On a geometric programming approach to profit maximization: the case of CES technology

In this note, we give a generalization of the results for the profit maximization problem in the case of the Cobb-Douglas production function presented by Liu in [Appl. Math. Comput. 182 (2006), 1093-1097]. By using geometric programming, we solve a profit maximization problem in the case of the CES production function and show how the results obtained by Liu can be derived from our results

Coreness of Cooperative Games with Truncated Submodular Profit Functions

Coreness represents solution concepts related to core in cooperative games, which captures the stability of players. Motivated by the scale effect in social networks, economics and other scenario, we study the coreness of cooperative game with truncated submodular profit functions. Specifically, the profit function $f(\cdot)$ is defined by a truncation of a submodular function $\sigma(\cdot)$: $f(\cdot)=\sigma(\cdot)$ if $\sigma(\cdot)\geq\eta$ and $f(\cdot)=0$ otherwise, where $\eta$ is a given threshold. In this paper, we study the core and three core-related concepts of truncated submodular profit cooperative game. We first prove that whether core is empty can be decided in polynomial time and an allocation in core also can be found in polynomial time when core is not empty. When core is empty, we show hardness results and approximation algorithms for computing other core-related concepts including relative least-core value, absolute least-core value and least average dissatisfaction value

AGRICULTURAL PRODUCTIVITY ASSESSMENT IN EUROPEAN COUNTRIES

This research work examines levels and trends in global agricultural productivity in fifteen European Union countries and four Eastern European countries that have already applied for European Union membership. The study makes use of data collected from the Food and Agriculture Organization of the United Nations and covers the period 1980-1998. An approach based on Data Envelopment Analysis is used to provide information on the peers of the (inefficient) i-th country and to derive the Malmquist productivity indices. This approach is chosen due to the non-availability of reliable input price data to measure total factor productivity change, technical efficiency change and technical change. Model results show France, Bel-Lux and Italy are on the frontier technology in the period of study. Although Bulgaria and Hungary do not belong to the European Union, these countries are on the frontier technology, too. These results also show that France posts the most spectacular performance, while the Eastern European region is the major performer region and the Mediterranean region is the weakest performer region over the period of study. These results indicate that technical efficiency is not a source of total factor productivity growth. Another interesting result is that there is not a degree of catch-up due to improved technical efficiency along with growth in technical change in European Union Countries and four Eastern European countries.Productivity Analysis,

POTENTIAL PITFALLS IN RENEWABLE RESOURCE DECISION MAKING THAT UTILIZES CONVEX COMBINATIONS OF DISCRETE ALTERNATIVES

Decision makers in renewable resource planning are often unable to specify their objective function a priori, and are presented with a discrete set of alternatives reflecting a range of options that are actually much more continuous. It is common for the decision maker to be interested in some other alternative than those originally developed. An iterative process thus often takes place between decision maker an analyst as they search for a satisfactory alternative. This paper analyzes the economic tenability of simply interpolating (taking convex combinations of) initial alternatives to generate new alternatives in this process. It is shown that convex combinations of outputs will be producible (feasible) with the interpolated input levels, under very common conditions. In fact, the cost estimate resulting from interpolating the cost of two (or more) alternatives will generally be an overestimate. The magnitude of this overestimate is investigated in a test case. It is concluded that this cost overestimate can be rather large, and is not systematically predictable. Only when the output sets in the original alternatives are very similar are the interpolated cost estimates fairly accurate.Resource /Energy Economics and Policy,