If you read carefully my post from yesterday, you may have noticed what a tricky question this is. “CEO” of course is a discrete position, and while there are companies with “zero” or “two” CEOs, those comparisons are not the correct ones to define marginal product; in any case they would give you two very different numbers.
Nor is it correct to compare “this CEO” to “his likely replacement.” That difference could be zero, but it does not mean the CEO adds zero value or will or should receive zero pay. Keep in mind that we are already juggling a few margins here, including “getting this CEO to work harder or better” and “this CEO vs. another.”
Alternatively, imagine there are ten firms in the economy, of differing size and import, all bidding for managers in a pool of fifty people. A credible CEO offer has to satisfy a participation constraint, namely getting the candidate to take the job over CEO at a lesser firm or working in a lesser job. But if a CEO can add 50 percent of value to a firm, that CEO will not in general be paid fifty percent of the firm’s value and need not be paid anything close to that. The shareholders know he will take the job for less and there are other candidates who might add forty-seven percent of value. The firm can make a credible offer of “two percent of value added” and it might be accepted.
Unlike hiring widget-makers for “less than their marginal product,” there is no subsequent disruption of equilibrium which must follow from this apparent disjunction of CEO pay and marginal product. For instance there is no firm-level incentive to further expand output or hire extra CEOs. There is one discrete slot, a wide range of potential compensation values, and the final sum is set by a bargain, determined by the context of principal-agent theory.
CEOS who can add so much value will try to start and grow their own firms, holding lots of equity from the very beginning, as Mark Zuckerberg has done. Those CEOs will indeed be paid something like their traditional marginal product, but they are a distinct minority and wealth and risk constraints limit their number.
In general, it is confusing to suggest that CEOs will be paid their marginal product. The traditional notion of marginal product does not apply to a CEO in the simple “widgets per worker” way. There are ways you can define “marginal product” to make the claim “CEOs are paid their marginal product” more or less true, but that is not my preferred way forward. Instead we should get more used to thinking intuitively within the principal-agent model, even though it is harder to do.