This paper proposes a new paradigm: generative blockchain, which aims to transform conventional blockchain technology by combining transaction generation and recording, rather than focusing solely on transaction recording. Central to our design is a novel consensus mechanism, Proof-of-Merit (PoM), specifically crafted for environments where businesses must solve complex problems before transactions can be recorded. PoM integrates the generation and recording of transactions within a unified blockchain system, fundamentally differing from prevailing consensus mechanisms that primarily record existing transactions. We demonstrate PoM on a ride service on-demand platform, where the task of solving complex transaction-generating problems is delegated to a pool of independent problem solvers. These solvers generate transactions, and their solutions are selected based on merit. The winning solvers then register these transactions onto the blockchain and are rewarded accordingly. We introduce a Decentralized Control Parameter (DCP) to balance two key performance metrics: efficiency and equity. The applicability of our generative blockchain is illustrated through a ridesharing context, where matchers (solvers) are tasked with matching riders to drivers. We demonstrate PoM's performance and nuanced properties using agent-based simulation, exploring how to find the optimal DCP value to achieve a desirable balance of efficiency and equity in a generative blockchain.