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About marginal cost setting on Jordi Gali's work

The equation is in logs. Thus, $$MC_{t}=\frac{W_{t}/P_{t}}{MPN_{t}}$$ $$mc_{t} = w_{t}-p_{t}-mpn_{t}$$ And after that use $$MPN_{t} = (1-\alpha)\frac{Y_{t}}{N_{t}} = (1-\alpha)A_{t}N_{t}^{-\alpha}$$ ...
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