# Customers

Thus far we have explored the conditions that lead to the dismissal of an employee or to a transfer of ownership, so far as these follow from the dominance relation. For completeness, something might be said about the possibility that a customer might be expelled.

Let t G B C S and consider the deviation D = S{t}. Here again we assume that S(t) is feasible in that the linkages among the members of S are not disrupted by the removal of t. It seems prima facie that the removal of one customer would reduce the consumers’ surplus and so the value of the coalition. This intuition is sound but the reasoning is more complex. Recalling that

subject to constraints (A11.1a-c), (A11.3d) and (A11.3e) in the appendix to the previous chapter, the parallel for D is

As before, we assume that the rational successor R = о (Q, D) is the naive successor. Now consider

subject in addition to the constraint that q* = 0. By the Le Chatelier- Samuelson principle, vt(Q S) # V*(Q S). Informally, V-f(Q S) = V*(Q S) only if the optimal q* = 0 in 1, and this will be so only if /(0) is less than the efficient marginal cost price for S. Now consider

subject, again, to the additional constraint qt = 0. Since qt is not a variable in this problem the constraint cannot bind, and indeed identically V-f(R D) = V*(R, D). On the other hand, the functions and constraints that define (12.20) and (12.21) are identical, so it must be that V-f(R, D) = V-f(Q S). Thus we have

In ordinary language, it is not as a rule profitable to drop a paying customer.