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This paper compares the implications of having constant versus variable markups on the Law of One Price (LOP) by decomposing the good-category level prices into marginal costs of production, markups, and trade costs. Using a trade model, it is shown that the case of constant markups corresponds to log-linear trade regressions, while the case of variable markups corresponds to lin-log trade regressions. Empirical results show that marginal costs of production contribute most to the deviations from LOP for both cases of constant and variable markups; the decomposition of marginal costs further shows that destination-specific quality measures play the biggest role.
Yilmazkuday, Hakan, "Constant versus Variable Markups: Implications for the Law of One Price" (2016). Economics Research Working Paper Series. 107.