We model capital accumulation in a dynamic New-Keynesian model with staggered price setting à la Calvo. It is assumed that firms do not have access to a rental market for capital. We compare our model with an alternative specification where households accumulate capital and rent it to firms. The difference in implied equilibrium dynamics is large, as we justify by proposing a simple metric. This result invites us to interpret some of the puzzling empirical findings that have been obtained using models with staggered price setting and a rental market for capital as an artefact of this particular set of assumptions.