R = B[0] / M[0] / (Net[W[0] / W[0]) > 1
(3) Thirdly, we look at productivity and employment. For this theorem, the worst case to start from is full employment. When we start with full employment at M[0], then M[0] provides the equilibrium of supply and demand. Let the supply price (or gross income or productivity) at the minimum be ms[0] and let the demand price (labour costs) at the minimum be md[0]. [96] Then in the assumed start situation of full employment M[0] = ms[0] = md[0]. Assuming balanced growth for demand and supply gives the development of the labour market situation at the bottom:
w = P rwi w[0] in general, i.e. for all w
md = P rwi md[0] & ms = P rwi ms[0]
This means that the supplied (inherent) productivity of those at the (original) minimum grows as fast as the labour costs which employers could afford. However, the true supply price is not productivity but the (actual) minimum wage M that grows with P J and thus faster than the md. People in the class [ms, M) will not find jobs paying the social minimum. They become unemployed.
Q.E.D.
Above theorem and proof may be regarded as a bit simple. However, they help to highlight some useful aspects:
· Differential indexation can have surprising consequences compared to conventional ideas.
· Instead of thinking that productivity growth reduces employment for the lowly productive, we grow aware that it is likelier that technology creates so many job possibilities that employers can finance even higher costs than subsistence. But the multiplier effect from wrongly indexing taxes can be even faster.