This note illustrates, by reconsidering the seminal optimal speed-of-transition model of Aghion, P., and O. J. Blanchard. (1994. "On the Speed of Transition in Central Europe." NBER Macroeconomics Annual 9: 283-319), that optimal transition paths, in general, exhibit nonlinearities and discontinuities. Aghion and Blanchard consider only an approximate solution with a constant unemployment rate over the transition process. The exact solution features an increasing unemployment rate with a discontinuity when the state sector is closed down at the optimally chosen endpoint of transition. Economic transition problems bear many similarities to scrap value problems with free terminal time, often encountered in resource economics. In relation to the transition to a green economy, the discussion in this note therefore casts doubt on the optimality of a green transition discussed in, e.g., the European Union in terms of politically specified rather than optimally designed milestones for emissions reductions, i.e., by -55 % compared to 1990 levels until 2030 and net zero until 2050.

Economic analysis of catastrophic risk is a topic that unfortunately has become more relevant since the 1960s. An important question when a vital resource stock is at risk is whether one should invest more in the stock to create a buffer against a catastrophe or allow the stock to decrease as risk makes its future value decrease. The present paper analyses exogenous catastrophic risk where the probability of catastrophe cannot be controlled. Conditions for when precautionary behaviour is optimal are given with general functional forms. The paper analyses both problems with a single catastrophe and problems with an infinite sequence of catastrophes. It is shown that most of the results pertaining to a single catastrophe carry over to the case with an infinite number of catastrophes.

The literature on how price changes affect optimally managed fisheries is mostly concerned with how fish stocks and harvest rates are affected in steady state. There is little published on how prices affect optimal harvest rates at stock levels outside of steady state. Here we show the effect of an unanticipated and permanent price increase. It is shown that in a model of a pure schooling fishery, if the stock is below the steady state, it is optimal to harvest less if the price goes up and vice versa. It is also shown that in a model with stock dependent harvest costs, the optimal response to a price increase is to reduce the harvest rate for low stock levels even if the optimal harvest rate increases close to the steady state. Empirical relevance is demonstrated by illustrating the theoretical results in an estimated model.

We study the optimal combination of short and long-lived options for reducing greenhouse gas emissions, using electrification of the car fleet as an example. A transition to electric vehicles (EVs) can be incentivized by subsidies on purchases of EVs or on fast chargers. Subsidizing purchases only leads to emissions reductions in the next few years (short-lived static option), whereas investment in fast chargers will reduce abatement costs in several years (long-lived dynamic option). The dynamic option may be socially profitable even if it is more expensive. Numerical simulations confirm the qualitative results of the theory model and point to subsidizing charging stations as the dominate policy. An international permit market affects the combination of static and dynamic abatement. The optimal number of EVs increases with future permit prices, thus making both EV subsides and charging station subsidies more profitable, but it is relatively more cost-efficient to subsidize charging stations.

The paper presents a very simple mathematical proposition that enables easy examination of comparative dynamics when the stock of a renewable biological resource is very low. The proposition is used to prove that in the canonical schooling fisheries model the optimal harvest rate is a decreasing function of the biological productivity of the resource for low stock levels even if the optimal steady state harvest rate is an increasing function of biological productivity. The results presented here carries over to the effect of technological change in the Ramsey model as the fisheries model used here and the Ramsey model are formally equivalent.

Abatement can be performed by measures that have an impact on present emissions, but no lasting effect, and by long-lived infrastructure investments. We study the optimal combination of short and long-lived options for reducing greenhouse gas (GHG) emissions, by specifying abatement cost functions depending on abatement from these two options. Electrification of the transport sector is used as an example. A transition from internal combustion engines vehicles (ICEVs) to electric vehicles (EVs) can be incentivized by both subsidies on purchases of EVs and increased density of fast chargers. Subsidizing the purchase of EVs only leads to emissions reductions in the next few years (static option), whereas investment in infrastructure also will reduce abatement costs in several years to come (dynamic option). We find that the present marginal abatement cost of the dynamic alternative exceeds the costs of static abatement in optimum, thus the dynamic option may be profitable even if it is more expensive. A higher expected abatement cost in later periods most likely makes it even more profitable to use the dynamic policy instrument. This framework is used for a numerical study on electrification of the transport sector in Norway. The numerical simulations confirm the results of the theory model. Flexibility in the domestic target over time and the presence of an international permit market affect the combination of static and dynamic abatement. This stresses the importance of early and time consistent plans for international regulations of GHG emissions.

