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The changing prices of bunker fuel open the door for substantial cost savings by adjusting the sailing speed of ships. A large ship may be burning up to 100 000 USD of bunker fuel per day, which may constitute more than 75% of its operating costs. Reducing the cruising speed by 20% reduces daily bunker consumption by 50%. However, in order to maintain liner service frequency and capacity, reducing the cruising speed may require additional ships to operate a route. We construct a cost model that we use to analyse the trade-off between speed reduction and adding vessels to a container line route, and devise a simple procedure to identify the sailing speed and number of vessels that minimize the annual operating cost of the route. Using published data, we demonstrate the potential for large-cost savings when one operates close to the minimal-cost speed. The presented methodology and procedure are applicable for any bunker fuel price.

We investigate the problem of minimizing a certainty equivalent of the total or discounted cost over a finite and an infinite horizon that is generated by a Markov decision process (MDP). In contrast to a risk-neutral decision maker this optimization criterion takes the variability of the cost into account. It contains as a special case the classical risk-sensitive optimization criterion with an exponential utility. We show that this optimization problem can be solved by an ordinary MDP with extended state space and give conditions under which an optimal policy exists. In the case of an infinite time horizon we show that the minimal discounted cost can be obtained by value iteration and can be characterized as the unique solution of a fixed-point equation using a \"sandwich\" argument. Interestingly, it turns out that in the case of a power utility, the problem simplifies and is of similar complexity than the exponential utility case, however has not been treated in the literature so far. We also establish the validity (and convergence) of the policy improvement method. A simple numerical example, namely, the classical repeated casino game, is considered to illustrate the influence of the certainty equivalent and its parameters. Finally, the average cost problem is also investigated. Surprisingly, it turns out that under suitable recurrence conditions on the MDP for convex power utility, the minimal average cost does not depend on the parameter of the utility function and is equal to the risk-neutral average cost. This is in contrast to the classical risk-sensitive criterion with exponential utility.

This paper presents sufficient conditions for the existence of stationary optimal policies for average cost Markov decision processes with Borel state and action sets and weakly continuous transition probabilities. The one-step cost functions may be unbounded, and the action sets may be noncompact. The main contributions of this paper are: (i) general sufficient conditions for the existence of stationary discount optimal and average cost optimal policies and descriptions of properties of value functions and sets of optimal actions, (ii) a sufficient condition for the average cost optimality of a stationary policy in the form of optimality inequalities, and (iii) approximations of average cost optimal actions by discount optimal actions.

Researchers typically invoke theoretical assumptions to estimate mark-ups. Instead, we directly obtain mark-ups by surveying Pakistani soccer-ball producers. We document six facts: (i) Mark-ups are more dispersed than costs; (ii) Mark-ups and costs increase with firm size; (iii) The mark-up elasticity with respect to size exceeds the cost elasticity; (iv) Costs increase with size because larger firms use higher-quality inputs; (v) Larger firms charge higher mark-ups because they have higher production shares of high-quality balls that carry higher mark-ups, and because they charge higher mark-ups conditional on ball type; (vi) Correlations suggest marketing efforts are important for generating higher mark-ups.

Climate change and global warming are significantly affected by carbon emissions that arise from the burning of fossil fuels, specifically coal, oil, and gas. Accurate prices are essential for the purposes of measuring, capturing, storing, and trading in carbon emissions at regional, national, and international levels, especially as carbon emissions can be taxed appropriately when the price is known and widely accepted. This paper uses a novel Capital (K), Labor (L), Energy (E) and Materials (M) (or KLEM) production function approach to calculate the latent carbon emission prices, where carbon emission is the output and capital (K), labor (L), energy (E) (or electricity), and materials (M) are the inputs for the production process. The variables K, L, and M are essentially fixed on a daily or monthly basis, whereas E can be changed more frequently, such as daily or monthly, so that changes in carbon emissions depend on changes in E. If prices are assumed to depend on the average cost pricing, the prices of carbon emissions and energy may be approximated by an energy production model with a constant factor of proportionality, so that carbon emission prices are a function of energy prices. Using this novel modeling approach, this paper estimates the carbon emission prices for Japan using seasonally adjusted and unadjusted monthly data on the volumes of carbon emissions and energy, as well as energy prices, from December 2008 to April 2018. The econometric models show that, as sources of electricity, the logarithms of coal and oil, though not Liquefied Natural Gas (LNG,) are statistically significant in explaining the logarithm of carbon emissions, with oil being more significant than coal. The models generally displayed a high power in predicting the latent prices of carbon emissions. The usefulness of the empirical findings suggest that the methodology can also be applied for other countries where carbon emission prices are latent.

