This dissertation consists of three essays. The first essay studies quality increases in the medical sector. A large and growing share of income is spent on medical goods and services each year. Existing measures of the price and quantity of medical goods and services do not take changes in quality into account. Ample micro evidence suggests the quality of medical goods and services has, in fact, improved over time. This essay estimates changes in medical quality at the aggregate level. To do so, this essay develops and estimates a dynamic structural model of the demand for medical purchases. The main result of this essay is that the quality of medical goods and services has increased by 2.2 percent per year between 1996 and 2007. One implication is that, after adjusting for changes in medical quality, the relative price of medical goods and services fell by 0.5 percent per year over this period, whereas Bureau of Labor Statistics estimates suggest it rose by 1.6 percent per year. The second essay develops a method to infer the life cycle profile of the quality of medical care in accumulating of health capital and the depreciation rate of health capital. To do so, this essay develops a life cycle model of the demand for medical purchases in which individuals invest in health capital. The use of these methods is illustrated by inferring the life cycle profile of the quality of medical care and the depreciation rate of health capital for 25-84 year old males between 1996 and 2007. The third essay studies implementable outcomes in partnership games. In this setting, it is well known that contracts which satisfy budget balance cannot implement efficient outcomes. Then, it is natural to ask which outcomes can be implemented. This essay characterizes the outcomes of all budget balancing contracts. With standard regularity conditions on production and utility functions, all outcomes which can be implemented by a budget balancing contract can be implemented by a linear contract. This implies that, with respect to welfare, we can consider a compact set of implementable outcomes without loss of generality. The budget-balancing contract whose outcome maximizes welfare, therefore, exists.