Over the past few years, ride-sharing has emerged as an effective way to relieve traffic congestion. A key problem for the ride-sharing platforms is to come up with a revenue-optimal (or GMV-optimal) pricing scheme and a vehicle dispatching policy that incorporate geographic and temporal information. In this paper, we aim to tackle this problem via an economic approach. Modeled naively, the underlying optimization problem may be non-convex and thus hard to solve. To this end, we use a so-called ``ironing'' technique to convert the problem into an equivalent convex optimization one via a clean Markov decision process (MDP) formulation, where the states are the driver distributions and the decision variables are the prices for each pair of locations. Our main finding is an efficient algorithm that computes the exact revenue-optimal (or GMV-optimal) randomized pricing scheme, which naturally induces the accompany vehicle dispatching policy. We also conduct empirical evaluations of our solution through real data of a major ride-sharing platform and show its advantages over fixed pricing schemes as well as several prevalent surge-based pricing schemes.