Preparing for catastrophic climate change

We study optimal adaptation to climate change when the harmful consequences of global warming are associated with stochastic occurrence of abrupt changes. The adaptation policy entails the accumulation of a particular sort of capital that will eliminate or reduce the catastrophic damage of an abrupt climate change when (and if) it occurs. The occurrence date is uncertain. The policy problem involves balancing the tradeoffs between the (certain) investment cost prior to occurrence and the benefit (in reduced damage) that will be realized after the (uncertain) occurrence date. For stationary economies the optimal adaptation capital converges to a steady state. For growing economies the optimal adaptation capital stock approaches the maximal economic level above which further accumulation is ineffective.climate change, adaptation, hazard, Environmental Economics and Policy, O13, Q54,

GLOBAL DYNAMICS IN A GROWTH MODEL WITH AN EXHAUSTIBLE RESOURCE

We revisit the seminal growth model with exhaustible resources, the so called Dasgupta-Heal-Stiglitz-Solow model (DHSS). For this optimal control problem with two state variables, we explicitly characterize the dynamics of all the variables in the model and from all possible initial values of the stocks. We determine the condition under which consumption is initially increasing with time and the condition under which initial investment is positive implying that overshooting of man-made capital occurs. We show that the initial consumption under a utilitarian criterion starts below the maximin rate of consumption if and only if the resource is abunduant enough and that under a utilitarian criterion, it is not necessarily the present generation that benefits most from a windfall of resources.

ON PRICE TAKING BEHAVIOR IN A NONRENEWABLE RESOURCE CARTEL-FRINGE GAME

We consider a nonrenewable resource game with one cartel and a set of fringe members. We show that (i) the outcomes of the closed-loop and the open-loop nonrenewable resource game with the fringe members as price takers (the cartel-fringe game a la Salant 1976) coincide and (ii) when the number of fringe firms becomes arbitrarily large, the equilibrium outcome of the closed-loop Nash game does not coincide with the equilibrium outcome of the closed-loop cartel-fringe game. Thus, the outcome of the cartel-fringe open-loop equilibrium can be supported as an outcome of a subgame perfect equilibrium. However the interpretation of the cartel-fringe model, where from the outset the fringe is assumed to be price taker, as a limit case of an asymmetric oligopoly with the agents playing Nash-Cournot, does not extend to the case where firms can use closed-loop strategies.

NONRENEWABLE RESOURCE OLIGOPOLIES AND THE CARTEL-FRINGE GAME

We specify and solve a closed-loop dominant firm nonrenewable resource game, with a price-taking fringe. We show that (i) the outcomes of the closed-loop and the open-loop dominant firm nonrenewable resource game (a la Salant 1976) coincide and (ii) when the number of fringe firms becomes arbitrarily large, the equilibrium outcome of the closed-loop oligopoly game does not coincide with the equilibrium outcome of the closed-loop dominant firm nonrenewable resource game. Thus, the interpretation of the dominant firm model, where the fringe is assumed from the outset to be the price-taker, as a limit case of an asymmetric oligopoly where the number of fringe firms tends to infinity, does not extend to the case where firms can use closed-loop strategies.

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 (Rev. Econ. Stud., 1974), Solow (Rev. Econ. Stud., 1974) and Stiglitz (Rev. Econ. Stud., 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.

Optimal Investment in Clean Production Capacity

For the mitigation of long-term pollution threats, one must consider that both the process of environmental degradation and the switchover to new and cleaner technologies are dynamic. We develop a model of a uniform good that can be produced by either a polluting technology or a clean one; the latter is more expensive and requires investment in capacity. We derive the socially optimal pollution stock accumulation and creation of nonpolluting production capacity, weighing the tradeoffs among consumption, investment, and adjustment costs, and environmental damages. We consider the effects of changes in the pollution decay rate, the capacity depreciation rate, and the initial state of the environment on both the steady state and transition period. The optimal transition path looks quite different with a clean or dirty initial environment. With the former, investment is slow and the price of pollution may overshoot the long-run optimum before converging. With the latter, capacity may overshoot.pollution accumulation, clean technology, capacity investment

Tradable emission permits in a federal system

A system of tradable permits in the standard setting is effective in attaining the policy objective with regard to pollution reduction at the least cost. This outcome is challenged in case of a tradable permit system in a federal state with individual states having discretionary power regarding environmental policy and where pollution is transboundary across states. This paper explores the opportunities of the central authority to influence the effectiveness of the system, under different institutional arrangements, through the initial allocation of permitstradable permits, trade bans, fiscal federalism.

Optimal Carbon Tax with a Dirty Backstop - Oil, Coal, or Renewables?

Optimal climate policy is studied. Coal, the abundant resource, contributes more CO2 per unit of energy than the exhaustible resource, oil. We characterize the optimal sequencing oil and coal and departures from the Herfindahl rule. “Preference reversal” can take place. If coal is very dirty compared to oil, there is no simultaneous use. Else, the optimal outcome starts with oil, before using oil and coal together, and finally coal on its own. The “laissez-faire” outcome uses coal forever or starts with oil until it is no longer profitable to do so and then switches to coal. The optimum requires a steeply rising CO2 tax during the oil-only phase and a less steeply rising CO2 tax during the subsequent oil-coal and coal-only phases to avoid the abrupt switch from oil to coal thus leaving a lot of oil in situ. Finally, we analyze the effects on the optimal transition times and carbon tax of a carbon-free, albeit expensive backstop (solar or wind). Without a carbon tax, a prohibitive coal tax leads to less oil in situ, substantially delays introduction of renewable, and thus curbs global warming substantially. Subsidizing renewables to just below the cost of coal does not affect the oil-only phase. The gain in green welfare dominates the welfare cost of the subsidy if the subsidy gap is small and the global warming challenge is acute.Herfindahl rule, Hotelling rule, non-renewable resource, dirty backstop, coal, global warming, carbon tax, renewables, tax on coal, subsidy on renewables