11.15 Property rights theory of the firm This problem has you work through some of the calculations associated with the numerical example in the Extensions. Refer to the Extensions for a discussion of the theory in the case of Fisher Body and General Motors (GM), who we imagine are deciding between remaining as separate firms or having GM acquire Fisher Body and thus become one (larger) firm.

Let the total surplus that the units generate together be SðxF , xGÞ ¼ x1/2 F þ ax1/2 G , where xF and xG are the investments undertaken by the managers of the two units before negotiating, and where a unit of investment costs $1. The parameter a measures the importance of GM’s manager’s investment. Show that, according to the property rights model worked out in the Extensions, it is efficient for GM to acquire Fisher Body if and only if GM’s manager’s investment is important enough, in particular, if a > ffiffi 3 p .