We propose the so-called domestic "embodied unit labor costs" (EULC) at the country-sector level as a new cost-related basis for measures of international competitiveness. EULC take into account that a sector's labor costs constitute only a small share of its total cost which to a large extent consist of expenses for intermediate goods from other sectors. In line with a simple Leontief-type model, the proposed measure is constructed as a weighted average of unit labor costs of all domestic sectors contributing to the final goods of a specific sector. The contribution is expressed in value-added terms and takes global supply chains into account. We also show how EULC can be consistently calculated for sectoral aggregates such as the tradable goods sector. Based on EULC we propose the "embodied real effective exchange rate" (EREER) at the country-sector level as a new competitiveness indicator where the relevance of trading partners is quantified by an appropriate value-added measure. The chosen value-added concept replaces gross exports traditionally used as the weight basis in effective exchange rates. Using the World Input-Output Database (WIOD) we employ the proposed indicators to shed new light on changes in cost competitiveness at the sectoral level for Germany, and compare the empirical evidence with selected other euro area countries.