This article presents a novel approach to investigate efficient resource allocation in the layered division multiplexing (LDM) system, a key technology in next-generation broadcasting systems. The LDM system provides diverse services, resulting in different channel capacities for each service, unlike the conventional non-orthogonal multiple access scheme that aims for equal channel capacity among users. To achieve efficient resource allocation among services, we proposed a new method that normalizes the channel capacities allocated to different services while maintaining high fairness. Our proposed method involves normalizing the channel capacities of each service and finding the point where the sum of normalized channel capacities is maximized. This point can be obtained using the Lagrange multiplier method, ensuring a high normalized fairness index. Through simulations, we confirmed that the proposed approach maintains high fairness in the LDM system and achieves the highest normalized channel capacities compared to other transmission techniques. These findings provide valuable insights into resource allocation strategies for the LDM system, enabling a fair comparison of efficiency and performance within a multi-service environment.