Nash bargaining

Consider a couple under a model of cooperative Nash bargaining. Utility of the wife net of her divorce threat point T_w is U_w - T_w = 2x_w - T_w.

Utility of the husband net of his divorce threat point T_h is U_h - T_h = 3x_h - T_h. The household budget constraint is 2x_h + x_w I_h + I_w.

(a) Write down the maximisation problem and form the Lagrangian to maximise the Nash

Product subject the household budget constraint.

(b) Solve for the optimal allocations of x_w and x_h given that I_h = 10 and I_w = 10 and T_w = 2

and T_h = 4.