irreversible investment with regime shifts under the real options approach to investment under uncertainty agents formulate optimal policies under the assumption that firms growth prospects do not vary over time this paper proposes and solves a model of investment decisions in which the growth rate and volatility of the decision variable shift between different states at random times a value maximizing investment policy is derived such that in each regime the firm s investment policy is optimal and recognizes the possibility of a regime shift under this policy investment is intermittent and increases with marginal q moreover investment typically is very small but in some states the capital stock jumps implications for marginal q and the user cost of capital are also examined

pricing carbon and adjusting capital to fend off climate catastrophes the optimal reaction to a potential productivity shock as a consequence of climate tipping is to substantially tax carbon in order to curb the risk of tipping but to adjust capital as well in order to smooth consumption when tipping occurs we also allow for conventional marginal climate damages and decompose the optimal carbon tax in two catastrophe components and the conventional component we distinguish constant and increasing marginal hazards moreover the productivity catastrophe is compared with recoverable catastrophes and with a shock to the climate sensitivity finally we allow for investments in adaptation capital as an alternative to counter the potential adverse effects of climate tipping quantitatively the results are investigated with a calibrated model for the world economy

pollution control under a possible future shift in environmental preferences abstract we examine how the possibility of a future shift in environmental preferences affects optimal pollution emissions for example is a more stringent carbon cap called for if excessive carbon emissions today may trigger a shift toward greener preferences in the future in contrast to the related literature which largely focuses on regime shifts in damages not preferences we find that the possibility of a shift in environmental preferences can induce higher or lower optimal current emissions this hinges on an economically interesting interplay between the magnitude of the possible shift whether the shift is endogenous and the magnitude of environmental damages this helps reconcile the tension between the conservationists view of pollution reduction to reduce damage and lessen the likelihood of regime shift and the traditional economic rationale emphasizing risk and discounting

complementarity impatience and the resilience of natural resource dependent economies we study how society s preferences affect the resilience of economies that depend on more than one type of natural resource in particular we analyze whether the degree of complementarity of natural resources in consumer preferences may give rise to multiple steady states and path dependence even when resources are managed optimally we find that for a given social discount rate society tends to be less willing to buffer exogenous shocks if resource good are complements in consumption than if they are substitutes the stronger the complementarity between the various types of natural resources the less resilient the economy is and even more so the higher is the social discount rate

welfare measurement under threats of environmental catastrophes abstract welfare measures under threats of environmental catastrophes are studied using the parable apparatus of weitzman and lofgren on the welfare significance of green accounting as taught by parable j environ econ manage 32 1997 139 153 the occurrence probability of the catastrophic events is driven at least partly by anthropogenic activities such as natural resource exploitation without external effects the green nnp is a genuine welfare measure vis a vis a particular parable economy often however the occurrence hazard constitutes a public bad treated as an externality by agents who ignore their own contribution to its accumulation in such cases the green nnp although accounting for the event hazard rate per se fails to properly internalize future effects on the hazard rate of current economic activities and as a result overestimates welfare the bias term associated with the green nnp is derived and expressed in a simple and interpretable form

nuclear power externalities and non standard pigouvian taxes the external effects arising from the use of nuclear power are in a fundamental way related to uncertainty in this paper we locate these external effects and derive a dynamic pigouvian tax in order to make the decentralized economy support the command optimum another interesting result is that a small constant energy tax which we interpret as a second best policy can take the decentralized economy reasonably close to the command optimum

climatic tipping points and optimal fossil fuel use the economics of climate change is characterized by many uncertainties regarding for instance climate dynamics economic damages and potentially irreversible climate catastrophes using an optimal growth model of a fossil fuel driven economy subject to climate externalities and potentially irreversible climatic regime shifts this paper contributes to the understanding of how the risk of such events impacts on optimal fossil fuel use carbon taxes and fossil fuel prices over time we show that in excess to an increase in the expected present value of marginal damages and an increase in the probability of triggering the event there also exists a third opposing effect this effect comes from the fall in value of remaining fossil fuel reserve which results from the potential regime shift which may or may not occur sometime in the future and implies that optimal fossil fuel policy shifts towards using more resources early on this effect is related to the idea of the green paradox we prove the existence of this effect and show under which circumstances it can become quantitatively important numerically the green paradox effect seems to be somewhat smaller than but comparable in size to the increase in expected marginal damages in general our findings highlight the importance of considering the supply side impacts on climate policy in response to catastrophic climate events

