The evaluation of dexterity and a theory of the growth of a firm

                                               

Determining which production resources embody various business skills is a very important issue not only for the investment function theory but for the theory of firm. Uzawa (1969) regards these nurtured skills as being entirely attributed to real capital and establishes a microeconomic foundation for Tobin's (1969) q theory.  

However, it is quite ambiguous how skills are embodied into real capital in Tobin-Uzawa theory, whereas, it seems natural that such skills are acquired by employees both explicitly and implicitly through  learning by doing (Arrow 1962) and/or formal education within a firm. Thus, we deal with labor as the quasi-fixed production resource instead of real capital.

We set the objective function of a firm as the discounted sum of the surplus from skilled employees, and solve the optimal path of accumulation of intangible skills by deploying an elementary calculus of variation owing to Uzawa (1969).

We obtain the following results. First, we obtain human-capital's q theory of the investment function that emphasizes the importance of internalization of the positive externality from skilled labor force to real capital. We call such an externality `the dexterity of employees'.

Second, we consider the case where an employer regards his firm as a standard neoclassical type. In such a case, since the contribution of the dexterity is neglected, the employer recognizes his production function is not constant return but decreasing returns to scale. As a result, the equilibrium growth rate of such a firm becomes zero in the long run. This finding implies that it is crucial for sustainint0 the growth of a firm to evaluate the (non-marketable) dexterity of employees correctly.