One of the most fundamental market mechanisms is the clearing house, where orders are accumulated over time and the market is cleared periodically. The issue addressed in this study is the statistical behavior of the market under this neutral mechanism in the framework of a tractable stochastic model which captures the underlying uncertainties and indivisibilities in the demand and supply schedules. Applying renewal theory, we derive closed-form results for the behavior of prices and quantities, and pursue the implications of the possibility of no-trade and the multiplicity of market-clearing prices.