This article analyses the effect of productivity improvements on optimal fisheries management. It is shown that when harvest costs are independent of resource stock and the stock is below its steady state level, then for any given stock it is optimal to reduce harvest levels in response to a productivity increase unless optimal harvest rate is already zero. If harvest costs are stock dependent this result is modified; for stock dependent harvest costs there exists an interval of stock sizes below the steady state where it is optimal to reduce the harvest rate for any given stock size whereas if the harvest rate is close to an economically optimal steady state it is optimal to increase the harvest rate.

The present article presents novel results on the Ramsey-Cass-Koopmans growth model. It is shown that the shadow price of capital goes to infinity as the capital stock goes to zero even if all functions are bounded with finite derivatives and that imposing the Inada condition of infinite derivative of the per capita production function at zero stock is irrelevant. It is also shown that unless marginal utility at zero consumption is infinity, there will be a non-empty interval where the Keynes-Ramsey rule does not hold. The paper also shows that the stable saddle path in a phase diagram with the state variable and the shadow price has an unrecognized economic interpretation that enables us to illustrate the value function as the integral of the stable saddle path.

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.

We analyse the standard optimal control fishery biomass model and derive some novel results on optimal management when fish stocks are low. We show that as long as it is not optimal to let the stock become extinct and the marginal benefit of harvesting is bounded below infinity for all harvest levels, there will always be an interval with low stock sizes where it is optimal not to harvest. This result does not depend on any assumption that marginal harvesting cost per unit increases with decreasing stock size. We then prove that under weak conditions the shadow price on the fish stock always goes to infinity as the stock approaches zero. The results are generalized to a particular class of age structured models.

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.

Screening for genetic diseases is performed in many regions and/or ethnic groups where there is a high prevalence of possibly malign genes. The propagation of such genes can be considered a dynamic externality. Given that many of these diseases are untreatable and give rise to truly tragic outcomes, they are a source of societal concern, and the screening process should perhaps be regulated. This paper incorporates a standard model of genetic propagation into an economic model of dynamic management to derive cost benefit rules for optimal screening. The highly non-linear nature of genetic dynamics gives rise to perhaps surprising results that include discontinuous controls and threshold effects. One insight is that any screening program that is in place for any amount of time should screen all individuals in a target population. The incorporation of genetic models may prove to be useful to several emerging fields in economics such as genoeconomics, neuroeconomics and paleoeconomics.

Safe Minimum Standards (SMSs) has been advocated as a policy rule for certain environmental problems where uncertainty about risks and consequences are thought to be profound. The present paper explores the rationale for such a policies and derives conditions for when a SMS can be summarily dismissed as a policy choice and for when SMS can be defended as an optimal policy based on standard economic criteria. It turns out that these conditions can be checked with quite limited information about damages and risks.

This paper focuses on two equity dimensions of climate policy, intra- and intergenerational, and analyzes the implications of equity preferences on climate policy, and on the production and consumption patterns in rich and poor countries. We develop a dynamic two-region model, in which each region suffers from global warming, but also has an inequality aversion over current consumption allocations. Inequality aversion generally lifts the consumption path of the poor region, while the rich region must take a greater share of the climate burden. Furthermore, with inequality aversion, the optimal climate policy generally leads to higher investment in clean capital in the North and in dirty capital in the South, thereby allowing the South to pollute more and develop faster. The optimal policy may even require the poor region to increase emissions relative to the uncoordinated Business-as-Usual case. Introducing local pollution and transfers confirm the main results.