Expected profit for the subsidiary is given by EP =R_{G}(AL)P + (1-P)R_{B}(AL) - wL - I. The first-order conditions are given by

MRP_{G}(AL)AP + (1-P)MRP_{B}(AL)A - w = 0

MRP_{G}(AL)LA'(I) + R_{G}(AL)P'(I) + (1-P)MRP_{B}(AL)LA'(I) - R_{B}(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 = (R_{G} - R_{B})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.