TARIFF AGREEMENTS AND NON-RENEWABLE RESOURCE INTERNATIONAL MONOPOLIES: PRICES VERSUS QUANTITITES

In this paper we model the case of an international non-renewable resource monopolist as a differential game between the monopolist and the governments of the importing countries, and we investigate whether a tariff on the resource importations can be advantageous for the importing countries. We find that the results depend crucially on the kind of strategies the importing country governments can play and on whether the monopolist chooses the price or the extraction rate. For a price-setting monopolist it is shown that the importing countries cannot use a tariff to capture monopoly rents if they are constrained to use open-loop strategies, even if the governments sign a tariff agreement. This result is drastically modified if the importing countries in the tariff agreement use Markov (feedback) strategies. For a quantity-setting monopolist the nature of the game changes and an open-loop tariff is advantageous for the importing countries. Moreover, in this case the importing countries in a tariff agreement enjoy a strategic advantage which allows them to behave as a leader.tariffs, tariff agreements, non-renewable resources, depletion effects, price-setting monopolist, quantity-setting monopolist, differential games, open-loop strategies, linear strategies, Markov-perfect Nash equilibrium, Markov-perfect Stackelberg equilibrium

ON THE COINCIDENCE OF THE FEEDBACK NASH AND STACKELBERG EQUILIBRIA IN ECONOMIC APPLICATIONS OF DIFFERENTIAL GAMES

In this paper the scope of the applicability of the Stackelberg equilibrium concept in differential games is investigated. Firstly, it is showed that for a class of differential games with state-interdependence the stationary feedback Nash equilibrium coincides with the stationary feedback Stackelberg equilibrium independently of the player being the leader of the game. Secondly, sufficient conditions for obtaining the coincidence between the two equilibria are defined. A review of different economic models shows that this coincidence is going to occur for a good number of economic applications of differential games. This result appears because of the continuous-time setting in which differential games are defined. In this setting the first movement advantage of the leader may disappears and then both equilibria coincide.Differential Games; Stationary Feedback Nash Equilibrium; Stationary Feedback Stackelberg Equilibrium; Coincidence.

On the Coincidence of the Feedback Nash and Stackelberg Equilibria in Economic Applications of Differential Games

In this paper the scope of the applicability of the Stackelberg equilibrium concept in differential games is investigated. Firstly, conditions for obtaining the coincidence between the Stackelberg and Nash equilibria are defined in terms of the instantaneous pay-off function and the state equation of the game. Secondly, it is showed that for a class of differential games with state-interdependence both equilibria are identical independently of the player being the leader of the game. A survey of different economic models shows that this coincidence is going to occur for a good number of economic applications of differential games. This result appears because of the continuous-time setting in which differential games are defined. In this setting the first movement advantage of the leader may disappear and the both equilibria coincide.Differential games, stationary feedback Nash equilibrium, stationary feedback Stackelberg equilibrium.

On Capturing Oil Rents with a National Excise Tax Revisited

In this paper the scope of Bergstrom’s (1982) results is studied. Moreover, his analysis is extended assuming that extraction cost is directly related to accumulated extractions. For the case of a competitive market it is found that the optimal policy is a constant tariff if extraction is costless. However, with depletion effects, the optimal tariff must ultimately be decreasing. For the case of a monopolistic market the results depend crucially on the kind of strategies the importing country governments can play and on whether the monopolist chooses the price or extraction rate. For a price-setting monopolist it is shown that the importing countries cannot use a tariff to capture monopoly rents if they are constrained to use open-loop strategies, even if the governments sign a tariff agreement. This result is drastically modified if the importing countries in the tariff agreement use Markov (feedback) strategies. For a quantity-setting monopolist the nature of the game changes and the importing country governments find it advantageous to set a tariff on resource importations. Moreover, in this case the importing countries in a tariff agreement enjoy a strategic advantage which allows them to behave as a leader.Tariffs, Tariff agreements, Non renewable resources, Depletion effects, Price-setting monopolist, Quantity-setting monopolist, Differential games, Open-loop strategies, Linear strategies, Markov-perfect Nash equilibrium, Markov-perfect Stackelberg equilibrium

An Infinite-Horizon Model of Dynamic Membership of International Environmental Agreements

Much of the literature on international environmental agreements uses static models, although most important transboundary pollution problems involve stock pollutants. The few papers that study IEAs using models of stock pollutants do not allow for the possibility that membership of the IEA may change endogenously over time. In this paper we analyse a simple infinite-horizon version of the Barrett (1994) model, in which unit damage costs increase with the stock of pollution, and countries decide each period whether to join an IEA. We show that there exists a steady-state stock of pollution with corresponding steady-state IEA membership, and that if the initial stock of pollution is below (above) steady-state then membership of the IEA declines (rises) as the stock of pollution tends to steady-state. As we increase the parameter linking damage costs to the pollution stock, initial and steady-state membership decline; in the limit, membership is small and constant over time.Self-enforcing international environmental agreements, Internal and external stability, Stock pollutant

