We now consider the decision of the coalition to recruit more customer members. Once again the parameters anticipated for a new customer are uncertain and will be considered as certainty equivalent expected values for a representative new customer. We suppose that, in an anticipated new optimum, the representative new customer would take q of the firm’s output and make a side payment z into the revenues of the coalition. Suppose then that the commitment of r units of incremental labor overhead will on the average bring b new customers. This will reduce the output available to insider customers by bq (in addition to whatever reduction results from diverting r of labor from production, and except insofar as increased effort may partially offset these deductions) and will increment the revenues of the coalition by bz.
Once again we first consider an intermediate case with variable recruitment costs but without monopoly power. Thus, in place of (A11.1a) we have
Again applying the bargaining model to the decision of the insiders to recruit new customers, we find that the necessary condition for an optimum positive rate of recruitment of new customers then is
(using A11.7h and A11.7j, which are unchanged). This is equation (A13.6b) in the appendix to this chapter. That is, the recruitment of new customers is carried on until the additional revenue gained per new customer is no more than the marginal labor cost of recruiting customers, evaluated at the common marginal disutility of labor, plus the output diverted from insider customers, at the margin, evaluated at the common marginal utility of the firm’s output. If we understand the right-hand side as the marginal cost of serving one additional customer, then this seems a natural extension of the neoclassical approach. Once again, however, we may not assume an interior solution. We may have a corner solution with no attempt to attract new customers. This may be uncommon, but see Lewis (1942) for a possible instance.