The discussion can be stated more formally. Let W represent wages in the absence of any investment, and let a productive wage increase costing an amount C be the only on-the-job investment. Total costs to the firm would be = W + C, and since the investment cost is received by employees as higher wages, ir would also measure total wages. The cost of on-the-job training is not received as higher wages, so this formally distinguishes a productive wage increase from other on-the-job investments. The term MP can represent the marginal product of employees when wages equal W, and G the gain to firms from the investment in higher wages. In full equilibrium,
MP+G=W+C=sr.