Decreasing Returns, Patent Licensing and Price-Reducing Taxes

Abstract

Patent licensing agreements among competing firms usually involve royalties which are often considered to be anticompetitive as they raise market prices. In this paper we propose simple tax policies than can alleviate the effect of royalties. Considering a Cournot duopoly where firms produce under decreasing returns and trade a patented technology, we show that the interaction of royalties with decreasing returns may generate the counter-intuitive result that market prices decrease in the magnitude of diseconomies of scale. In such cases there exist progressive quantity taxes on firms that weaken the effect of royalties and lower the market prices. These taxes collect sufficient revenue to compensate firms for their losses. As a result, it is possible to design deficit neutral tax-transfer schemes that strictly Pareto improve the welfare of consumers as well as firms.

Fee versus royalty licensing in a Cournot duopoly with increasing marginal costs

“…Additionally, we show that our model is able to replicate the results in Wang (2002), which analyzes the same question in a differentiated duopoly with constant marginal costs and also replicate, as an extension of the model, the results in the papers by Sen and Stamatopoulos (2019) and Mukherjee (2014), which analyze models with homogeneous goods and increasing marginal costs, departing from the model with differentiated goods and constant marginal costs used in Fauli‐Oller et al. (2013).…”

“…It is direct to see that, in this case, the equivalence between the substitution coefficient γ in Fauli‐Oller et al. (2013) and the slope of the marginal cost b in Sen and Stamatopoulos (2019) is given by: $$$\gamma =\frac{1}{1+\frac{b}{2}}=\frac{2}{2+b}.$$$ …”

“…Sen and Stamatopoulos (2019) study a duopoly market, formed by firms 1 and 2, serving a linear demand. The pre‐licensing cost functions of firms 1 and 2 are given by $$C\left({q}_{1}\right)=(c-\varepsilon ){q}_{1}+\left(\frac{b}{2}\right){q}_{1}^{2}$$ and $$C\left({q}_{2}\right)=c{q}_{2}+\left(\frac{b}{2}\right){q}_{2}^{2}$$ respectively.…”

“…It is straightforward to show that in the optimal two‐part tariff licensing contract that can be found in point (III) of Proposition 1 in Sen and Stamatopoulos (2019), the optimal royalty can be written as follows: if $$\varepsilon \le e\left(\frac{2}{2\,+\,b}\right)=\frac{{(b\,+\,1)}^{2}(a\,-\,c)}{{b}^{3}\,+\,5{b}^{2}\,+\,7b\,+\,1}$$, the optimal royalty is ɛ . if $$\varepsilon > e\left(\frac{2}{2\,+\,b}\right)$$, the optimal royalty is $$r\left(\frac{2}{2\,+\,b}\right)=\frac{{(b\,+\,1)}^{2}(a\,-\,c\,+\,\varepsilon )}{(b\,+\,2)\left({b}^{2}\,+\,4b\,+\,1\right)}$$. …”

“…The literature on patent licensing is huge and most of the papers share the assumption that firms operate at constant marginal costs. Lately, some papers have relaxed this assumption by introducing non‐constant returns in licensing models (Sen and Stamatopoulos (2009, 2016 and 2019), Mukherjee (2014) and Karakitsiou and Mavrommati (2013). Mukherjee (2014) considers that firms produce with increasing linear marginal costs and deals with the case of a drastic process innovation.…”