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We measure the extent of inefficient fluctuations in the relative price of investment in the US using an estimated two-sector New Keynesian model. In the presence of these fluctuations, inefficiencies in the economy are summarized by the variation in the following policy objects: the relative price gap, sectoral output gaps, and sectoral price and wage inflation. The welfare-maximizing monetary authority cannot reduce the volatility of the relative price gaps due to nominal rigidity in both sectors. However, it can manage trade-offs among the other policy objects, both across and within sectors. Identifying the nature of shocks that drive the relative price of investment is important for central banks in deciding the optimal weights on sectoral price inflation under the composite inflation targeting rule. This is because the property of trade-offs depends on whether shocks alter the efficient relative price or not.