· w = net labour income + (direct + indirect) taxes + premia + other nonwage costs
· tax = T[w] = (direct + indirect) taxes + premia
· gross labour income = labour costs - other nonwage costs = net labour income + tax
· Neglecting the “other nonwage costs” gives w = labour costs = gross labour income. (Thus the w are labour earnings only if the other nonwage costs are zero.)
Observed labour costs have a density fw[w]. Since the product is y = w (1 +
), equalisation of profit rates with respect to labour would give the labour cost density fw[w] as a shift of the productivity density fy[y]. Normally, though, the profit rates are equalised in terms of capital, which for example causes different Labour Cost Quotes (LCQ) per sector of industry, and then the relation between fw[w] and fy[y] is a more complicated affair.
The proper labour supply density sp[.] depends on net labour income (w - T[w]). But supply can, with the neglect of “other wage costs”, be regarded as a function of labour cost w, as:
s[w] = sp[w - T[w]