Expected profit for the subsidiary is given by EP =RG(AL)P + (1-P)RB(AL) - wL - I. The first-order conditions are given by
MRPG(AL)AP + (1-P)MRPB(AL)A - w = 0
MRPG(AL)LA'(I) + RG(AL)P'(I) + (1-P)MRPB(AL)LA'(I) - RB(AL)P'(I) - 1 = 0,
where L*= AL augmented, w is the wage rate given, and A'(I) and P'(I) are the derivatives for A and P, the jointly determined technology transfer indexes. After substitution and rearrangement,
X + d F = I/wL,
where X is the investment elasticity of augmentation, F is the investment elasticity of reliability, d is a weighting parameter (d = (RG - RB)P/wL), and I/wL is the labor-cost intensity of investment in technology transfer. The model is assumed to give the equilibrium amounts of L and I.