The fast development of location-based social networks (LBSNs) has led to significant changes in society, resulting in popular studies of using LBSN data for socioeconomic prediction, e.g., regional population and commercial activity estimation. Existing studies design various graphs to model heterogeneous LBSN data, and further apply graph representation learning methods for socioeconomic prediction. However, these approaches heavily rely on heuristic ideas and expertise to extract task-relevant knowledge from diverse data, which may not be optimal for specific tasks. Additionally, they tend to overlook the inherent relationships between different indicators, limiting the prediction accuracy. Motivated by the remarkable abilities of large language models (LLMs) in commonsense reasoning, embedding, and multi-agent collaboration, in this work, we synergize LLM agents and knowledge graph for socioeconomic prediction. We first construct a location-based knowledge graph (LBKG) to integrate multi-sourced LBSN data. Then we leverage the reasoning power of LLM agent to identify relevant meta-paths in the LBKG for each type of socioeconomic prediction task, and design a semantic-guided attention module for knowledge fusion with meta-paths. Moreover, we introduce a cross-task communication mechanism to further enhance performance by enabling knowledge sharing across tasks at both LLM agent and KG levels. On the one hand, the LLM agents for different tasks collaborate to generate more diverse and comprehensive meta-paths. On the other hand, the embeddings from different tasks are adaptively merged for better socioeconomic prediction. Experiments on two datasets demonstrate the effectiveness of the synergistic design between LLM and KG, providing insights for information sharing across socioeconomic prediction tasks.