T(H, t)
H - N(t) ; T(L, t)
L - K(t) (1-t)
Two points share a line. Hence, the tax system can be represented by a straight line, with an intercept and a marginal tariff. These implied ‘parameters’ (actually: reduced form variables) are defined in (2-t), with 2 pairs of 2 equations & 2 unknowns, giving tax exemption X(t) and marginal rate R(t). The line is the reduced form representation, while the statutory system which guides people’s actions could be anything. Each regime gives a set of reduced form lines; our interest concerns the boundary line.
R(t) (y - X(t))
T(y, t) (2-t)
Relation (3-t) defines national income Y(t), where the personal incomes are multiplied by the numbers of persons involved. Revenues h H + b 0 = h H are regime independent. Depending upon the regime the l bring in L or not.