We study a highly aggregated fossil-based world economy with two competing stochastic thresholds or tipping points. Current production generates emissions that add to a stock of GHGs that affect the probability distribution of hitting a climate threshold with severe consequences (the “ugly” scenario). The fossil-intensive output is used either for current consumption or as R&D-investment in knowledge production, with the stock of knowledge affecting the probability distribution for hitting a “good” threshold or having a technological breakthrough (the “good” scenario) providing a clean emission-free substitute to fossil energy. We characterize an optimal strategy for allocating resources over time, given that no threshold has been hit, with the strategy or decision rules being continuously revised due to the induced changes in the derived probability distribution. To avoid the ugly scenario, while pushing for the good one, we find that the conditional expected marginal benefit or willingness-to-pay for knowledge will be increasing over time, with a non-decreasing rate of R&D investment and a non-increasing rate of consumption. Implementation of this strategy requires a global organization with coercive power, equipped with instruments so as to tax the negative stock externality and to subsidize the provision of the public good or stock of knowledge. An important task for the global planner is continuously to update the hazard rates for hitting the two thresholds. JEL Classification C02, H23, H41, Q54, Q55

We analyze optimal wealth management, within a global setting, where accumulation of GHGs caused by extraction of fossil resources affects the probability distribution for hitting a threshold or tipping point, indicating a climate change. We derive an optimal strategy for overall wealth management, within a Ramsey-Hotelling-framework. We have two assets; one being reproducible (reversible capital equipment) and another being non-reproducible (stock of exhaustible natural resources – fossil fuels). Resources, along with capital equipment, are inputs in the production of an aggregate output allocated to consumption and net investment. Resource extraction adds to a stock of GHGs that affects the likelihood for a catastrophic event. If, and when, such an event occurs there is a downscaling of production opportunities. We derive a first-best precautionary global tax on using fossil fuel, which internalizes the present value of (conditional) expected welfare loss of hitting a threshold, as well as a set of risk-modified optimality conditions for overall wealth management, as long as no catastrophe has occurred.

The econometrician Trygve Haavelmo pursued a research programme in macroeconomic theory that was highly original for its time. We present his macro model for an economy with deregulated financial markets and a policy determined interest rate path. Disequilibria arise in the interface between asset markets and the real economy. A mismatch between the marginal return to capital and investors' required rate generates endogenous switching between recession and full employment regimes. Haavelmo regarded the switching mechanism' as a substitute for liquidity constraints, and together with his ideas of price dynamics, there is a clear Keynesian and Wicksellian influence on his macroeconomic theorizing.

An intertemporal optimal strategy for accumulation of reversible capital and management of an exhaustible resource is analyzed for a global economy when resource depletion generates discharges that add to a stock pollutant that affects the likelihood for hitting a tipping point or threshold of unknown location, causing a random“disembodied technical regress”. We characterize an optimal strategy by imposing the notion “precautionary tax” on current extraction for preventing a productivity shock driven by stock pollution and a capital subsidy to promote capital accumulation so as to build up a buffer for future consumption opportunities should the threshold be hit. The precautionary tax will internalize the expected welfare loss should a threshold be hit, whereas the capital subsidy will internalize the expected post-catastrophic long-run return from current capital accumulation.

An intertemporal optimal strategy for accumulation of reversible capital and management of an exhaustible resource is analyzed for a global economy when resource depletion generates discharges that add to a stock pollutant that affects the likelihood for hitting a tipping point or threshold of unknown location, causing a random“disembodied technical regress”. We characterize the optimal strategy by imposing the notion “precautionary tax” on current extraction. Such a tax will internalize future expected damages or expected welfare loss should a threshold be hit. With reversible capital the presence of a stochastic threshold should speed up accumulation as long as no threshold is hit so as to build up a buffer or stock for future consumption should a threshold be hit.

Haavelmo’s “A study in the theory of investment” from 1960 is a tour de force in macroeconomic theorising. His later offerings in this area are less known outside Norway. In this paper, we present his models of business cycles (crises) and inflation dynamics. The business cycle model generates cycles as an endogenous outcome of the mismatch between the return to capital and investors’ required rate. Haavelmo approached inflation dynamics from two different perspectives: First, in the spirit of Knut Wicksell, he included a “cumulative process” into his business cycle model. His second formulation is related to conflict theories of inflation.

