Blog-Reference and Blog-Reference and Blog-Reference on Mar 9
Even if it were true that a falling wage rate increases employment in a subsector of the labor market, it would be a blatant Fallacy of Composition to generalize this inverse relationship for the economy as a whole.
To cut a meticulous formal derivation short, the most elementary version of the axiomatically correct Employment Law for the economy as a whole is given on Wikimedia AXEC62
(i) An increase in the expenditure ratio ρE leads to higher employment (the letter ρ stands for ratio). An expenditure ratio ρE>1 indicates credit expansion, a ratio ρE<1 indicates credit contraction/debt repayment of private households.
(ii) Increasing investment expenditures I exert a positive influence on employment, a slowdown of growth does the opposite.
(iii) An increase in the factor cost ratio ρF≡W/PR leads to higher employment.
The complete Employment Law is a bit longer and contains in addition profit distribution, public deficit spending, and import/export. The Law contains only measurable variables and is testable.
Item (i) and (ii) are familiar since Keynes. What is missing in the Keynesian employment multiplier, though, is the ratio ρF as defined in (iii). This variable embodies the macroeconomic price mechanism. It works such that overall employment INCREASES if the AVERAGE wage rate W increases relative to average price P and productivity R.
The Employment Law says that an increase in investment expenditure or deficit spending increases employment. The multiplier, though, is different from Keynes’ flawed multiplier (2012). The crucial difference consists of ρF.
The fact of the matter is that an increase in productivity counteracts the expansive effect of investment or household sector deficit spending. The same holds for price increases.
To increase overall employment requires an increase in ρF and this means that the expansion must be wage-driven, i.e., the increase in the wage rate must be such that it OVERCOMPENSATES the retrograde employment effects of productivity and price increases.
All this is clearly beyond the horizon and the intuition of Econ 101 economists (2014).
Kakarot-Handtke, E. (2012). Keynes’ Employment Function and the Gratuitous Phillips Curve Disaster. SSRN Working Paper Series, 2130421: 1–19. URL
Kakarot-Handtke, E. (2014). Towards Full Employment Through Applied Algebra and Counter-Intuitive Behavior. SSRN Working Paper Series, 2456184: 1–25. URL
Related 'Have data, lack theory' and 'Austerity and the utter scientific ignorance of economists'.
For details of the big picture see cross-references Employment.
For the correct/testable Phillips Curve see Sec. 7 of Keynes' Employment Function and the Gratuitous Phillips Curve Disaster.
REPLY to mulp on Mar 10
Wi denotes the average wage rate in the investment good sector and W sub c denotes the average wage rate in the consumption good sector. Both are NOT equal but have here been set equal in order to simplify the formula and to focus the argument.
For more details see Sec. 4 of Essentials of Constructive Heterodoxy: Employment.