Profits are given by:

P1 = P(Q=q1+q2)Aq1 - C(q1) - F1 and P2 = P(Q)q2 - C(q2),

where F1 is the fixed cost of doing business in a foreign country and parameter (0<A) is a quality index of effective output (degree of product differentiation) relative to the host output, q2. The first-order conditions:

MP1 = MR1(q1+q2)A - MC(q1) = 0 and MP2 = MR2(q1+q2) - MC(q2) = 0,

give the reaction functions q1=R1(q2) and q2=R2(q1), from which the Nash solution at CE is given by q*1(A) and q*2(A), implicitly a function of A and other parameters suppressed. By substitution, the optimum profits are obtained and the FDI = K1* and K2* from the respective production functions. The foreign intensity ratio, K1/(K1+K2), is a positive function of A. The collusive solution is given by JPE, with profits distributed equally. Any division of profits along the locus qM, qM is possible. A Nash bargaining solution is given by max U(P1)U(P2) s.t. the profit constraint JP= P1+ P2, where [U1/U2] = 1, but due to different utility functions, profit shares will not be equal. (Ref: Hong-gue Lee, Kon-Kuk University, 1999 and S. Martin, 1994)