The choice between multiplicative and additive production uncertainty

When modeling output uncertainty, the multiplicative specification is consistently chosen over the additive form, despite the latter being arguably intuitively more obvious. The rationale for this seems to be that when production risk is the only source of uncertainty, additive uncertainty does not reduce output below the certainty level, while multiplicative uncertainty does. We show that, in the absence of hedging, this result is drastically modified when there is simultaneous price and output uncertainty. In this situation the theoretical implications of the two specifications are sufficiently similar to preclude any a priori choice between the two. Thus the choice between the additive and multiplicative formulations may be dictated by how each performs in empirical analyses.     

Uncertainty,Learning and Heterogeneity in International Environmental Agreements

This paper concerns the formation of International Environmental Agreements under uncertainty about environmental damage with different models of learning (complete learning, partial learning or no learning). The results of the existing literature are generally pessimistic: the possibility of either complete or partial learning generally reduces the level of global welfare that can be achieved from forming an IEA relative to no learning. That literature regards uncertainty as a parameter common to all countries, so that countries are identical ex ante as well as ex post. In this paper we extend the literature to the case where there is no correlation between damage costs across countries; each country is uncertain about a particular parameter (in our case the benefit-cost ratio) drawn from a common distribution but, ex post, each country’s realized parameter value is independently drawn. Consequently, while countries remain identical ex ante, they may be heterogeneous ex post. We show that this change reinforces the negative conclusions about the effects of partial learning on international environmental agreements, but, under certain conditions, moderates the negative conclusions about the effects of complete learning.     

Random capital service in labor-managed and profit-maximizing firms

The labor-managed firm and the profit-maximizing firm may experience random production due to a variety of fundamental sources of uncertainty. This paper demonstrates that the nature of the source of uncertainty leads to alternative specifications of the problem and to different conclusions. The specific source of uncertainty modeled in this presentation is random capital failure in the labor-managed firm and in the profit-maximizing firm. In each case, the choice of primary capital, reserve capital, and labor is considered.     

On the existence of optimal processes in non-stationary environments

We consider an aggregative model of intertemporal allocation under uncertainty, in which the utility and production functions are allowed to be time dependent, the random shocks occurring in each period are entirely arbitrary, and the production functions are permitted to be non-concave. In this framework, we provide a theorem on the existence of infinite-horizon optimal processes. In the course of establishing this result, we obtain the existence of optimal policy functions and we show that they are monotone in the stock levels.This paper has benefitted from the comments of two referees of the journal. Research of the first author was supported by a National Science Foundation Grant.     

RISKY PRODUCTION WITH EX-ANTE PRICES UNDER MONOPOLY ANALYTICAL AND SIMULATION RESULTS

This paper concerns the case of a monopolist facing multiplicative uncertainty in demand. Karlin and Carr (1962), henceforth KC, show that, when price and production are both chosen ex ante , the uncertainty price exceeds the certainty price. They also give a sufficient condition under which the firm locates above the certainty demand curve, but they do not consider the effect on the output level. In this note we replicate the KC results and then go further. In the special case that the price elasticity of certainty demand is constant, and the probability distribution for the uncertainty parameter in the demand function is uniform, output is unambiguously lower under uncertainty, and KC's condition for the firm to locate above the certainty demand curve can be strengthened to one that is both necessary and sufficient. The robustness of these results is tested under less stringent assumptions on demand, abandoning symmetry for a lognormal distribution of the uncertainty parameter. Simulation confirms that the results hold up, and also determines the effects upon the firm's decisions of an increase in demand uncertainty.     

Information Advantage in a Public Good Economy with Multiplicative Structure of Utilities

This paper extends results on information advantage in Cournot oligopoly to a public good economy with uncertainty and private information where the state‐dependent utilities have a multiplicative structure. We show that in a Bayesian–Nash equilibrium where consumers’ contributions are positive in all states of nature, a consumer with superior information is rewarded with a higher ex ante expected utility. Our counter example shows that in the case where one consumer does not contribute, information disadvantage might emerge. Thus, the interiority assumption is essential to obtain our results.     

The value of information in a simple duopoly model

This paper is concerned with the evaluation of information in a duopoly model in which the cost functions are subject to uncertainty. It explores how changes in information about the costs available to either firm affects the welfare of both firms along with the welfare of consumers. By comparing the ten possible types of information structures, it is shown that information may be detrimental, that improved information for one firm may or may not benefit the other firm and/or the consumer, and that it may be more desirable for a firm to gather information about the rival's cost rather than its own. All of these “irregular” results depend on the values of the variances of the costs and their correlation coefficient.     

