This paper makes three advances: 1) It fixes the empty-core problem of the Coase theorem; 2) it provides the smallest upper bound of transaction costs below which the optimal or efficient outcomes can be achieved; and 3) it establishes two mathematical theorems that capture the main insights and major aspects of the Coase theorem. A simpler version of the theorems says that in a coali... https://www.roneverhart.com/Cyspera-Pigment-Corrector-1-75oz-52ml/