Thesis: In a context of population ageing, the demand for long-term care is rising. While relatives remain the major source of care provision for disabled elderly, most OECD countries tend to foster the use of professional care, also called formal care, when individuals live at home. This thesis studies the determinants of home care arrangements for the disabled elderly in the context of France. What are the determinants of formal care consumption, at both the extensive and intensive margins? How do formal and informal care providers adjust to their provision constraints? The four chapters present original empirical evidence on these questions in the French context. They build on micro-econometric frameworks and use national survey data, administrative data or management files from a professional provider. The first Chapter studies the care provided by children to a disabled elderly parent. The second Chapter estimates the price-elasticity of the demand for formal care. The third Chapter analyzes how the decision to consume formal care is affected by the generosity of the public financing and the regulation of home care providers. The fourth Chapter focuses on the travel costs borne by home-care providers and their effect on the home care provision. The demand for formal care is found to be fairly little sensitive to its price, while the regulation of the supply is more likely to affect care arrangements.