Monopoly in Bilateral Exchange: Some Historico‐Analytical Remarks

In this paper, we characterize, under the assumption that the aggregate demand of the atomless part for the commodity held by the monopolist is invertible, the monopoly quantity setting solution proposed by Kats (1974a) as the monopolist's most preferred commodity bundle in the complement of the atomless part's offer curve which is feasible with respect to the aggregate initial endowments. Then, we show that the monopoly solution in bilateral exchange introduced by Busetto et al. (2023) coincides with the monopoly quantity setting solution proposed by Kats (1974a). Finally, we reformulate, the Shitovitz paradox, first exhibited by Busetto et al. (2025), in terms of the Kats monopoly solution. In particular we show that, for any allocation corresponding to a Kats' monopoly solution, there is an allocation in the core, which is, utility‐wise, advantageous for the monopolist and nonadvantageous for the small traders, and which is not in the feasible complement of the atomless part's offer curve.