Competitiveness and subsidy or tax policy for new technology adoption in duopoly

We consider a problem of subsidy or tax policy for new technology adoption by duopolistic firms. The technology is developed in and transferred by a foreign country to the domestic country. It is free but each firm must expend some fixed set-up cost for education of its staff to adopt and use it. Assuming that each firm maximizes the weighted average of absolute and relative profits, we examine the relationship between competitiveness and subsidy or tax policies for technology adoption, and show that when firm behavior is not competitive (the weight on the relative profit is small), the optimal policy of the government may be taxation; when firm behavior is competitive (the weight on the relative profit is large), the optimal policy is subsidization or inaction and not taxation. However, if firm behavior is extremely competitive (close to perfect competition), taxation case re-emerges

Negative royalty in duopoly and definition of license fee: general demand and cost functions

We examine the relationship between the definition of license fee and a possibility of negative royalty in a duopoly with an outside innovator which has an option to enter the market and imposes a combination of a royalty per output and a fixed fee under general demand and cost functions. We consider two scenarios about determination of license fee. One is a scenario which does not assume entry of the innovator, and the other is a scenario which takes a possibility of entry of the innovator into the market. We will show that the optimal royalty rate for the innovator in the former case is smaller than that in the latter case, and the sign of the optimal royalty rate depends on whether the goods of firms are strategic substitutes or strategic complements

Subsidy for New Technology Adoption in Duopoly with Differentiated Goods under Absolute and Relative Profit Maximization

Abstract. We present an analysis about subsidy policy for adoption of new technology in duopoly with differentiated goods under absolute and relative profit maximization. Technology itself is free, however, firms must expend fixed set-up costs to adopt new technology. There are various cases about optimal policies depending on the level of the set-up cost and whether the goods of the firms are substitutes or complements. In particular, under relative profit maximization there is a case such that the social welfare is maximized when one firm adopts new technology, but no firm adopts new technology without subsidy. Then, the government should give a subsidy to only one firm. It is a discriminatory policy. The government gives a chance to receive a subsidy to only one firm.Keywords. Subsidy for new technology adoption, Absolute and relative profit maximization, Duopoly.JEL. D43, L13

On a strictly convex and strictly sub-additive cost function with positive fixed cost

We investigate the existence of a strictly convex and strictly sub-additive cost function with positive fixed cost. If there is a positive fixed cost, any cost function can not be super-additive, and concavity (including linearity) of cost function implies strict sub-additivity. Then, does there exist a strictly convex and strictly sub-additive cost function? We will present such a cost function. It is close to a linear function although it is strictly convex

Royalty and license fee under oligopoly with or without entry of innovator: Two-step auction

When an outside innovating firm has a cost-reducing technology, it can sell licenses of its technology to incumbent firms, or enter the market and at the same time sell licenses, or enter the market without license. We examine the definitions of license fees in such situations under oligopoly with three firms, one outside innovating firm and two incumbent firms, considering threat by entry of the innovating firm using a two-step auction. Also we suppose that the innovating firm sells its licenses using a combination of royalty per output and a fixed license fee

Subsidy or tax policy for new technology adoption in duopoly with quadratic and linear cost functions

We present an analysis about subsidy (or tax) policy for adoption of new technology in a duopoly with a homogeneous good. Technology itself is free. However, firms must expend fixed set-up costs for adoption of new technology, for example, education costs of their staffs. We assume linear demand function, and consider two types of cost functions of firms. Quadratic cost functions and linear cost functions. There are various cases of optimal policies depending on the level of the set-up cost and the forms of cost functions. In particular, under linear cost functions there is the following case. The social welfare is maximized when one firm adopts new technology, however, both firms adopt new technology without subsidy nor tax. Then, the government should impose taxes on one firm or both firms. Under quadratic cost functions there exists no taxation case. There are subsidization cases both under quadratic and linear cost functions

License and entry strategies for outside innovator in duopoly

In Proposition 4 of Kamien and Tauman(1986), assuming linear demand and cost functions with fixed fee licensing it was argued that for the outside innovating firm under oligopoly when the number of firms is small (or very large), strategy to enter the market with license of its cost-reducing technology to the incumbent firm (entry with license strategy) is more profitable than strategy to license its technology to the incumbent firm without entering the market (license without entry strategy). However, their result depends on their definition of license fee, and it is inappropriate if the innovating firm can enter the market. If we adopt an alternative more appropriate definition based on the threat by entry of the innovating firm, license without entry strategy is more profitable in the case of linear demand and cost functions. Also we investigate the problem in the case of quadratic cost functions in which entry with license strategy may be optimal. Further we will show that the optimal strategies for the innovating firm when license fees are determined under the assumption that the licensor takes all benefit of new technology and its optimal strategies when license fees are determined according to Nash bargaining solution are the same