Model of bribes and estimation of losses from corruption

In the article the genesis of modern corruption, which is a combination of discretionary power, the set of power management solutions, with different economic consequences, and low responsibility for the selection of non-optimal solutions for society is given. Economic and mathematical model of bribes, which helps to find the most profitable strategy for the bribe-taker, namely maximizing his annual income under different reaction of a bribe-taker to a certain size of bribes is built. Reaction of briber is described by a function that characterizes the probability of disagreement on bribery, which increases linearly from 0.0 to 1.0 when the value of the bribe increases from zero to the maximum permissible values for it. The optimal strategy for the bribe-taker in these circumstances is to ask for half of the maximum allowable amount for the briber. In this case, only 50% of potential givers react to the desired to bribe extractor way to his deviant behavior. Economic losses to society are considered to be equal to benefit of a bribe extractor and proportional to the fourth maximum permissible size of bribes: bribe extractor gets half of the maximum permissible value of bribes and only half of potential givers agrees to such a size (with the consent of the linear dependence on bribe). Maximum permissible size of bribe is in economic and mathematical model for its external factor determined by the action and the legal, economic, ethical, psychological, religious factors, developed in practice at a given time in a given place on the specific tasks of relations between officials and businessmen, and other factors. In the article, to remain in the realm of rationality and to eliminate significant for the final result irrational factors in a form of emotional and intuitive response to the offer of a bribe, only economic factors are considered. And among them those related to investment considerations are selected. More precisely the maximum allowable size of a bribe is defined by the maximum allowable increase return on investment.