In industries where private and public production coexist, public production can incentivize private competition and address distributional concerns. Using a structural model that incorporates affordable but capacity-constrained public health care producers into a framework with price-setting private producers and consumer demand, I examine how increasing public production's capacity affects waiting times, private practices' prices, and the distribution of consumer surplus. I estimate the model using consumer-level visit data on the Finnish dental care industry. In the counterfactual simulation, I increase the number of dentists in public practices by 20%. This reduces waiting times at public practices on average by 5%, or 1.5 days, but does not affect private practice prices as consumers do not switch from private to public practices. Consumer surplus increases, particularly for higher-income consumers, while the use of dental care services rises, especially among low-income consumers.