OPTIMAL STEADY STATES AND THE EFFECTS OF DISCOUNTING

A simple expression for finding and characterizing the optimal steady state of a general dynamic optimization problem is derived. This expression is easy to interpret and easy to apply for various purposes as, for example, to analytically investigate the effect of the discount rate upon optimal steady state stock levels. It is shown that an increase in the discount rate may result in higher optimal stock levels even in the one-dimensional (single species) case in nonlinear models. An important result is that if demand is inelastic at the optimal steady state, a higher discount rate will unequivocally imply higher standing stock(s). Increasing marginal cost of harvest will further strengthen this result. In the multidimensional case it is demonstrated that an increased discount rate may result in higher optimal stock levels for all stocks included in the model.Research Methods/ Statistical Methods,

The Premium of Marine Protected Areas: A Simple Valuation Model

The article addresses the induced cost, the premium, from establishing a marine protected area in a deterministic model of a fishery. Outside the protected area, the fishery is managed optimally through total allowable catch quotas. The premium is found to be increasing and convex along the protection parameter. Biological measures are introduced to increase the understanding of the mechanisms in the bioeconomic system. Time-series solutions show that the net return per unit of fish increases after the protected area is established.Bioeconomics, dynamic programming, fisheries management, marine protected areas, migration, modeling, optimization, renewable resources., International Development, International Relations/Trade, Political Economy, Research and Development/Tech Change/Emerging Technologies, C61, Q22, Q57.,

Approximating Closed Form Solutions to a Class of Feedback Policies

Dynamic optimization problems cover a large class of problems in theoretical and applied economics. A simple iterative algorithm with fast convergence is proposed. It is demonstrated that the algorithm in a few steps produce excellent analytic (closed form) approximations including error bounds to a class of nonlinear problems. The algorithmic scheme is also well suited to produce numerical solutions. The notions of dynamic and potential rents are operationalized. The algorithm is utilizing a relation balancing these concepts. The result is particularly strong in the case of zero discounting where the exact CU-optimal policy is determined in a single step. Applying a particular seed in the general convergent scheme reproduces in a simple way results (formulas) published in the last decade in bioeconomics.Closed form approximations; Contraction algorithm; Renewable resource economics; Capital dynamic modeling; Zero discounting and optimality

Stochastic Stackelberg equilibria with applications to time dependent newsvendor models

In this paper we prove a sufficient maximum principle for general stochastic differential Stackelberg games, and apply the theory to continuous time newsvendor problems. In the newsvendor problem a manufacturer sells goods to a retailer, and the objective of both parties is to maximize expected profits under a random demand rate. Our demand rate is an Ito-Levy process, and to increase realism information is delayed, e.g., due to production time. We provide complete existence and uniqueness proofs for a series of special cases, including geometric Brownian motion and the Ornstein-Uhlenbeck process, both with time variable coefficients. Moreover, these results are operational because we are able to offer explicit solution formulas. An interesting finding is that more precise information may be a considerable disadvantage for the retailer.Stochastic differential games; newsvendor model; delayed information; Ito-Levy processes

A Subgame Perfect Approach to a Multi-Period Stackelberg Game with Dynamic, Price-Dependent, Distributional-Robust Demand

This paper investigates a multi-periodic channel optimization facing uncertain, price dependent, and dynamic demand. The picture of the market uncertainty is incomplete, and only the price and time-dependent mean and standard deviation are known and may depend on the price history. The actual demand distribution itself is unknown as is typically the case in real world problems. An algorithm finding the optimized decentralized channel equilibrium is developed when the downstream member optimizes her expected profit stream by a distributional-robust approach, and the upstream member (leader) considers it as the follower’s reaction function. The algorithm allows for strategic decisions whereby the current demand is scaled by the previous price setting

Multi-Periodic Distributional-Robust Stackelberg Game with Price-History-Dependent Demand and Environmental Corrective Actions

The paper investigates a multi-period supply channel facing uncertain and price-history dependent demands and environmental regulations. The knowledge about the demands is limited to its mean and standard deviation in each period, .e., there is incomplete information on the actual distribution. A distributional robust approach is conducted to address incompleteness. The chain is incorporating environmental policies such as pollution constraints and (optimal) corrective taxes. A single contract covers all periods. Numerical examples highlight the benefits of a single contract

A Survey and Analysis of Outsourcing in East China

The aim of this study is to investigate whether outsourcing activities in east china are associated with a theoretical framework derived from the literature. By the methodology of Statistics Package for the Social Science (SPSS), the results of survey indicate that outsourcing will more extensively practiced in the future, the principal outsourcing motivation are to reduce costs and focus on core businesses. The purchasing outsourcing has the largest correlation coefficients with short-term contract, the total outsourcing has a significant correlation coefficient with long-term contract at the level of =0.05. The findings indicate that high service quality and mutual trust are the main criteria for selecting outsourcing vendors. However, it is found that outsourcing satisfaction is generally low. The main benefits of outsourcing are to reduce cost, concentrate on core businesses and improve the service quality, while the main problems with outsourcing are legal disputes, disclosure of commercial secrets and conflicts with vendors.Outsourcing; strategy; contract; survey

ON THE DYNAMICS OF COMMERCIAL FISHING AND PARAMETER IDENTIFICATION

This paper has two main objectives. The first is to develop a dynamic model of commercial fisheries different from most existing models that assume optimizing behavior. The industry is assumed to have a well-defined index of performance. Based upon this index, the decision to invest or not is made. We do not, however, assume that the industry or firm is efficient or optimal in its operations. The second is that a new approach of fitting model dynamics to time series data is employed to simultaneously estimate the poorly known initial conditions and parameters of nonlinear fisheries dynamics. The approach is a data assimilation technique known as the variational adjoint method. Estimation of the poorly known initial conditions is one of the attractive features of the variational adjoint method.Resource /Energy Economics and Policy,

Mixed contracts for the newsvendor problem with real options

In this paper we consider the newsvendor model with real options. We consider a mixed contract where the retailer can order a combination of q units subject to the conditions in a classical newsvendor contract and Q real options on the same items. We provide a closed form solution to this mixed contract when the demand is discrete and study some of its properties. We also offer an explicit solution for the continuous case. In particular we demonstrate that a mixed contract may be superior to a real option contract when a manufacturer has a bound on how much variance she is willing to accept.Newsvendor model; real options; discrete demand; mixed contract

Fisheries Management under Irreversible Investment: Does Stochasticity Matter?

We present a continuous, nonlinear, stochastic and dynamic model for capital investment in the exploitation of a renewable resource. Both the resource stock and capital stock are treated as state variables. The resource owner controls fishing effort and the investment rate in an optimal way. Biological stock growth and capital depreciation rate are stochastic in the model. We find that the stochastic resource should be managed conservatively. The capital utilization rate is found to be a non-increasing function of stochasticity. Investment could be either higher or lower depending on the interaction between the capital and the resource stocks. In general a stochastic capital depreciation rate has only weak influence on optimal management. In the long run, the steady state harvest for a stochastic resource becomes lower than the deterministic level.Physical capital; irreversible investment; stochastic growth; long-term sustainable optimal