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The Annals of Regional Science

Erschienen in:

13.10.2015 | Original Paper

How to license a transport innovation

verfasst von: John S. Heywood, Zheng Wang

Erschienen in: The Annals of Regional Science | Ausgabe 2-3/2015

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Abstract

This paper identifies the optimal method to license an innovation that reduces transport cost in a duopoly model of spatial price discrimination. An inside innovator finds licensing by a distance fee more profitable than by a fixed fee, an ad valorem royalty or a per unit royalty. Moreover, the social welfare associated with distance fee licensing is larger than that associated with not licensing. In contrast, an outside innovator never finds licensing by a distance fee the most profitable choice.

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Equating the delivered prices from the two firms: \(t_2 ({L_2 -x^{*}})=t_1 (x^{*}-L_1)\Rightarrow x^{*}=\frac{t_1 L_1 +t_2 L_2}{t_1 +t_2}\).

In order to guarantee that \(\pi _2^{NL} >0\) for any locations, c should be less than \(\frac{t}{({1-L_1})^{2}}({1+L_1 L_2 +L_1^2 -3L_1 -L_2^2 +L_2 -\sqrt{({1-L_2})^{2}({L_2^2 -2L_1 L_2 +1-2L_1 +2L_1^2})}})\).

Solving the constraint for r yields two roots, but one of them makes \((t-c)(1-L_1)<r+ (t-c)({1-L_2})\) for any values of \(L_1 \in \left( {0,\frac{1}{2}}\right) \) and \(L_2 \in \left( {\frac{1}{2},1}\right) \).

We thank an anonymous reviewer for emphasizing this point.

While the expressions are complicated, this demonstration is straightforward and available upon request.

Firm 2’s profit declines monotonically with \(d: \frac{\partial \pi _2^D}{\partial d}=-\frac{2(t-c)^{2}d^{4}+21(t-c)^{3}d^{3}+72(t-c)^{4}d^{2} +96d(t-c)^{5}+40(t-c)^{6}}{\left( {2d^{2}+7d(t-c)+8(t-c)^{2}}\right) ^{3}}<0\).

Solving the constraint for d1 yields two roots but only \(d1=c\) results in firms’ locations within the unit market.

Solving the constraint for d yields two roots, but the negative one is discarded.

We also note that reversing the timing so that location happens after licensing does not change the fact that the distance fee is always dominated and so will not be adopted by the outside innovator (see Heywood and Wang 2014).

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Titel: How to license a transport innovation
verfasst von: John S. Heywood
Zheng Wang
Publikationsdatum: 13.10.2015
Verlag: Springer Berlin Heidelberg
Erschienen in: The Annals of Regional Science / Ausgabe 2-3/2015
Print ISSN: 0570-1864
Elektronische ISSN: 1432-0592
DOI: https://doi.org/10.1007/s00168-015-0710-0

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