the management of fragile resources a long term perspective excessive exploitation diminishes the capacity of natural resources to withstand environmental stress increasing their vulnerability to extreme conditions that may trigger abrupt changes the onset of such events depends on the coincidence of random environmental conditions and the resource state determining its resilience examples include species extinction ecosystem collapse disease outburst and climate change induced calamities the policy response to the catastrophic threat is measured in terms of its effect on the long term behavior of the resource state to that end the l methodology developed originally to study autonomous systems is extended to non autonomous problems involving catastrophic threats

coping with multiple catastrophic threats we study intertemporal policies for dealing with multiple catastrophic threats with endogenous hazards allowing inter alia for gradual mitigation efforts that accumulate to reduce occurrence risks the long run properties of the optimal policies are characterized in terms of the key parameters damage hazard sensitivity and natural degradation rate associated with each type of catastrophic threat effects of background threats on the optimal response to a potential catastrophe are illustrated numerically

managing the endogenous risk of disease outbreaks with non constant background risk there is a growing concern that risks of disease outbreak and pandemics are increasing over time we consider optimal investments in prevention before an outbreak using an endogenous risk approach within an optimal control setting using the threat of pandemic influenza as an illustrative example we demonstrate that prevention expenditures are relatively small in comparison to the potential losses facing the usa and these expenditures need to be flexible and responsive to changes in background risk failure to adjust these expenditures to changes in background risk poses a significant threat to social welfare into the future

inertia risk improving economic models of catastrophes we model endogenous catastrophic risk in a new way we call it inertia risk which accounts for delays between physical variables and the hazard rate a characteristic often observed in reality the added realism significantly affects optimal policies relative to the standard model of catastrophic risk the probability of a catastrophe occurring at some point in time can span the entire interval 0 1 and is not 0 or 1 as is typical in standard models inertia risk can also generate path dependences we illustrate the implications for policy in a simple model of climate change

relationships between oil price shocks and stock market an empirical analysis from china this paper investigates the interactive relationships between oil price shocks and chinese stock market using multivariate vector auto regression oil price shocks do not show statistically significant impact on the real stock returns of most chinese stock market indices except for manufacturing index and some oil companies some important oil price shocks depress oil company stock prices increase in oil volatility may increase the speculations in mining index and petrochemicals index which raise their stock returns both the world oil price shocks and china oil price shocks can explain much more than interest rates for manufacturing index

does the optimal size of a fish stock increase with environmental uncertainties we analyze the effect of environmental uncertainties on optimal fishery management in a bio economic fishery model unlike most of the literature on resource economics but in line with ecological models we allow the different biological processes of survival and recruitment to be affected differently by environmental uncertainties we show that the overall effect of uncertainty on the optimal size of a fish stock is ambiguous depending on the prudence of the value function for the case of a risk neutral fishery manager the overall effect depends on the relative magnitude of two opposing effects the convex cost effect and the gambling effect we apply the analysis to the baltic cod and the north sea herring fisheries concluding that for risk neutral agents the net effect of environmental uncertainties on the optimal size of these fish stocks is negative albeit small in absolute value under risk aversion the effect on optimal stock size is positive for sufficiently high coefficients of constant relative risk aversion

catastrophes and ex post shadow prices how the value of the last fish in a lake is infinity and why we should not care much abstract catastrophic risk is currently a hotly debated topic this paper contributes to this debate by showing two results first it is shown that for a certain class of optimal control problems the derivative of the value function with respect to the initial state may approach infinity as the state variable goes to zero even when the first order partial derivatives of the integrand and transition functions are finite in the process it is shown that standard phase diagrams used in optimal control theory contain more information than generally recognized and that the value function itself may be easily illustrated in these diagrams second we show that even if the value function has an infinite derivative at some point it is not correct to avoid this point in finite time at almost any cost the results are illustrated in a simple linear quadratic fisheries model and proven for a more general class of growth functions

abrupt positive feedback and the social cost of carbon optimal climate policy should act in a precautionary fashion to deal with tipping points that occur at some future random moment the optimal carbon tax should include an additional component on top of the conventional present discounted value of marginal global warming damages this component increases with the sensitivity of the hazard to temperature or the stock of atmospheric carbon if the hazard of a catastrophe is constant no correction is needed of the usual pigouvian tax the results are applied to a tipping point resulting from an abrupt and irreversible release of greenhouse gases from the ocean floors and surface of the earth which set in motion a positive feedback loop convex enough hazard functions cause overshooting of the carbon tax but a linear hazard function gives rise to undershooting a more convex hazard function and a high discount rate speed up adjustment

