This paper analyzes the equilibria involved in the dimerization of monomeric receptors with homo-bifunctional ligands. We provide analytical expressions that can be used to estimate the concentration of each species present in a mixture of homo-bifunctional ligand and monomeric proteins, given initial conditions defining the total concentration of bivalent ligand [L2]0, the total concentration of protein [P]0, one dissociation constant Kd, and a parameter to account for cooperativity alpha. We demonstrate that the fraction of protein present in a complex of two proteins and one bivalent ligand (P x L2 x P) is maximized at [L2]0 = Kd/2 + [P]0/2.