Splitting the replicator: Generalized Darwinism and the place of culture in nature

The concept of Replication has been turned around, moved about and hammered upon in search for a good fit in the puzzle of Generalized Darwinism for a long time. The present paper represents a different take on the formulation of a Generalized Darwinism and on Replication. Replication in evolutionary biology is argued to combine two functions: (i) the production of propositions (Synthesis) and (ii) the retention of propositions over time (Memory). By insisting on universally grouping these two functions together the Replicator–Interactor (RI) framework is here argued to suffer from a fundamental ontological mismatch that no amount of bending and stretching of the concept can avoid. When we allow different packaging of Interaction, Synthesis and Memory (ISM) for different systems, we produce much less empirical friction. Replication then emerges as an important special case, but where replication is not the right model, the ISM model brings a range of issues into the open that remain hidden from an RI viewpoint. Also, when we reserve replication for the cases where it really fits we retain the strong theoretical power and empirical relevance by which it gained its fame in evolutionary biology.     

Government incentive strategies and private capital participation in China’s Shale gas development

Shale gas development investments are uncertain and irreversible in the initial stage in China. Flexible incentive strategy is needed for governments to guide private capital participation at different development stages. This study aims to provide analysis governments can use to encourage private investment in shale gas projects according to its plans in an extended real options framework. A social benefits variable is introduced to determine the threshold of social benefits that determine whether the government will choose a deferred or instant incentives strategy. By considering the efficiency factor, we show the optimal arrangements of two kinds of incentives: tax cuts and production subsidies, to implement incentive targets. The results indicate that current market demand and social benefits are the key factors that affect the government’s choice of incentive strategy. We also find that the optimal level of incentives, either tax cuts or production subsidies, are independent of current market demand and future market uncertainty under the delayed incentive strategy, but which affect the optimal level of incentives under the instant motivation strategy, and ignoring the negative influence of unpredictable random events on future market demand might lead to insufficient government incentives in this case.     

Comparing Fuzzy and Probabilistic Approaches to Preference Uncertainty in Non-Market Valuation

In seeking to value environmental amenities and public goods, individuals often have trouble trading off the (vague) good or amenity against a monetary measure. Valuation in these circumstances can best be described as fuzzy in terms of the amenity being valued, perceptions of property rights, and the numbers chosen to reflect values. In this paper, we apply fuzzy logic to contingent valuation, employing a fuzzy clustering approach for incorporating preference uncertainty obtained from a follow-up certainty confidence question. We develop a fuzzy random utility maximization (FRUM) framework where the perceived utility of each individual is fuzzy in the sense that an individual’s utility belongs to each cluster to some degree. The model is then applied to a Swedish survey that elicited residents’ willingness to pay for enhanced forest conservation and to a Canadian survey of agricultural landowners that elicited their willingness to accept compensation for a tree planting program. Both the WTP and WTA measures we obtain using the fuzzy approach are well below those obtained using standard probability methods. Based on goodness of fit measures and Monte Carlo experimentation, a case can be made for using a fuzzy preference approach for modeling preference uncertainty as opposed to incorporating respondent uncertainty within the random utility maximization framework.      

Risk taking with additive and multiplicative background risks

We examine the effects of background risks on optimal portfolio choice. Examples of background risks include uncertain labor income, uncertainty about the terminal value of fixed assets such as housing and uncertainty about future tax liabilities. While some of these risks are additive and have been amply studied, others are multiplicative in nature and have received far less attention. The simultaneous effect of both additive and multiplicative risks has hitherto not received attention and can explain some paradoxical choice behavior. We rationalize such behavior and show how background risks might lead to seemingly U-shaped relative risk aversion for a representative investor.     

Resisting economic integration when industry location is uncertain

This paper analyses the political determination of transportation costs in a new economic geography model. In a benchmark case with certainty about where agglomeration takes place, a majority of voters favour economic integration and the resulting equilibrium is an industrialised core and a de-industrialised periphery. Allowing for uncertainty, a high level of trade costs may win the election and maintain the initial distribution of industry. The reason is that a coalition of risk-averse immobile factors of production votes for the status quo due to uncertainty about which region will attract industry if economic integration is pursued. Finally, the standard view that agglomeration is unambiguously beneficial to residents in the industrial centre is challenged by introducing costs of undertaking economic integration.     

