ɪn ðiːz mˈɑːdəlz, wˌɪtʃ ɪŋklˈuːd pɹˈaɪs slˈæʃ kˈɔst mˈɑːɹkʌps baɪ ðə pɹədˈuːsɪŋ fˈɜːmz ɪmpˈɜːfɛkt kˌɑːmpətˈɪʃən, ðɪ ˈɔːθɚz ʃˈoʊ ðæt ɐn ɐnˈæləɡəs kˈɑːnsɛpt wˌɪtʃ ðeɪ kˈɔːl kˈɔstbˈeɪst dəmˈɑːɹ wˈeɪts mˈoːɹ ˈækjʊɹətli ɐpˈoːɹʃənz pɹˌɑːdəktˈɪvᵻɾi wɛn ˈæɡɹɪɡˌeɪɾɪŋ tə ðə nˈæʃənəl ˈæɡɹɪɡˌeɪt lˈɛvəl.
In these models, which include price/cost markups by the producing firms (imperfect competition), the authors show that an analogous concept which they call cost-based Domar weights more accurately apportions productivity when aggregating to the national aggregate level.