This paper presents the business cycle model that Trygve Haavelmo developed as part of his research program in macroeconomic and monetary theory. Driven by a mismatch between the marginal return to capital and the rate of return required by capital owners, this model generates endogenous cycles. The theory leads to a distinct analysis of the scope and limitations of monetary policy. A main message of the model is that care should be taken when conducting 'autonomous' monetary policy and that special emphasis should be put on the soundness of nancial mar- kets. Adopting a strict nominal anchor as the main objective of monetary policy might generate imbalances in the capital market.

Professor Leif Johansen (1930 – 1982) made significant contributions to a large number of fields in economics. A short survey of his contributions is presented. The main focus in the paper is on his growth – production program constituting an important part of his research. The key concepts are embodied technical change, irreversibility, sunk cost, rigidities and heterogeneity. The impact of these factors on the nature of economic growth at the macro level is the point of departure of gradually disaggragating the level of analysis right down to the individual firm. An important tool for the analysis for dynamic structural change at the industry level is the short-run function capturing the underlying heterogeneity of the technologies of the firms within an industry. Technical rigidities represent constraints on how an economy develops from the level of a single industry up to the aggregated macro level of an economy.

Professor Leif Johansen (1930 – 1982) made significant contributions to a large number of fields in economics. A short survey of his contributions is presented. The main focus in the paper is on his growth – production program constituting an important part of his research. The key concepts are embodied technical change, irreversibility, sunk cost, rigidities and heterogeneity. The impact of these factors on the nature of economic growth at the macro level is the point of departure of gradually disaggragating the level of analysis right down to the individual firm. An important tool for the analysis for dynamic structural change at the industry level is the short-run function capturing the underlying heterogeneity of the technologies of the firms within an industry. Technical rigidities represent constraints on how an economy develops from the level of a single industry up to the aggregated macro level of an economy.

Discounting in the presence of catastrophic risk is a hotly debated issue, in particular with respect to climate change. Many scientists and laymen concerned with potentially catastrophic impacts feel that if an increase in the discount rate drastically increases the likelihood of catastrophic outcomes, this discredits economic cost-benefit calculations. This paper argues that this intuition is sound and that if cost-benefit calculations are done within a model that encompasses the type of catastrophic risk that these scientists worry about, the resulting stabilization target will only be slightly influenced by the discount rate. This is shown within a stylized model of a risk neutral decision maker facing a problem with a catastrophic threshold with unknown location.

We model the choice of transportation mode in a simplified Hotelling-like city, with a fixed number of total travellers, fixed road capacity and with no trade-off between when to travel and the time spent in a queue. A person that chooses to take her own car will inflict a congestion cost on all travellers. To get the travellers to internalise these external costs, a congestion charge has to be imposed. We derive an optimal congestion charge within in a discrete-choice framework, with a benevolent government maximising expected tax-adjusted social surplus. The congestion charge to be imposed on private driving, beyond the opportunity cost – equal to the fare on public transportation – is shown to be a weighted average of a Ramsey-like term (capturing the goal to raise public revenue) and a Pigou-term capturing the environmental cost of a person’s private driving. This property is similar to the optimal environmental tax derived by Sandmo (1975). However, the behavioural assumption underlying the present framework is quite different from the standard theory of consumer choice adopted by Sandmo.

A central theme in the international debate on genetic testing concerns the extent to which insurance companies should be allowed to use genetic information when offering insurance contracts. We provide a welfare analysis of this issue within a model of an insurance market with asymmetric information, having the following crucial feature: in addition to a state-contingent consumption profile, a person's well-being depends on her attitude towards resolution of future health uncertainty, and this attitude varies across the population. We present stylized facts that motivate this approach. In the formal analysis, we find that both tested high-risks and untested individuals are equally well off whether or not test results can be used by insurers. Individuals who test for being low-risks, on the other hand, are made worse off by not being able to verify this to insurers. This implies that, in terms of welfare, a regulatory regime in which the use of genetic information by insurers is allowed is better than one in which it is not allowed.