Serverless computing platforms currently rely on basic pricing schemes that are static and do not reflect customer feedback. This leads to significant inefficiencies from a total utility perspective. As one of the fastest-growing cloud services, serverless computing provides an opportunity to better serve both users and providers through the incorporation of market-based strategies for pricing and resource allocation. With the help of utility functions to model the delay-sensitivity of customers, we propose a novel scheduler to allocate resources for serverless computing. The resulting resource allocation scheme is optimal in the sense that it maximizes the aggregate utility of all users across the system, thus maximizing social welfare. Our approach gives rise to a natural dynamic pricing scheme that is obtained by solving an optimization problem in its dual form. We further develop feedback mechanisms that allow the cloud provider to converge to optimal resource allocation, even when the users' utilities are private and unknown to the service provider. Simulations show that our approach can track market demand and achieve significantly higher social welfare (or, equivalently, cost savings for customers) compared to existing schemes.