We employ laboratory methods to study stability of competitive equilibrium in Scarf's economy (International Economic Review, 1960). Tatonnement theory predicts that prices are globally unstable for this economy, i.e. unless prices start at the competitive equilibrium they oscillate without converging. Anderson et al. (Journal of Economic Theory, 2004) report that in laboratory double auction markets, prices in the Scarf economy do indeed oscillate with no clear sign of convergence. We replicate their experiments and confirm that tatonnement theory predicts the direction of price changes remarkably well. Prices are globally unstable with adverse effects for the economy's efficiency and the equitable distribution of the gains from trade. We also introduce a novel market mechanism where participants submit demand schedules and prices are computed using Smale's global Newtonian dynamic (American Economic Review, 1976). We show that for the Scarf economy, submitting a competitive schedule, i.e. a set of quantities that maximize utility taking prices as given, is a weakly dominant strategy. The resulting outcome corresponds to the unique competitive equilibrium of the Scarf economy. In experiments that employ the schedule market, prices do not oscillate but instead converge quickly to the competitive equilibrium. Besides stabilizing prices, the schedule market is more efficient and results in highly egalitarian outcomes.