Fighting Over the Harberger Rectangle

A diagram from Arnold C. Harberger's 1954 paper "Monopoly and Resource Allocation", annotated to highlight the contention for the "excess profits":

Harberger was interested in estimating the dead weight loss due to monopoly power, and found that it was low. Subsequently the same basic machinery was re-used to analyze the dead weight loss due to any externally imposed costs, such as excise taxes:

For the case of taxation, the dead weight loss comes from both consumer and producer surplus (two triangles), instead of just the single triangle of loss in the monopoly case.

The existence of the dead weight losses under monopoly or taxation is widely accepted. 

What's much more contentious is what to do with the rectangle of "excess profit". That becomes a normative "problem" immediately. The reader can fill in their own opinion for the case of taxation. For monopoly, some have said it's an attractive nuisance, some that it's a reward for superior design and production, others that the firm is more likely to redeploy the capital productively, and others assume that any diminution of consumer surplus is theft.

Certainly investors and economists have strongly differing views on monopoly "excess profit". Empirically, certain sectors have historically returned more excess profit than others. Active investors not only seek out such sectors and companies, but they count on there being such differentiation in the market. Their job is to seek out superior ROIC and put their capital there. Passive investors don't care, but to get results that match their Stigleresque expectation, active investors must exist, else there wouldn't be any reversion to the mean! 

The best use of excess profits, in the sense of "what causes the greatest societal economic growth?", may depend very strongly on the hands it is placed in. Hence the normative answer to the excess profits rectangle turns on the data. I get the sense that historically the economics literature more or less follows the normative expectations of those who bring normative values to the profession, while neutral researchers find a variety of mixed answers. This implies that ultimately the best way to answer the question is to let the market decide. Which in turn indicates that excess profits "should" belong to the monopolist, who will be rewarded or punished further based on how well they treat that newly received capital.