It has been proposed that natural monopolists should be allowed to determine their profit-maximizing outputs and prices and then government should tax their profits away and distribute them to consumers in proportion to their purchases from the monopoly. Is this proposal as socially desirable as requiring monopolists to equate price with marginal cost or average total cost

This proposition isn't socially alluring. On the off chance that regular monopolists are permitted to decide their benefit amplifying yields and costs, at that point the yield of the common monopolist would in any case be at the problematic level where cost surpasses minor expense, demonstrating an under-designation of assets to the item.  

It would be progressively alluring to constrain the normal monopolist to charge a value equivalent to minor cost and sponsor any misfortunes. Reasonable return valuing, that is, setting value equivalent to Average Total Cost would be an improvement over this proposition. The imposing business model firm could gain ordinary benefit by settling on reasonable return valuing proposition.

are you looking for a specific answer?