Over the last decades, health economics has turned into one of the most active research fields within economics. The structure of health care markets varies enormously across countries, largely influenced by competition among suppliers, the regulation of markets and patient preferences. This dissertation presents an analysis of health care markets especially focusing on price competition and quality competition. Under price competition, a pair of asymmetric pure strategy price equilibria exists in a model with income constraints for the specific case that two physicians locate at the maximum distance from each other and patients pay the same marginal transportation cost. Under quality competition, I investigate the interplay of market transparency and semi-altruism - a specific and interesting aspect unique to markets for health care. Market transparency and semi-altruism show ambiguous effects on welfare. The more altruistic physicians provides weakly higher quality than the less altruistic one. Moreover, I explore individual and social incentives for hospital mergers and their interaction with transparency and find that higher transparency does not always lead to higher quality and higher social welfare. The results indicate that quality is lower after merger. A hospital merger leads to a higher social welfare if the efficiency gains from the merger are sufficiently large.