What are the conditions and scope of application for the hold-up problem? Academic views are not unified. A theoretical model based on outsourcing situation was constructed and deduces the conditions of the hold up problem: when the factors cannot obtain all marginal returns and the contract is incomplete at the same time, the hold up problem arises. When this condition is met, intermediate product manufacturers will reduce the investment in production activities not specified in the contract. Final product manufacturers will require over investment in the contracted parts to avoid output decline due to underinvestment, resulting in investment distortion. Subsequently, the article further explores the economic laws behind the hold up problem, creatively introduces broad externality to explain the general laws that arise when it affects decision-making on variable factor input or output levels, and explains the relationship between broad externality and Pareto optimality. Finally, the paper reveals the setting rules of hold up problem related to broad externality in the model, emphasizing that the judgment of theoretical models should not be limited to conclusions, but should also focus on whether the mechanism corresponding to assumptions and conclusions match reality.