This paper proposes a hierarchical economic dispatch (HED) mechanism for computing distribution locational marginal prices (DLMPs). The HED mechanism involves three levels: The top level is the national (regional) transmission network, the middle level is the distribution network, while the lowest level reflects local embedded networks or microgrids. Each network operator communicates its generalized bid functions (GBFs) to the next higher level of the hierarchy. The GBFs approximate the true cost function of a network by a series of affine functions. The concept of Benders cuts are employed in simulating the GBFs. The AC optimal power flow (ACOPF) is convexified and then used for dispatching generators and calculating GBFs and DLMPs. The proposed convexification is based on the second order cone reformulation. A sequential optimization algorithm is developed to tighten the proposed second order cone relaxation of ACOPF. The properties of the sequential tightness algorithm are discussed and proved. The HED is implemented in the GAMS grid computing platform. The GBFs and DLMPs are calculated for the modified IEEE 342 node low voltage test system. The numerical results show the utility of the proposed HED and GBF in implementing DLMP.