y - r (y - x)

B & equality at M

M = (B - r x) / (1 - r)

Malthus has subsistence B enforced by nature. Under current rules of (European) welfare states, B can be higher, since people who cannot earn subsistence B are entitled to a benefit of that level. [46] Table 3 gives the Dutch example.

Table 3: Tax wedge at subsistence (single person)

Dutch legal minimum wage 2002 (per annum)
Gross minimum wage in the official statute 15,638
Net, after deduction of taxes incl. premiums for the employee (single person) 12,516
Gross minimum wage: gross + premiums for the employer 18,265
All taxes incl. premiums (though exclusive of VAT etc.) 5,749
Tax as a percentage of gross minimum wage 31.5 %
Tax as a percentage of net income 45.9 %

The Dutch situation is depicted in Figure 7, the tax plot. The horizontal axis gives income y, the vertical axis the tax t. The tax line T[y] gives the Dutch tax brackets. Net income is given by the difference between the tax and the 45-degrees line (t = y). Subsistence causes the line y - B parallel to the 45-degrees line. This line cuts off a part of net income. The intersection of the subsistence and tax lines gives y - B = T[y], and this solves into the minimum wage y = M. You must earn at least M to satisfy the minimum net income requirement B.

Figure 7: Tax plot