Network utility maximization (NUM) for Multipath TCP (MPTCP) is a challenging task, since there is no well-defined utility function for MPTCP [6]. In this paper, we identify the conditions under which we can use Kelly's NUM mechanism, and explicitly compute the equilibrium. We obtain this equilibrium by using Tullock's rent-seeking framework from game theory to define a utility function for MPTCP. This approach allows us to design MPTCP algorithms with common delay and/or loss constraints at the subflow level. Furthermore, this utility function has diagonal strict concavity, which guarantees a globally unique (normalized) equilibrium.