Variation of Gini and Kolkata indices with saving propensity in the Kinetic Exchange model of wealth distribution: An analytical study

Success of social inequality measures in predicting critical or failure points in some models of physical systems

“…The Gibbs distribution ( [4]) of kinetic energy among the particles in a classical ideal gas in equilibrium can also be analyzed in terms of the corresponding Lorenz function L(f) and then extracting the Gini (g) and Kolkata (k) indices for the kinetic exchange models of market by exploiting the formal similarity between the energy of the gas molecules in the kinetic theory and wealth of an individual and that between temperature and noise in trade ( [13][14][15]). Similarly, the distributions of cluster sizes ( [6]) in the percolation models on lattices can be analyzed in terms of the g and k indices.…”

Success of Social Inequality Measures in Predicting Critical or Failure Points in Some Models of Physical Systems

“…In the g → 0 limit, the above expression gives [15] k = 1/2 + (3/8)g, which suggests k = g = 0.8, the Pareto value under extreme competition [10]. Of course, the full relation (3) gives g = k ≃ 0.74, which is much smaller than the observed values around 0.86 [3,12] and even the Pareto value 0.80 (corresponding to Pareto 80-20 law [10]).…”

“…A saving propensity λ(0 ≤ λ ≤ 1) of the agents is introduced in this model, such that during each (two-body) trade event, each of the agents save a fraction λ of their money in possession at that point of time (trade) and the rest of money gets again exchanged randomly among the two trade partners. The exchange of money m i (t) between two traders (i and j) at time t can be expressed as c) We now proceed with an approximate expansion [15] of the Lorenz function L(p), employing Landau-like argument [4] for the expansion of free energy. A Landau-type minimal expansion of the Lorenz function L(f ) up to quadratic term f gives…”

“…These bursts of elastic energy released (experimentally detected as acoustic emissions) until the complete breakdown of the material, are widely studied [13]. These bursts or avalanches are also studied often in models, like the Fiber Bundle Model (FBM) [14,15], both analytically and numerically. An avalanche is defined as the size or mass of the failure events taking place in the system in going from one stable state to the next, as the external load on the system is increased further to trigger a failure activity (load gradually increased) while the (relatively faster) internal dynamics continues due to load redistribution among the surviving fibers and consequent failures due to such increased load on them.…”

“…The Gibbs distribution (see e.g., [4]) of kinetic energy among the particles in a classical ideal gas in equilibrium can also be analyzed in terms of the corresponding Lorenz function L((f ) and then extracting the Gini (g) and Kolkata (k) indices for the kinetic exchange models of market (see e.g., [13][14][15]). Similarly, the distributions of cluster sizes (see e.g., [6]) in the percolation models on lattices can be analyzed in terms of the g and k indices.…”