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Subsidizing new technology adoption in a Stackelberg duopoly: Cases of substitutes and complements

Hattori, Masahiko and Tanaka, Yasuhito (2016): Subsidizing new technology adoption in a Stackelberg duopoly: Cases of substitutes and complements. Forthcoming in: Italian Economic Journal

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Abstract

Economic growth requires that firms adopt new technologies. However, it may be insufficient in less competitive industries from the social welfare point of view. In this case, a government subsidy is necessary. We present an analysis of firms' adoption of new technology and government subsidization policy in a Stackelberg duopoly with differentiated goods. The technology itself is free, but each firm must expend a fixed set-up cost, such as training employees. There are several cases related to optimal policies depending on the set-up costs and whether the goods are substitutes or complements. In particular, there are two cases. (1) Social welfare is maximized when only the Stackelberg leader adopts the new technology, but no firm adopts the new technology without a subsidy. Then, the government should subsidize only the leader, which is a discriminatory policy. (Case 5 of Theorem 1 and Case 3-(1)-ii of Theorem 2)

(2) Social welfare is maximized when both firms adopt the new technology, but only the leader adopts the new technology without a subsidy. Then, the government should subsidize only the follower. This policy is not discriminatory because adoption is the dominant strategy for the leader. (Case 2 of Theorem 1)

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