Endogenous R&D Investment and Market Structure: A Case Study of the Agricultural Biotechnology Industry

Over the past three decades, the agricultural biotechnology sector has been characterized by rapid innovation, market consolidation, and a more exhaustive definition of property rights. The industry attributes consistently identified by the literature and important to this analysis include: (i) endogenous sunk costs in the form of expenditures on R&D; (ii) seed and agricultural chemical technologies that potentially act as complements within firms and substitutes across firms; and (iii) property rights governing plant and seed varieties that have become more clearly defined since the 1970s. This paper adds to the stylized facts of the agricultural biotechnology industry to include the ability of firms to license technology, a phenomenon observed only recently in the market as licensing was previously precluded by high transactions costs and “anti-stacking” provisions. We extend Sutton's theoretical framework of endogenous sunk costs and market structure to incorporate the ability of firms to license technology under well-defined property rights, an observed characteristic not captured in previous analyses of the sector. Our model implies that technology licensing leads to lower levels of industry concentration then what would be found under Sutton's model, but that industry concentration remains bounded away from perfect competition as market size becomes large.licensing, market structure, R&D, agricultural biotechnology, Research and Development/Tech Change/Emerging Technologies, L22, L24, Q16,

The Chevalley Basis for a Split Semi-simple Lie Algebra

Let g be a split, semi-simple real Lie algebra. This implies, in particular, that there exists a Cartan subalgebra for g for which the associated root space decomposition of g is real. For such Lie algebras there is a very special basis called the Chevalley basis. In this worksheet we calculate the Chevalley basis for the Lie algebra sp(6, R) and illustrate the various properties of this basis

The Octonions and the Exceptional Lie Algebra G2

The octonions O are an 8-dimensional non-commutative, non-associative normed real algebra. The set of all derivations of O form a real Lie algebra. It is remarkable fact, first proved by E. Cartan in 1908, that the the derivation algebra of O is the compact form of the exceptional Lie algebra G2. In this worksheet we shall verify this result of Cartan and also show that the derivation algebra of the split octonions is the split real form of G2. PDF and Maple worksheets can be downloaded from the links below

Higher Order Symmetries of the KdV Equation

In this worksheet we symbolically construct the formal inverse of the total derivative operator and use it to construct the recursion operator for the higher-order symmetries of the KdV equation. Using this recursion operator we generate the first 5 generalized symmetries of the KdV equation and verify that they all commute. PDF and Maple worksheets can be downloaded from the links below

Spontaneus Hypoglycaemia

Abstract Not Provided

How to Create a Lie Algebra

We show how to create a Lie algebra in Maple using three of the most common approaches: matrices, vector fields and structure equations. PDF and Maple worksheets can be downloaded from the links below