The Optimum Allocation of Consumption of the Fisherian Shipwrecked Sailors

The theory of interest of Irving Fisher was designed to explain positive, zero, and negative interest rate. One of the intertemporal equilibria with the zero interest is an economy with a given supply of hardtacks for shipwrecked sailors. Hardtacks can be fully saved for the future, but their stock cannot be enlarged by production. Fisher presented several streams of consumption of hardtacks over time. This paper shows that the Fisherian paths are not consistent with the dynamic optimization model. Different trajectories of the optimum consumption are calculated and sketched. Their shape depends on the value of the subjective discount rate, the intertemporal elasticity of substitution in consumption, and the lifetime horizon of the shipwrecked sailors. None of them resemble the original Fisher examples.

Optimal Composition of Chloride Cells for Osmoregulation in a Randomly Fluctuating Environment

Fish live in water with a different osmotic pressure from that in the body. Their gills have chloride cells that transport ions to maintain an appropriate level of osmotic pressure in the body. The direction of ion transport is different between seawater and freshwater. There are two types of chloride cells that specialize in unidirectional transport and generalist cells that can switch their function quickly in response to environmental salinity. In species that experience salinity changes throughout life (euryhaline species), individuals may replace some chloride cells with cells of different types upon a sudden change in environmental salinity. In this paper, we develop a dynamic optimization model for the chloride cell composition of an individual living in an environment with randomly fluctuating salinity. The optimal solution is to minimize the sum of the workload of chloride cells in coping with the difference in osmotic pressure, the maintenance cost, and the temporal cost due to environmental change. The optimal fraction of generalist chloride cells increases with the frequency of salinity changes and the time needed for new cells to be fully functional but decreases with excess maintenance cost.

Intertemporal Optimization Model of Entrepreneurs Behavior

The intertemporal problem of consumer’s behavior is the basis of modern models. The interest in this kind of problems is determined by the attempt to widen the range of directions within which it is possible to conduct additional mathematical research in the theory of consumption. The article considers the problem of maximizing discounted utility derived from an entrepreneur’s consumption due to optimal allocation of monetary means which he gets as profit from his production company and interest on assets. The difference of this problem from the basic dynamic problem of consumer’s behavior lies in the fact that an entrepreneur as an individual acts in two roles: as a consumer and as a manufacturer. Furthermore, the problem is characterized by two peculiarities: a distinctive budget limitation which includes production function and reveals an irregular differential relation and also by the presence of mixed boundary conditions on the value of capital and assets. Formalization of the problem as a dynamic optimization model is given. It was studied with the use of mathematical analysis and the means of the optimal control theory. According to parameter correlations of the model, two strategies were identified which can be recommended for an entrepreneur as the most optimal ones. The model that was developed in the course of research can serve as a tool for taking decisions because it suggests optimal strategies of allocation of financial means in an enterprise which leads to maximization of consumption utility.

Dynamic Optimization Model for Estimating In-Situ Production Quantity of PC Members to Minimize Environmental Loads

CO2 emissions account for 80% of greenhouse gases, which lead to the largest contributions to climate change. As the problem of CO2 emission becomes more and more prominent, research on sustainable technologies to reduce CO2 emission among environmental loads is continuously being conducted. In-situ production of precast concrete members has advantages over in-plant production in reducing costs, securing equal or enhanced quality under equal conditions, and reducing CO2 emission. When applying in-situ production to real projects, it is vital to calculate the optimal quantity. This paper presents a dynamic optimization model for estimating in-situ production quantity of precast concrete members subjected to environmental loads. After defining various factors and deriving the objective function, an optimization model is developed using system dynamics. As a result of optimizing the quantity by applying it to the case project, it was confirmed that the optimal case can save 7557 t-CO2 in CO2 emissions and 6,966,000 USD in cost, which resulted in 14.58% and 10.53% for environmental loads and cost, respectively. The model developed here can be used to calculate the quantity of in-situ production quickly and easily in consideration of dynamically changing field conditions.

Monetary Base Controllability after an Exit from Quantitative Easing

This study examines the problem that a central bank may face after exiting a monetary quantitative easing policy. It develops a simple dynamic optimization model of a central bank, which finds that if the bank needs to absorb a substantial amount of excess reserves when exiting, the monetary base may become uncontrollable. In this case, the bank has no option but to increase the monetary base by more than the target amount, which leads to an undesirable money supply expansion and, ultimately, to inflation pressures. The model shows the condition when a central bank faces such a challenging situation.