SELF-ENFORCING INTERNATIONAL ENVIRONMENTAL AGREEMENTS REVISITED

In Barrett's (1994) paper on transboundary pollution abatement is shown that if the signatories of an international environmental agreement act in a Stackelberg fashion, then, depending on parameter values, a self-enforcing IEA can have any number of signatories between two and the grand coalition. Barrett obtains this result using numerical simulations and also ignoring the fact that emissions must be non-negative. Recent attempts to use analytical approaches and to explicitly recognize the non-negativity constraints have suggested that the number of signatories of a stable IEA may be very small. The way such papers have dealt with non-negativity constraints is to restrict parameter values to ensure interior solutions for emissions. We argue that a more appropriate approach is to use Kuhn-Tucker conditions to derive the equilibrium of the emissions game. When this is done we show, analytically, that the key results from Barrett's paper go through. Finally, we explain why his main conclusion is correct although his analysis can implicitly imply negative emissions.international externalities, self-enforcing environmental agreements, Stackelberg equilibrium, non-negative emissions constraints

FOREIGN MONOPOLIES AND TARIFF AGREEMENTS UNDER INTEGRATED MARKETS

In this paper the optimal policy and the stability of a tariff agreement among the importers of a monopolized good that is sold in an integrated market are studied. To analyze the stability, the tariff agreement formation is modelled as a two-stage game. In the first stage each importer decides whether or not to sign the agreement and in the second stage the signatories and non-signatories choose their tariff whereas the monopoly chooses the quantity or the price. The findings show that the optimal policy of the importers depends on which strategic variable is selected by the monopolist but that, on the contrary, this decision has no effects on the level of cooperation that can be reached by a self-enforcing tariff agreement that, in any case, is very low.foreign monopolies, self-enforcing tariff agreements, integrated markets, rent-shifting hypothesis, prices versus quantities

Strategic behavior and efficiency in a groundwater pumping differential game

In this paper socially optimal and private exploitation of a common property aquifer are compared. Open-loop and feedback equilibria in nonlinear strategies have been computed to characterize the private solution. The use of these two equilibrium concepts aIlows us to distinguish between cost and strategic externalities. The open-Loop solution captures only the cost externality, whereas the feedback solution captures both externalities. The results show that strategic behavior increases the overexploitation of the aquifer compared to the open-loop solution. However, if the groundwater storage capacity is large, the difference between the socIally optImal and private exploitation, characterized by a feedback equilibrium, is negligible and can be ignored for practical purposes. En este trabajo se comparan la explotación privada y socialmente óptima de un acuífero de propiedad común. Para caracterizar la solución privada se han calculado los equilibrios' openloop' y 'feedback' en estrategias no lineales. El uso de estos dos conceptos de equilibrio nos ha permitido distinguir entre efectos externos estratégicos y de coste. La solución 'open-loop' captura solamente el efecto externo de los costes mientras que la SolucIón 'feedback' captura ambos efectos externos. Los resultados muestran que el comportamiento estratégico aumenta la sobreexplotación del acuífero comparado con la solución 'open-loop' o Sin embargo, si la capacidad de almacenamiento del acuífero es grande, la diferencia entre la explotación privada y la socialmente óptima, caracterizada por un equilibrio 'feedback', es despreciable y puede Ignorarse para propósitos prácticos.Explotación de aguas subterráneas, recursos de propiedad común, efecto externo estratégico, juegos diferenciales, solución 'feedback', estrategias no lineales Groundwater exploitation, common property resources, strategic externality, differential games, feedback solution, nonlinear strategies

Optimal growth and land preservation

A model of optimal economic growth with a constant population subject to a constraint on the availability of land is presented. It takes account of the dual character of land as a production factor and as a consumption good (environmental amenities) by determining the optimal intertemporal allocation of land between productive and recreational uses. An extension of the analysis for the case of a growing population with endogenous growth based on human capital accumulation shows that if the rate of discount is not very low then there exists a set of balanced growth paths compatible with a constant allocation of land. En este trabajo se presenta un modelo de crecimiento económico óptimo con una población constante sujeto a una restricción sobre la disponibilidad de tierra. En el modelo se tiene en cuenta el carácter dual de la tierra como factor productivo y como bien de consumo para usos recreacionales y se determina cual es la asignación intertemporal óptima de la tierra entre estos dos usos. En la segunda parte del trabajo, se presenta una extensión del análisis para el caso de una población creciente con crecimiento endógeno basado en la acumulación de capital humano y se demuestra que si la tasa de descuento no es muy pequeña existe un conjunto de sendas de crecimiento equilibrado compatibles con una asignación constante de la tierra.Crecimiento óptimo, asignación intertemporal de la tierra, preservación medioambiental, crecimiento de la población, crecimiento endógeno, capital humano Optimal growth, intertemporal land allocation, environmental preservation, population growth, endogenous growth, human capital