rate of intergenerational income transfers from young to old or child care cost is low, competitive equilibrium leads toward overpopulation and capital accumulation in a modified Pareto optimal sense; a social security program in such a case is therefore Pareto improving. A fully-funded system is not neutral when financed by child taxes. Finally, it is also shown that unlike in the case of exogenous fertility where competitive equilibrium attains steady state only asymptotically, fertility, when endogenous, may attain a unique globally steady state in finite time.     

Technology Strategy And Product Diversity

This paper considers a three-stage game of a differentiated oligopoly: firms first make their entry decisions, then they choose production technologies and in the third stage of the game they decide product prices. The technology choice can be understood as selecting one from a pool of those recently available as well as developing a new technology through innovative activities. The resulting market equilibrium is then compared with the social optimum. The main conclusions are that a monopolistically competitive market will typically undersupply both product variety and production scale. R&D competition in a free entry differentiated oligopoly will lead to insufficient R&D investment at firm and industry levels.     

Concealment and verification over environmental regulations: a game-theoretic analysis

We consider a strategic situation in which a firm may conceal the illegal activity of violating environmental regulations and a regulator seeks to verify the illegality to punish the firm. We study two main factors, fines and social monitoring, that influence the firm’s decision in that situation. First, we find all the possible equilibria of our model and examine conditions of those two factors that lead to each equilibrium. Using the equilibrium conditions, we then study the optimal enforcement policies that induce the most socially desirable equilibrium and improve social welfare within each equilibrium. Our main findings are as follows. First, the two factors have a complementary relationship in getting the most desirable equilibrium: Certain high levels of fines and social monitoring are both needed. Second, if making the social monitoring above the certain critical level is impossible, setting the level of the fines as high as possible may be the optimal enforcement policy. Finally, if setting the fines above the certain critical level is not available, either, setting the level of the fines as low as possible might be optimal, and the higher level of the social monitoring does not necessarily bring higher social welfare.     

Intergenerational Altruism and the Environment

We construct an overlapping generations model of pollution externality in which individuals are altruistically linked to their offspring as in Barro (1974). It is shown that steady-state consumption may be a decreasing function of the intergenerational degree of altruism. Despite individuals' altruism, the competitive equilibrium is not optimal. We thus study the social optimum and show that it can be decentralized.
JEL classification: D 62; D 64; D 91     

Lindahl Pricing, Nonrival Infrastructure, and Endogenous Growth

The paper constructs a model of endogenous growth where infrastructure is an accumulable stock generating a nonrival input service. A typical market economy cannot attain the socially optimum steady state path, since nonrivalry precludes competitive pricing of infrastructure. However, there exist agent specific prices for the infrastructural service, a price for the infrastructural stock, a rate of interest, and a subsidy for the representative household that can sustain the optimal path as a dynamic Lindahl equilibrium. The rates of return from physical and infrastructural capital equal the rate of interest. Investment programs are socially optimum. The government's budget is balanced.     

Implementing Steady State Efficiency in Overlapping Generations Economies with Environmental Externalities

We consider in this paper overlapping generations economies with pollution resulting from both consumption and production. The competitive equilibrium steady state is compared to the optimal steady state from the social planner's viewpoint. We show that the dynamical inefficiency of a competitive equilibrium steady state with capital–labor ratio exceeding the golden rule ratio still holds. Moreover, the range of dynamically efficient steady state capital ratios increases with the effectiveness of the environment maintenance technology, and decreases for more polluting production technologies. We characterize some tax and transfer policies that decentralize as a competitive equilibrium outcome the transition to the social planner's steady state.     

