Abstract
In this chapter, an approach for evaluation of agreements on transnational projects during the negotiation process is proposed. One can show that the negotiation process can be represented as the behavior of decision-making units (countries) in the multidimensional space of economic indicators using Data Envelopment Analysis (DEA) models. In this case, the goals, which can be achieved by units as a result of accomplishment of a joint project, can be determined as points in the multidimensional space. Optimal directions toward these goals and cones of possible directions can be found with the help of Analytic Hierarchy Process (AHP). The efficiency measures for countries are calculated as ratios of the values of potential functions at the initial (intermediate) and final points. The increments of efficiencies measures are considered as arguments in the negotiation process. The approach is illustrated by the real-life data set taken from open international sources.
TopBackground
At the first stage, the production possibility set is determined in the multidimensional space based on the indicators of the countries activities. In essence, the production possibility set can be built using two major groups of methods. The methods of the first group develop and complicate the concept of the production function, but with an attempt to retain the clear analytical form of the function and some of its properties, for example, when making elasticity of substitution constant (CES functions) (Panzar & Willig, 1977; Starrett, 1977).
In our opinion, this goal more likely reveals the desire of theoreticians to have a convenient object of study rather than making an attempt to adequately describe the functioning of real complex objects.
However, the functioning of real production units (countries, regions, companies etc.) takes place in the multidimensional space of the indicators of the units’ activities. Therefore, the mapping of the resource (input) vector into the set of output vectors is considered in the modern neoclassical approach (Banker, Charnes, & Copper, 1984; Cooper, Seiford, & Tone, 2007). It is called in mathematics point-to-set mapping. The boundary of the production possibility set is then built as a convex hull of observations of actual production units. The boundary of the set is weakly Pareto efficient under this approach (Krivonozhko, Utkin, Volodin & Sablin, 2005; Krivonozhko, Utkin, Volodin, Sablin, & Patrin, 2004). This approach reflects the economic reality much more adequately. The data envelopment analysis approach (DEA) unites the methods and models of the second group, the multidimensional production possibility set is introduced in this approach and the behavior of socio-economic units is investigated in it. In this work, we will use the DEA approach for our constructions.
Key Terms in this Chapter
Multidimensional Visualization: Multidimensional visualization can be accomplished with the help of constructions of intersections of the two-dimensional planes or the three-dimensional affine set and the production possibility set. It is worthy to note that obtained intersections are generalization of the well-known functions of economic theory such as production function, input and output isoquant, isocost etc.
Weak Pareto Efficiency: A production unit is weakly efficient if it is not possible to improve all inputs and outputs simultaneously.
Pareto (Strong) Efficiency: A production unit is strongly Pareto-efficient if it is not possible to improve any input or output without worsening some other input or output.
Isoquant: Graph in space of two inputs, on which weakly efficient production units producing the same outputs are located.
Marquee: The marquee is a cone of possible directions taken with the negative sign. The marquee cuts off some area on the boundary of the production possibility set. The unit associated with this marquee is aiming at this area during the planning of operating steps of its development.
Potential Function: In our approach the term “potential function” is taken in order to evaluate unit’s (country’s) position in the multidimensional space of inputs and outputs. The potential function is used to determine the efficiency measure of a unit as a ratio between the values of the potential function at the initial and final (goal) points. Two types of potential function are considered in this work, linear and convex functions.
Cone of Possible Directions: The cones of possible directions are directed upwards, towards the growth in the output indicators. The tops of the cones are placed at the points of achievable goals for the units under consideration.
Analytic Hierarchy Process (AHP): The AHP method of Saaty was proposed for calculating the weight coefficients of the significance of each factor (indicator) that takes part in the model with the help of experts. In our approach the AHP method is used in order to determine a gradient of the potential function.
Production Function: In theoretical economics production function is determined in a multi-input/one-output production model as maximum output that can be produced for any specific input.
Conjugate Cone: The boundary of a conjugate cone represents the equipotential surface of a convex potential function. Any vector that belongs to the conjugate cone indicates the direction of function value increasing.