We discuss some difficulties in a dynamic New-Keynesian model with staggered price setting à la Calvo and a convex capital adjustment cost at the firm level, as considered by Woodford (2003, Ch. 5). It is shown that the implied simultaneous price setting and investment decision has not been analyzed properly. Our work fills that gap by proposing a tractable solution to the key problem of describing the inflation dynamics associated with that structure. We use our framework to assess to what extent capital accumulation matters for inflation and output dynamics.