In two-sided platforms (e.g., video streaming or e-commerce), viewers and providers engage in interactive dynamics: viewers benefit from increases in provider populations, while providers benefit from increases in viewer population. Despite the importance of such "population effects" on long-term platform health, recommendation policies do not generally take the participation dynamics into account. This paper thus studies the dynamics and recommender policy design on two-sided platforms under the population effects for the first time. Our control- and game-theoretic findings warn against the use of the standard "myopic-greedy" policy and shed light on the importance of provider-side considerations (i.e., effectively distributing exposure among provider groups) to improve social welfare via population growth. We also present a simple algorithm to optimize long-term social welfare by taking the population effects into account, and demonstrate its effectiveness in synthetic and real-data experiments. Our experiment code is available at https://github.com/sdean-group/dynamics-two-sided-market.