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This study demonstrates the crucial role the specification of the cost function plays in identifying the market power parameter in autarky models. For constant marginal cost or marginal cost with quantity interacting with input prices, the market power parameter in autarky models in identified without a rotation of the demand curve. If a comodity is sold in both domestic and foreign markets, the market power parameters are identified regardless of the specific form of the marginal cost and demand specifications.
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Devadoss et al. (2013) studied this question.
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