We show an equivalence result in the representative-agent New-Keynesian model after demand, wage-markup and correlated price-markup and TFP shocks: assuming sticky prices and flexible wages yields identical allocations for GDP, consumption, labor, inflation and interest rates to the opposite case—flexible prices and sticky wages. This equivalence arises with identical price and wage Phillips-curve slopes and generalizes to any slopes' pair whose sum and product are identical. Equilibrium profits and wages are, however, substantially different; equivalence breaks when these factor-distributional implications matter for aggregate allocations, e.g. in New-Keynesian models with heterogeneous agents, endogenous firm entry, and non-constant returns to scale.