Cooperation in a Stochastic Transboundary Fishery: The Effects of Implementation Uncertainty Versus Recruitment Uncertainty

This paper examines how non-binding cooperative agreements on fisheries management can be sustained when the management plans in participating countries are implemented imperfectly, and compares the effects of implementation uncertainty and of recruitment uncertainty on the potential for cooperation. The model developed assumes two countries that share a fish stock. Reproduction depends on how much fish each country leaves behind after harvesting and hence on random variation in each country’s achieved abandonment level. A self-enforcing agreement is proposed that accounts for the random variation. The agreement is illustrated with a numerical example. A self-enforcing cooperative solution can only be sustained when uncertainty is not pronounced and when the two countries control close to equal shares of the fishery. Even when a cooperative agreement can be achieved, frequent phases of reversion to non-cooperative harvest levels are needed to support the agreement. A comparison of the effects of recruitment and implementation uncertainty on implicit cooperation indicates that implementation uncertainty is more likely to hamper cooperation.     

A general equilibrium model of production with a random marginal rate of substitution

This paper examines the qualitative effects of risk aversion in a two-sector general equilibrium model where uncertainty is due to random production in one of the sectors. Technology is more general than used previously and provides for a random marginal rate of substitution. Also, the possibility that risk is decreasing in factor usage is considered. Results show that earlier qualitative conclusions on the effects of changing risk may be reversed under these cases.     

Precautionary Principle and Robustness for a Stock Pollutant with Multiplicative Risk

The interest shown by policy makers and economists in the precautionary principle indicates the importance of model uncertainty in global warming policy. I show that through robust control, policy makers can implement the precautionary principle to regulate a stock pollutant, and I analyze its effect on expected steady state pollution taxes, stocks and welfare. The paper is broadly comprised of a theoretical part and an application to global warming policy. I find that: (1) an increase in either uncertainty about the model or risk about abatement cost increases expected steady state pollution taxes; (2) a robust policy is preferred for any level of model uncertainty and this preference increases for either higher model uncertainty or higher multiplicative risk and (3) the effect on expected steady state pollution taxes and stock of introducing model uncertainty is relatively small for high levels of model uncertainty. These results advocate using robust policies for a stock pollutant in the presence of model uncertainty.      

Uncertainty averse preferences

We study uncertainty averse preferences, that is, complete and transitive preferences that are convex and monotone. We establish a representation result, which is at the same time general and rich in structure. Many objective functions commonly used in applications are special cases of this representation.     

Optimal choice of prevention and cure under uncertainty on disease effect and cure effectiveness

This paper studies optimal prevention and cure when an agent copes with two different sources of uncertainty: uncertainty on disease effect and uncertainty on cure effectiveness. We first analyze how optimal choices are affected by uncertainty when prevention and cure do not interact. Under both types of uncertainty, we obtain that the optimal level of prevention rises. Furthermore, we characterize for each source of uncertainty the conditions for the optimal level of cure to increase. We show that these conditions are related to different measures of prudence in health and cross-prudence in wealth. Lastly, we generalize our results to the case where prevention and cure interact and characterize for each source of uncertainty the conditions for the optimal level of prevention and cure to jointly increase. These conditions are similar to those obtained in the case without uncertainty but, in this context, Edgeworth–Pareto complementarity is also required.     

The Effect of Confidence in Valuation Estimates on Arbitrager Behavior and Market Prices

The authors develop a complete framework for optimizing trading decisions that incorporates investors' confidence in their valuation estimates. Quantified estimates of arbitragers' uncertainty about their appraisals of asset values are shown to be extractable from market prices alone. An empirical investigation over the 1977–2015 interval indicated that confidence levels exhibit persistence subject to mean reversion, with a positive relationship found with the magnitude of existing mispricings. Higher returns are discovered to long (short) arbitrage of an asset, whose intrinsic value is higher (lower) than the market price, after rises in uncertainty among informed investors.     

Information, flexibility, and value added

Information technologies used in production activities facilitate the acquisition of more detailed and more timely information concerning the state of the production environment. While the effects of distribution shifts on decisions under uncertainty have been much studied, less is known about the effects of information acquisition on revenue generation and choice. In this article we consider the firm level impacts of information acquisition on revenue, on input use, and on profitability. A choice made under uncertainty depends upon the distribution of a random parameter but not upon its realization, while the choice depends only on the realization when this realization is known. Impacts are determined by interactions between second and third cross derivatives of the primal revenue function.     

Information, flexibility, and value added

Information technologies used in production activities facilitate the acquisition of more detailed and more timely information concerning the state of the production environment. While the effects of distribution shifts on decisions under uncertainty have been much studied, less is known about the effects of information acquisition on revenue generation and choice. In this article we consider the firm level impacts of information acquisition on revenue, on input use, and on profitability. A choice made under uncertainty depends upon the distribution of a random parameter but not upon its realization, while the choice depends only on the realization when this realization is known. Impacts are determined by interactions between second and third cross derivatives of the primal revenue function.