consumption pollution tradeoffs in an environment vulnerable to pollution related catastrophic collapse abstract this paper considers the consequences of an avoidable risk of irreversible environmental catastrophe for society s optimal long run consumption pollution tradeoffs the risk is assumed to be a nondecreasing function of pollution concentration which evolves as a dynamic environmental renewal process the main objective of the paper is to derive qualitative insights regarding the effects of such risk on optimal management

optimal incentives for income generation in universities the rule of thumb for the compton tax abstract in this paper we propose a novel framework to model one of the key links between universities and industry the undertaking of applied research we postulate that a basic objective of universities is to undertake fundamental research and that they receive public funding to do so nevertheless faced with tight budget constraints universities may have incentives to allow their staff to devote some of their time to income generating activities such as applied research or consultancy this opens up two channels by which universities can ease their budget constraint i by allowing academics to supplement their income universities may be able to hold down academic salaries ii universities can effectively tax the income that academics raise through applied research or consultancy for example through the imposition of overhead charges by easing their budget constraint universities may be able to take on sufficient extra staff to more than offset the time that existing staff are spending on non fundamental research and thus increase the amount of fundamental research that they can achieve with a given public budget we develop a model of this link between universities and firms and use it to determine the optimal tax that universities should impose on applied research income the compton tax used at mit in the 1930s is an early example of the use of this instrument

accounting for global warming risks resource management under event uncertainty abstract optimal management of atmospheric pollution is discussed with a special emphasis on the uncertainty concerning the occurrence of undesirable events associated with the greenhouse effect the uncertainty considered here stems from our ignorance of the exact pollution level required to trigger the event rather than from the genuinely stochastic nature of the processes involved taking atmospheric pollution level as the state variable it is found that uncertainty implies the existence of an equilibrium interval within which the emission rate of the greenhouse gases should be kept equal to the natural removal rate of these gases processes initiated outside the equilibrium interval must converge monotonically to its nearest endpoint the determination of the interval requires no knowledge of the optimal policy in contrast ignoring event occurrence risk implies a single equilibrium level attracting the optimal process from any initial level

optimal management with potential regime shifts we analyze how the threat of a potential future regime shift affects optimal management we use a simple general growth model to analyze four cases that involve combinations of stock collapse versus changes in system dynamics and exogenous versus endogenous probabilities of regime shift prior work in economics has focused on stock collapse with endogenous probabilities and reaches ambiguous conclusions on whether the potential for regime shift will increase or decrease intensity of resource use and level of resource stock we show that all other cases yield unambiguous results in particular with endogenous probability of regime shift that affects system dynamics the potential for regime shift causes optimal management to become precautionary in the sense of maintaining higher resource stock levels

carbon prices for the next hundred years this paper examines the socially optimal pricing of carbon emissions over time when climate change impacts are unknown potentially high consequence events the carbon price tends to increase with income but learning about impacts or their absence decouples the carbon price from income growth the price should grow faster than the economy if the past warming is not substantial enough for learning the true long run social cost it grows slower than the economy as soon as the warming generates information about events that could have arrived but have not done so a quantitative assessment shows that the price grows roughly at the rate of the economy for the next 100 years

optimal regulation of eutrophying lakes fjords and rivers in the presence of threshold effects eutrophication is a biological process that has an unfavorable economic impact on the economic value of the water basins it affects eutrophication depends on thresholds effects and optimal policies for the regulation of eutrophication must take this into account such optimal policies are derived in the present article by utilizing a novel technique in optimal control theory this technique facilitates a proper analysis of deterministic stock pollutants with thresholds effects a topic it is argued has been poorly understood in the literature copyright 2001 oxford university press

uncertainty and irreversibility in groundwater resource management abstract optimal exploitation of renewable groundwater resources when extraction affects the probability of occurrence of an irreversible event is studied the term irreversible signifies that the event occurrence renders the resource obsolete it is found that uncertainty concerning the event occurrence has a profound effect under certainty when the stock level below which the event occurrence has a profound effect the optimal state process converges to a unique equilibrium state under uncertainty when the event occurrence level is unknown we identify equilibrium intervals and show that optimal processes initiated elsewhere converge to a boundary of one of these intervals inside an equilibrium interval the expected loss due to the event occurrence is so high that it does not pay to extract in excess of recharge even though under certainty doing so would be beneficial