Background The aim of this study was to determine the social/economic costs and health-related quality of life (HRQOL) of patients with epidermolysis bullosa (EB) in eight EU member states. Methods We conducted a cross-sectional study of patients with EB from Bulgaria, France, Germany, Hungary, Italy, Spain, Sweden and the United Kingdom. Data on demographic characteristics, health resource utilisation, informal care, labour productivity losses, and HRQOL were collected from the questionnaires completed by patients or their caregivers. HRQOL was measured with the EuroQol 5-domain (EQ-5D) questionnaire. Results A total of 204 patients completed the questionnaire. Average annual costs varied from country to country, and ranged from €9509 to €49,233 (reference year 2012). Estimated direct healthcare costs ranged from €419 to €10,688; direct non-healthcare costs ranged from €7449 to €37,451 and labour productivity losses ranged from €0 to €7259. The average annual cost per patient across all countries was estimated at €31,390, out of which €5646 accounted for direct health costs (18.0 %), €23,483 accounted for direct non-healthcare costs (74.8 %), and €2261 accounted for indirect costs (7.2 %). Costs were shown to vary across patients with different disability but also between children and adults. The mean EQ-5D score for adult EB patients was estimated at between 0.49 and 0.71 and the mean EQ-5D visual analogue scale score was estimated at between 62 and 77. Conclusion In addition to its negative impact on patient HRQOL, our study indicates the substantial social/economic burden of EB in Europe, attributable mostly to high direct non-healthcare costs.

This paper deals with discrete-time Markov control processes on a general state space. A long-run risk-sensitive average cost criterion is used as a performance measure. The one-step cost function is nonnegative and possibly unbounded. Using the vanishing discount factor approach, the optimality inequality and an optimal stationary strategy for the decision maker are established.

Statisticians generally consider statistical modeling superior (or at least a useful supplement) to experience-based intuition for estimating the outputs of a complex system. But recent psychological research has led to an enhancement of experience-based intuition known as reference class forecasting. The reference class forecasting approach has been championed as a superior alternative to statistical modeling and is already well-regarded in the planning community. This presents a challenge to statistical modeling. To address this challenge, this article uses a Bayesian approach for combining the reference class forecast and the model-based forecast. The Bayesian prior is informed by the reference class information. A likelihood function was constructed to reflect the model's information. This approach was used to estimate healthcare costs under a voluntary employee benefit association (VEBA). The resulting Bayesian posterior forecast had lower variance (and lower forecast error) than either the model-based forecast or the reference-class forecast.

We consider the average cost problem for partially observable Markov decision processes (POMDP) with finite state, observation, and control spaces. We prove that there exists an -optimal finite-state controller (FSC) functionally independent of initial distributions for any > 0, under the assumption that the optimal liminf average cost function of the POMDP is constant. As part of our proof, we establish that if the optimal liminf average cost function is constant, then the optimal limsup average cost function is also constant, and the two are equal. We also discuss the connection between the existence of nearly optimal finite-history controllers and two other important issues for average cost POMDP: the existence of an average cost that is independent of the initial state distribution, and the existence of a bounded solution to the constant average cost optimality equation.

If inflation expectations become firmly anchored at the inflation target even when average inflation deviates from the target, the long-run Phillips curve becomes nonvertical During 1997-2011, average inflation expectations in Sweden have been close to the inflation target of 2 percent, whereas average inflation has fallen short of the target by 0,6 percentage points. The estimates reported suggest that the slope of the long-run Phillips curve is about 0.75. Then the average unemployment rate has been about 0.8 percentage points higher than if average inflation had been on target. This is a large unemployment cost of undershooting the inflation target.