The Theory of Training Investment, Education Expenditures, and Net Social Benefits

in the Context of FDI (By James Gander, University of Utah)

No distinction is made between firm-specific and general training. The same disclaimer applies to public education. The focus is on a single subsidiary firm (or industry composite). The market structure is ignored. The wage rate is in real terms. The labor market process is such that more education (as indexed by E expenditures) results in a higher wage rate. Also, more training and, thus, technology transfer (as indexed by T investment) results in a higher wage rate. These assumptions greatly simplify the model. Other assumptions (like, a fixed amount of labor) are implicit.

The model is in the context of a non-cooperative game. The firm (subsidiary) maximizes profit by selecting the optimum level of investment in training (T*), subject to the amount of education given by E for the labor force relevant to the industry. The government in maximizing net social benefits selects the optimum level of educational expenditures, subject to the firm's level of training, T. The two reaction functions give the Nash solution (T*,E*).

The subsidiary's profit function is given by:

(1) P = R(T, E) - C(T, E) - T,

where R is revenue, C is production cost, and T is the investment in training which goes hand-in-hand with the transfer of technology. Further, all first derivatives are positive, all second derivatives are negative, and all cross derivatives are positive (complementarity).

An increase in T increases cost by increasing the wage rate needed to be paid for the higher skilled work force. But, productivity is higher so revenue increases as output increases. Similarly, an increase in E also increases the wage rate because workers are better educated and better able to respond to the training given by the firm and hence their skill level is higher. This too increases productivity and output and revenue. The first-order condition is (graph):

(2) MRT(T, E) - MCT(T, E) - 1 = 0,

where marginal revenue from T minus marginal cost of T equals 1. The second-order condition is R_{TT} < C_{TT}, the second derivatives. Implicitly, T* = F_{1}(E), the
reaction function. If R_{ET} > C_{ET}, then the reaction function is positively sloped (complementarity case). If the relationship is <, then the reaction function is
negatively sloped (substitution case).

The net social benefits function for the host government relevant to the industry is :

(3) S = C(T, E) - E,

where total cost C is labor income (or local factor income and gross benefits to society). The first-order condition is (graph):

(4) MCE(T, E) - 1 = 0,

where the second-order condition is C_{EE} < 0. The implicit reaction function is E* = F_{2}(T) and it is positively sloped.

The game solution (T*, E*) for the complementarity case is given by the intersection of the two reaction functions (graph). For stability, F_{2} is steeper than F_{1}.
The ratio (T*/E*) =, <, or > 1 reflects the relative burden. For example, if it is less than one, then the government is bearing the relative burden. If it is greater
than one, then the firm is bearing it. The substitution case is similar.