The two chapters of my dissertation develop and estimate economic models to analyze the demand for and the provision of health care services. Specifically, I analyze the optimal design of health care markets to promote higher quality and lower cost, which can have profound implications for the well-being of people. The first chapter, An Equilibrium Analysis of the Long-Term Care Insurance Market," uses a model of family interactions to explain why the long-term care insurance market has not been growing. By developing and estimating a structural model of family interactions, I study how family care affects the workings of the long-term care insurance market. I argue that private information about the availability of family care induces adverse selection where individuals with limited access to family care heavily select into insurance coverage. I demonstrate that pricing on family demographics substantially mitigates adverse selection by reducing the amounts of private information. I propose child demographic-based pricing as an alternative risk adjustment that could decrease the average premium, invigorate the market, and generate welfare gains. The second chapter, Partial Rating Area Offering in the ACA Marketplaces," joint with Hanming Fang, studies insurance companies' plan offering decisions in the marketplaces established by the Patient Protection and Affordable Care Act of 2010 (ACA). Under the ACA, insurance companies can vary premiums by ``rating areas" which usually consist of multiple counties. In a given rating area, the ACA mandates uniform pricing for all counties, but, it does not mandate universal offering. We first demonstrate that it is not uncommon to observe insurance companies selling plans to only a subset of counties within a rating area. Using both theoretical and empirical approaches, we find evidence that partial rating area coverage is explained by insurers' incentive to risk screen consumers. While the ACA allows price discrimination based on rating areas and not on counties, we argue that insurers are effectively price discriminating consumers based on counties by endogenously determining their service area within a rating area.