Intermediate Case

To represent the decision of a coalition to commit r(l) of their resources to recruitment to add an expected value of C to their effective labor, we revisit the optimum model in the appendix to Chapter 11. For this purpose the disagreement payoffs wt will be the payoffs expected in the case of no recruitment, not the insiders’ outside options, since in this case “no decision” means no recruiting. We will first consider an intermediate case in which there are recruitment costs but no monopsony power. In the appendix to Chapter 11, the labor resource allocated to production is

where L0 is a labor overhead comprising supervisory labor and other labor allocated to purposes other than the production of goods and services to satisfy the wants of customers. Within this category are activities of recruiting new employees (“human resources”) and recruiting new customers (“marketing”). The decision to recruit is made at an earlier (noncooperative) stage of the multistage decision process than is the decision on the allocation of that labor, but the succession of stages is logical rather than chronological and describes an ongoing process. In any case a larger workforce in production will require a larger allocation of labor to recruit and maintain that workforce as links spontaneously disappear through deaths, retirements, and quits. We may suppose that, in an ongoing firm, the labor set aside for recruiting is insider labor. In any case, the insiders of the coalition will decide how much of its labor power to allocate to recruiting in such a way as to increase their own surplus.

Allowing for recruitment, in place of (13.1) we have

This is equation (A13.1a) in the appendix to this chapter. Again applying the bargaining model to determine the insiders’ decision to recruit, for this intermediate case, if C> 0, that is, if the coalition does recruit, it will allocate resources to recruiting up to the point that

This is equation (A13.2d) in the appendix. On its face this is a straightforward extension of the traditional theory, since Z = hk is the wage cost of one unit of effective labor from a representative new recruit, and 0L is the value of the marginal product of effective labor, evaluated at the common marginal utility of the firm’s output. In a perfectly competitive model

= 0, so 3 would say that recruitment is carried on to the point that that the VMP is equal to the wage cost per unit of effective labor. More generally, we replace the VMP with the VMP net of the labor cost of recruiting a marginal unit of effective labor.

Recall, however, that this is a condition on newly recruited labor. That is, it characterizes the rate of recruitment of new labor, not the allocation of the labor resource, as it would in a neoclassical model. Moreover, in given circumstances the coalition may not recruit, but nevertheless not dismiss insider employees - it may reduce its labor force only by attrition, or not at all. This corresponds to a corner solution, as expression (A13.2e), if in addition (drawing on Chapter 12, subsection 12.1.3) the insider employees are paid no more than their marginal value product.

 
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