contagious cooperation temptation and ecosystem collapse real world observations suggest that social norms o f cooperation can be effective in overcoming social dilemmas such as the joint management of a c ommon pool resource but also that they can be subject to slow erosion and sudden collapse we show that these patterns of erosion and 15 collapse emerge endogenously in a model of a closed community harvesting a renewable natural resource in which individual agents face the tempta tion to overexploit the resource while a cooperative harvesting norm spreads through the community via interpersonal relations we analyze under what circumstances small changes in key parameters including the size of the community and the rate of technological progress trigger catastrophic transitions from 20 relatively high levels of cooperation to widespread norm violation causing the social ecological system to collapse

scientific progress and irreversibility an economic interpretation of the precautionary principle abstract we consider the problem of the optimal use of a good whose consumption can produce damages in the future scientific progress is made over time that provides information on the distribution of the intensity of damages we show that this progress induces earlier prevention effort only if prudence is larger than twice absolute risk aversion this paper thus identifies the class of quite restrictive but plausible conditions such that scientific uncertainties justify an immediate reduction of the consumption of a potentially toxic substance

pollution control in an uncertain environment abstract the effects of the threat of occurrence of environmental catastrophes on optimal pollution control are considered recent analysis of irreversible events is extended to two types of reversible events single occurrence and multiple occurrence recurrent events while it is possible that the threat of irreversible events induces more pollution we show that reversible events under quite general conditions induce more conservation less pollution the analysis is carried out via a simple method the h method to identify optimal steady states by comparing steady state policies with small variations from them for recurrent events the optimal state process must approach a unique steady state from any initial level in this case the h method characterizes the dynamic behavior of the optimal state process without actually solving for it

transboundary pollution game with potential shift in damages abstract complex systems exposed to pollution may suddenly and permanently shift to a dangerous regime this paper studies a dynamic game among countries that face the prospect of such a shift each country derives some flow utility from its own emissions which are chosen unilaterally but flow emissions by all countries increase the pollution stock in the world in addition to generating global damages such as global warming the pollution stock may trigger an irreversible and abrupt jump in global damages or catastrophe at an unknown date in the future we ask whether endogenous and exogenous threats of such a jump in damages or catastrophe mitigate the tragedy of the commons and examine their implications on welfare our analysis yields different emission responses to these threats as compared to the related literature that focuses only on the single polluter case for example when the hazard rate is exogenous and countries commit to nonlinear strategies we find that the threat of a possible jump in damages or catastrophe may induce a lower or larger emission level and initial welfare due to multiple equilibria these results are maintained when the hazard rate endogenously depends on emission decisions

regulating environmental threats environmental consequences of natural resource exploitation often entail threats of future occurrences of detrimental abrupt events rather than or in addition to inflicting a damage gradually the possibility of abrupt occurrence of climate change related calamities is a case in mind the uncertainty associated with the realization of these threats and their public bad nature complicate the design of optimal economic response we derive a pigouvian hazard tax schedule that implements the socially optimal outcome the tax is based on the expected cost of the hazard generating activities and serves to reduce hazardous emissions well in advance of the catastrophic occurrence a numerical example illustrates possible effects of the proposed regulation scheme implications for climate policy are discussed

market liquidity hedging and crashes in the absence of significant news hedging strategies were blamed for the stock market crash of october 1987 but traditional models cannot explain how a relatively small amount of selling could cause so large a price drop the authors develop a rational expectations model in which prices play an important role in shaping expectations markets are much less liquid in their model than in traditional models discontinuities or crashes can occur even with relatively little hedging the model is consistent with theories as disparate as keynes beauty contest insights and thom s catastrophe analysis and suggests means to reduce volatility copyright 1990 by american economic association

optimal fishery management with regime shifts an assessment of harvesting strategies this paper compares outcomes from informed and uninformed harvesting strategies for a fish stock with switching dynamics where the probability of switching is influenced by climate using data on sea surface temperature anomalies the impacts of climate on the conservation and the welfare that can be extracted from the stock are investigated results indicate that an informed management policy leads to stock biomass and resource rents that are up to 2 7 and 2 times higher respectively than under an uninformed policy also the fishery is open 54 longer under the informed policy the magnitude of these effects depends on the choice of the discount rate indicating that when the future is highly discounted gains from the informed policy dissipate