After defining biproportion (or RAS) rigorously, we recall two fundamental theorems: unicity of biproportion (any biproportional algorithm leads to the same solution than biproportion, which turns biproportion into a mathematical tool as indisputable than proportion), ineffectiveness of...

MFA (Minimal Flow Analysis) is a method of qualitative input-output analysis used for identifying national of regional industrial clusters. It is based on the analysis of layers (in an input-output model, flow matrices generated at each iteration toward equilibrium). We show through theory that...

The Markov inequality is a classical nice result in statistics that serves to demonstrate other important results as the Chebyshev inequality and the weak law of large numbers, and that has useful applications in the real world, when the random variable is unspecified, to know an upper bound for...

We examine the consistency of the Ghosh supply-driven input-output model (SM) by respect to the traditional Leontief demand-driven input-output model (LM); the variants considered are: primal and dual, quantity and value; input prices are not considered. SM offers solutions of limited interest,...

We address two problems of traditional cost functions: the discontinuity caused by the production capacity (the marginal cost abruptly becomes infinite when production capacity is reached) and the production capacity is artificially exogenous. So, we introduce a smoothed form of marginal cost...

In this paper, by using the game theory toolbox, we demonstrate that relative proportional compensation is better than other types of compensation, mainly maximin and equal compensation. By considering Phelps' curve, the best disagreement point (BATNA) and the gains of negotiation, we examine...

We examine three families of one-parameter functional forms for estimating Lorenz curves: power (elementary and Pareto), exponential (elementary and Gupta) and fractional (Rohde). The computing difficulties to determine the headcount ratio (i.e., the percentage of poor) have been underestimated....

We discuss the mathematical difficulties encountered in Patinkin's classical cartel model. It may be impossible to derive Patinkin's cartel by finding the reciprocal marginal cost functions: it could be impossible for cartel members to compute a solution, unless certain assumptions are made to...

The Supply-Use input-output model of the SNA and Eurostat is examined. For the product-by-product IO tables, two hypothesis are possible: quot;product technologyquot;, largely adopted (Eurostat A) and examined here, and quot;industry technologyquot; (Eurostat B). One examines the calculability...