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27. These relations are similar to the the linear relationship between labor market tightness and the marginal utility of consumption derived by Ravn (2008) in a one-sector search and matching model with endogenous participation. By taking the ratio of tightness in the two sectors and considering the steady-state equilibrium, we obtain the relationship of Proposition 1. θM θS = ϑM 1−ϑM ϑS 1−ϑS κS κM .
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