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Public blockchains implement a fee mechanism to allocate scarce computational resources across competing transactions. Most existing fee market designs utilize a joint, fungible unit of account (e.g., gas in Ethereum) to price otherwise non-fungible resources such as bandwidth, computation, and storage, by hardcoding their relative prices. Fixing the relative price of each resource in this way inhibits granular price discovery, limiting scalability and opening up the possibility of denial-of-service attacks. As a result, many prominent networks such as Ethereum and Solana have proposed multidimensional fee markets. In this paper, we provide a principled way to design fee markets that efficiently price multiple non-fungible resources. Starting from a loss function specified by the network designer, we show how to dynamically compute prices that align the network’s incentives (to minimize the loss) with those of the users and miners (to maximize their welfare), even as demand for these resources changes. We derive an EIP-1559-like mechanism from first principles as an example. Our pricing mechanism follows from a natural decomposition of the network designer’s problem into two parts that are related to each other via the resource prices. These results can be used to efficiently set fees in order to improve network performance.