Kantian economics, Impure altruism, Berge equilibrium, Arrow-Lind principle, with linear-cost equilibrium

In this paper we will review some results in Kantian economics, (im)pure altruism (warm-glow model), Berge equilibrium altruism and social welfare Arrow-Lind principle and a linear-cost-share equilibrium which is a special case of a Lindahl equilibrium. A strategy profile is a Kantian equilibrium if no player would like all players to alter their contributions by the same multiplicative factor. We study Kantian equilibrium here in Laffont,1975 setting of macroeconomic constraints. Simulations show Kantian equilibrium is in the upper part of efficiency curve, while the ethics utility is maximized, meaning that Kantian equilibrium is efficient but with ethics taken into consideration. Also, as in the case of Nash equilibrium individual utility is more maximized than societal. In a setting with money neutrality as macroeconomic constraint, impure altruism equilibrium or warm-glow equilibrium is at the same point as Berge equilibrium and that is the highest point of efficiency utility line. Kantian and Nash equilibrium are on the same point in this setting while modified Lindahl equilibrium (linear-cost share equilibrium) is as efficient as Pareto equilibrium, other equilibriums are all settled on the efficiency line except for the Kantian, Nash that also are on the warm glow utility line. Pareto equilibrium together with Kantian-Nash equilibrium are on warm glow, and ethics utility line. In the second simulation Kantian is same as Pareto and modified Lindahl equilibrium, impure altruism remains the most efficient equilibrium, Berge equilibrium now is the second most efficient. If marginal cost (Arrow-Lind principle) line crosses sum of marginal benefits (Samuelson condition), then the best equilibrium based on welfare is Nash Equilibrium