The paper investigates price dynamics under market liberalization, with a focus on the effects of lowering price floors. We analyze price dynamics by specifying and estimating a dynamic Tobit model under time-varying volatility, where the market price is censored by a government-set support price. The model is applied to the U.S. butter market over the last three decades. The econometric results show how the price support program affects both expected prices and the volatility of prices. It is found that the censoring effects of a price support program can be significant and large even if the price support is set relatively low.