Public Expenditure,Environment, and Economic Growth

This paper attempts to develop a model of endogenous growth with special consideration to the role of productive public expenditure in the presence of congestion effect of private capital and environmental pollution. We analyze the properties of the optimal fiscal policy in the steady‐state equilibrium when the level of production of the final good is the source of emission. Government allocates its income tax revenue between pollution abatement expenditure and productive public expenditure. In the steady‐state equilibrium, optimum ratio of productive public expenditure to national income is less than the competitive output share of the public input; and this ratio varies inversely with the magnitude of the emission‐output coefficient. The steady‐state equilibrium appears to be a saddle point; and the market economy growth rate is not necessarily less than the socially efficient growth rate in the steady‐state equilibrium.     

Perfect Competition and Endogenous Comparitive Advantage

This paper analyzes a dynamic Ricardian model of international trade in which relative differences in technology are endogenously determined by investments in innovation by competitive firms. It considers the impact of these investments on trade patterns and the effect of trade patterns on rates of innovation and growth. The main result is that the dynamic effects of trade need not be positive when both countries specialize investments in the goods in which they have a comparitive advantage. In addition, trade can lead to an inefficient pattern of specialization in innovation and have negative welfare effects.     

Fiscal policies, environmental pollution and economic growth

This paper develops a model of endogenous economic growth with special consideration to the role of productive public expenditure and environmental pollution; and analyses the properties of optimal fiscal policy in the steady state growth equilibrium. We consider the level of consumption as the source of pollution. Government allocates its tax revenue between pollution abatement expenditure and productive public expenditure. Optimum ratio of productive public expenditure to national income is equal to the competitive output share of the public input, when productive public expenditure is depicted as tax revenue minus abatement expenditure. However, the proportional income tax rate exceeds the competitive output share of the public input. There is no conflict between the social welfare maximizing solution and the growth rate maximizing solution in the steady state growth equilibrium. The unique steady state growth equilibrium appears to be a saddle-point when the growth rate is above a critical level and the steady state equilibrium growth rate in the market economy is not necessarily lower than the socially efficient growth rate.     

A Model of Creative Destruction with Undiversifiable Risk and Optimising Households

This paper studies optimal household behaviour in a model of creative destruction. The saving technology is characterised by stochastic returns that follow a Poisson process. It is shown that equilibrium conditions with optimising households differ substantially from equilibrium conditions where investment in R&D is determined by firms. Three out of four market failures disappear and a new market failure resulting from a complementarity in financing R&D is identified. Studying the social optimum shows that it contains as the special case of risk neutrality the social optimum derived in the literature.     

社会保障基金最优持股比例研究

在不考虑信息不对称和外部性的条件下,在无穷期生命期限模型中,中央计划经济和竞争性均衡经济的结果是完全等价的;但是在有限生命期限模型中(如代际交叠模型等),中央计划经济和竞争性均衡经济的等价关系就不一定成立,而且在"动态无效率"的情况下,竞争性均衡是帕累托无效的,这时就有必要引入政府来调节经济效率。本文在代际交叠模型中引入国有股形式的社会保障来研究最优社会保障基金持有国有股的比例。研究发现:通过调节社会保障基金的持股比例可以实现中央计划经济和竞争性均衡经济的等价,实现最大的社会福利,从这个角度出发就可以确定最优的社会保障基金的持股比例。本文的结论对全国社会保障基金在未来的实际运作有指导意义。     

Climate Policy under Technology Spillovers

We study climate policy when there are technology spillovers between countries, as there is no instrument that (directly) corrects for these externalities. Without an international climate agreement, the (non-cooperative) equilibrium depends on whether countries use tradable quotas or carbon taxes as their environmental policy instruments. All countries are better-off in the tax case than in the quota case. Two types of international climate agreements are then studied: One is a Kyoto type of agreement where each country is assigned a specific number of internationally tradable quotas. In the second type of agreement, a common carbon tax is used domestically in all countries. None of the cases satisfy the conditions for the social optimum. Even if the quota price is equal to the Pigovian level, R&D investments will be lower than what is socially optimal in the quota case. It is also argued that the quota agreement gives higher R&D expenditures and more abatement than the tax agreement.