This paper studies the effects of heterogeneity in planning propensity on wealth inequality and asset prices. I consider an economy populated by "attentive" and "inattentive" agents. Attentive agents plan their consumption period by period, while inattentive agents plan every other period. Infrequent planning increases uncertainty concerning future income or future asset returns. In general equilibrium, inattentive consumers trade at unfavorable prices. If the only source of uncertainty is future income, inattentive consumers will still accumulate more wealth. In contrast, in a version of the model driven by uncertain asset returns, infrequent planning produces the opposite result: inattentive investors accumulate less wealth, in line with empirical evidence. Moreover, asset prices are much more volatile than in a representative agent model with full attention, because changes in asset prices must induce attentive consumers to voluntarily bear the burden of adjusting to aggregate shocks.