This is a bargaining problem of splitting, say $100, between two persons, say A and B. x represents the amount Person A can get; and y the amount Person B can get. Instead of a negative line, the problem can be equivalently posted in a horizontal line. When measured from left to right, the share of x increases; from right to left, the money obtained by
B increases. If A gets the whole amount, x=100, and y=0. If B gets the whole amount, y=100, and x=0. If they both get half of the amount, x+y=50+50=100. Lindahl proposed to equalize MU for solution. If marginal utility is diminishing, the left decreasing curve belongs to A, while the right one to B. The slope of the MU curve is dictated by their respective coefficient, alpha and beta. And the intersection of the two curves delivers the result. For example, if al=0.6, be=0.4, the intersection shows that A gets $60, and B $40. If al=0.8, be=0.2, A gets $80, and B $20. Hence, everbody wants to be A, and claims to have a higher alpha, in order to obtain more of the $100. When everybody wants a larger share, Will there be a solution, ultimately? Can Lindahl’s method or MU really settle the bargaining problem?